1 Introduction
Researcher(s) | Mathematical Model | Advantages | Limitations | MCGDM |
---|---|---|---|---|
Atanassov (1986) | Intuitionistic fuzzy sets or IFSs | It deals with belongingness and non-belongingness functions | It cannot deal with belongingness and non-belongingness degrees whose sum is above 1 | No |
Yager (2013) | Pythagorean fuzzy sets or PFSs | It increases the space of belongingness and non-belongingness evaluations | It cannot deal with belongingness and non-belongingness degrees whose sum of squares is above 1 | No |
Senapati and Yager (2020) | Fermatean fuzzy sets or FFSs | It provides more flexibility to the belongingness and non-belongingness evaluations as compared to IFSs and PFSs | It cannot deal with belongingness and non-belongingness degrees whose sum of cubes is above 1 | No |
Aydemir and Gunduz (2020) | Fermatean fuzzy TOPSIS method | It can deal with Fermatean fuzzy information with TOPSIS method | Its limitations are similar to FFSs | No |
Molodtsov (1999) | Soft sets | It has ability to describe data by multiple attributes | It cannot deal with fuzzy information and multiple experts opinions | No |
Alkhazaleh and Salleh (2011) | Soft expert sets | It can capture the evaluations of multiple experts | It cannot deal with fuzzy evaluations | Yes |
Alkhazaleh and Salleh (2014) | Fuzzy soft expert sets | It can tackle evaluations of multiple experts in fuzzy environment | It only considers the membership function | Yes |
Akram et al. (2021) | m-Polar fuzzy soft expert sets | It has ability to deal with multiple experts opinions under m-polar fuzzy information | It cannot consider non-membership function | Yes |
Broumi and Smarandache (2015) | Intuitionistic fuzzy soft expert sets | It can deal with multiple experts opinions in an intuitionistic fuzzy environment | Its limitations are similar to IFSs | Yes |
2 Preliminaries
-
if \(h({\mathfrak {F}}_1)> h({\mathfrak {F}}_2)\) then \({\mathfrak {F}}_1>{\mathfrak {F}}_2\),
-
if \(h({\mathfrak {F}}_1)= h({\mathfrak {F}}_2)\) then \({\mathfrak {F}}_1={\mathfrak {F}}_2\),
3 Fermatean fuzzy soft expert sets
\((\lambda ,A)\) | \(p_1\) | \(\ldots\) | \(p_n\) |
---|---|---|---|
\(({e}_1, {q}_1, 1)\) | \(\big (\mu _{({e}_1, {q}_1, 1)}(p_1),\nu _{({e}_1, {q}_1, 1)}(p_1)\big )\) | \(\ldots\) | \(\big (\mu _{({e}_1, {q}_1, 1)}(p_n),\nu _{({e}_1, {q}_1, 1)}(p_n)\big )\) |
\(({e}_1, {q}_2, 1)\) | \(\big (\mu _{({e}_1, {q}_2, 1)}(p_1),\nu _{({e}_1, {q}_2, 1)}(p_1)\big )\) | \(\ldots\) | \(\big (\mu _{({e}_1, {q}_2, 1)}(p_n),\nu _{({e}_1, {q}_2, 1)}(p_n)\big )\) |
\(\vdots\) | \(\vdots\) | \(\vdots\) | \(\vdots\) |
\(({e}_m, {q}_t, 1)\) | \(\big (\mu _{({e}_m, {q}_t, 1)}(p_1),\nu _{({e}_m, {q}_t, 1)}(p_1)\big )\) | \(\ldots\) | \(\big (\mu _{({e}_m, {q}_t, 1)}(p_n),\nu _{({e}_m, {q}_t, 1)}(p_n)\big )\) |
\(({e}_1, {q}_1, 0)\) | \(\big (\mu _{({e}_1, {q}_1, 0)}(p_1),\nu _{({e}_1, {q}_1, 0)}(p_1)\big )\) | \(\ldots\) | \(\big (\mu _{({e}_1, {q}_1, 0)}(p_n),\nu _{({e}_1, {q}_1, 0)}(p_n)\big )\) |
\(({e}_1, {q}_2, 0)\) | \(\big (\mu _{({e}_1, {q}_2, 0)}(p_1),\nu _{({e}_1, {q}_2, 0)}(p_1)\big )\) | \(\ldots\) | \(\big (\mu _{({e}_1, {q}_2, 0)}(p_n),\nu _{({e}_1, {q}_2, 0)}(p_n)\big )\) |
\(\vdots\) | \(\vdots\) | \(\vdots\) | \(\vdots\) |
\(({e}_m, {q}_t, 0)\) | \(\big (\mu _{({e}_m, {q}_t, 0)}(p_1),\nu _{({e}_m, {q}_t, 0)}(p_1)\big )\) | \(\ldots\) | \(\big (\mu _{({e}_m, {q}_t, 0)}(p_n),\nu _{({e}_m, {q}_t, 0)}(p_n)\big )\) |
\((\lambda ,A)\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) |
---|---|---|---|---|---|
\((e_1,q_1,1)\) | (0, 5, 0.7) | (0.8, 0.4) | (0.7, 0.6) | (0.4, 0.8) | (0.6, 0.4) |
\((e_1,q_2,1)\) | (0.9, 0.3) | (0.4, 0.9) | (0.5, 0.7) | (0.4, 0.7) | (0.7, 0.5) |
\((e_1,q_3,1)\) | (0.8, 0.7) | (0.4, 0.8) | (0.7, 0.6) | (0.4, 0.6) | (0.4, 0.9) |
\((e_2,q_1,1)\) | (0.5, 0.7) | (0.7, 0.4) | (0.8, 0.4) | (0.4, 0.6) | (0.6, 0.7) |
\((e_2,q_2,1)\) | (0.6, 0.5) | (0.4, 0.6) | (0.8, 0.4) | (0.5, 0.4) | (0.9, 0.2) |
\((e_2,q_3,1)\) | (0.5, 0.7) | (0.8, 0.4) | (0.6, 0.5) | (0.4, 0.6) | (0.8, 0.7) |
\((e_3,q_1,1)\) | (0.8, 0.4) | (0.9, 0.4) | (0.7, 0.6) | (0.8, 0.4) | (0.4, 0.6) |
\((e_3,q_2,1)\) | (0.7, 0.5) | (0.6, 0.6) | (0.8, 0.5) | (0.7, 0.5) | (0.3, 0.6) |
\((e_3,q_3,1)\) | (0.8, 0.4) | (0.4, 0.5) | (0.7, 0.5) | (0.5, 0.6) | (0.6, 0.7) |
\((e_4,q_1,1)\) | (0.5, 0.6) | (0.8, 0.7) | (0.4, 0.9) | (0.4, 0.5) | (0.7, 0.3) |
\((e_4,q_2,1)\) | (0.2, 0.9) | (0.8, 0.2) | (0.6, 0.5) | (0.7, 0.3) | (0.4, 0.6) |
\((e_4,q_3,1)\) | (0.8, 0.4) | (0.6, 0.4) | (0.8, 0.3) | (0.4, 0.7) | (0.9, 0.2) |
\((e_1,q_1,0)\) | (0.5, 0.9) | (0.8, 0.6) | (0.9, 0.2) | (0.5, 0.5) | (0.9, 0.1) |
\((e_1,q_2,0)\) | (0.6, 0.5) | (0.8, 0.4) | (0.5, 0.4) | (0.9, 0.3) | (0.5, 0.4) |
\((e_1,q_3,0)\) | (0.8, 0.7) | (0.9, 0.4) | (0.7, 0.8) | (0.5, 0.7) | (0.4, 0.7) |
\((e_2,q_1,0)\) | (0.6, 0.8) | (0.5, 0.8) | (0.9, 0.3) | (0.8, 0.4) | (0.7, 0.6) |
\((e_2,q_2,0)\) | (0.8, 0.7) | (0.7, 0.6) | (0.5, 0.3) | (0.7, 0.6) | (0.9, 0.2) |
\((e_2,q_3,0)\) | (0.5, 0.8) | (0.9, 0.5) | (0.8, 0.6) | (0.9, 0.6) | (0.8, 0.7) |
\((e_3,q_1,0)\) | (0.5, 0.7) | (0.7, 0.8) | (0.5, 0.4) | (0.9, 0.1) | (0.7, 0.6) |
\((e_3,q_2,0)\) | (0.9, 0.3) | (0.5, 0.4) | (0.6, 0.8) | (0.5, 0.6) | (0.9, 0.3) |
\((e_3,q_3,0)\) | (0.9, 0.1) | (0.6, 0.6) | (0.9, 0.4) | (0.8, 0.4) | (0.2, 0.9) |
\((e_4,q_1,0)\) | (0.5, 0.4) | (0.8, 0.5) | (0.7, 0.2) | (0.5, 0.6) | (0.8, 0.3) |
\((e_4,q_2,0)\) | (0.8, 0.4) | (0.9, 0.3) | (0.6, 0.2) | (0.7, 0.5) | (0.5, 0.8) |
\((e_4,q_3,0)\) | (0.7, 0.6) | (0.8, 0.3) | (0.5, 0.8) | (0.5, 0.7) | (0.8, 0.1) |
\((\lambda ,A)\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) |
---|---|---|---|---|---|
\((e_1,q_1,1)\) | (0, 4, 0.7) | (0.7, 0.4) | (0.6, 0.6) | (0.4, 0.8) | (0.5, 0.4) |
\((e_1,q_2,1)\) | (0.8, 0.3) | (0.4, 0.9) | (0.5, 0.7) | (0.4, 0.7) | (0.6, 0.5) |
\((e_1,q_3,1)\) | (0.6, 0.7) | (0.4, 0.8) | (0.6, 0.6) | (0.4, 0.6) | (0.4, 0.9) |
\((e_3,q_1,0)\) | (0.5, 0.7) | (0.6, 0.8) | (0.5, 0.4) | (0.8, 0.1) | (0.6, 0.6) |
\((e_3,q_2,1)\) | (0.6, 0.5) | (0.6, 0.6) | (0.7, 0.5) | (0.6, 0.5) | (0.3, 0.6) |
\((e_3,q_3,0)\) | (0.8, 0.1) | (0.6, 0.6) | (0.7, 0.4) | (0.7, 0.4) | (0.2, 0.9) |
\((\zeta ,B)\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) |
---|---|---|---|---|---|
\((e_1,q_1,1)\) | (0, 5, 0.6) | (0.8, 0.4) | (0.7, 0.5) | (0.4, 0.6) | (0.6, 0.4) |
\((e_1,q_2,1)\) | (0.9, 0.3) | (0.4, 0.7) | (0.5, 0.6) | (0.4, 0.6) | (0.7, 0.5) |
\((e_1,q_3,1)\) | (0.8, 0.6) | (0.4, 0.7) | (0.7, 0.6) | (0.4, 0.6) | (0.4, 0.7) |
\((e_3,q_1,0)\) | (0.5, 0.6) | (0.7, 0.6) | (0.5, 0.4) | (0.9, 0.1) | (0.7, 0.5) |
\((e_3,q_2,1)\) | (0.7, 0.5) | (0.6, 0.6) | (0.8, 0.5) | (0.7, 0.5) | (0.3, 0.6) |
\((e_3,q_3,0)\) | (0.9, 0.1) | (0.6, 0.6) | (0.9, 0.4) | (0.8, 0.4) | (0.2, 0.8) |
\((\lambda ,A)_1\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) |
---|---|---|---|---|---|
\((e_1,q_1,1)\) | (0, 5, 0.7) | (0.8, 0.4) | (0.7, 0.6) | (0.4, 0.8) | (0.6, 0.4) |
\((e_1,q_2,1)\) | (0.9, 0.3) | (0.4, 0.9) | (0.5, 0.7) | (0.4, 0.7) | (0.7, 0.5) |
\((e_1,q_3,1)\) | (0.8, 0.7) | (0.4, 0.8) | (0.7, 0.6) | (0.4, 0.6) | (0.4, 0.9) |
\((e_2,q_1,1)\) | (0.5, 0.7) | (0.7, 0.4) | (0.8, 0.4) | (0.4, 0.6) | (0.6, 0.7) |
\((e_2,q_2,1)\) | (0.6, 0.5) | (0.4, 0.6) | (0.8, 0.4) | (0.5, 0.4) | (0.9, 0.2) |
\((e_2,q_3,1)\) | (0.5, 0.7) | (0.8, 0.4) | (0.6, 0.5) | (0.4, 0.6) | (0.8, 0.7) |
\((e_3,q_1,1)\) | (0.8, 0.4) | (0.9, 0.4) | (0.7, 0.6) | (0.8, 0.4) | (0.4, 0.6) |
\((e_3,q_2,1)\) | (0.7, 0.5) | (0.6, 0.6) | (0.8, 0.5) | (0.7, 0.5) | (0.3, 0.6) |
\((e_3,q_3,1)\) | (0.8, 0.4) | (0.4, 0.5) | (0.7, 0.5) | (0.5, 0.6) | (0.6, 0.7) |
\((e_4,q_1,1)\) | (0.5, 0.6) | (0.8, 0.7) | (0.4, 0.9) | (0.4, 0.5) | (0.7, 0.3) |
\((e_4,q_2,1)\) | (0.2, 0.9) | (0.8, 0.2) | (0.6, 0.5) | (0.7, 0.3) | (0.4, 0.6) |
\((e_4,q_3,1)\) | (0.8, 0.4) | (0.6, 0.4) | (0.8, 0.3) | (0.4, 0.7) | (0.9, 0.2) |
\((\lambda ,A)_0\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) |
---|---|---|---|---|---|
\((e_1,q_1,0)\) | (0.5, 0.9) | (0.8, 0.6) | (0.9, 0.2) | (0.5, 0.5) | (0.9, 0.1) |
\((e_1,q_2,0)\) | (0.6, 0.5) | (0.8, 0.4) | (0.5, 0.4) | (0.9, 0.3) | (0.5, 0.4) |
\((e_1,q_3,0)\) | (0.8, 0.7) | (0.9, 0.4) | (0.7, 0.8) | (0.5, 0.7) | (0.4, 0.7) |
\((e_2,q_1,0)\) | (0.6, 0.8) | (0.5, 0.8) | (0.9, 0.3) | (0.8, 0.4) | (0.7, 0.6) |
\((e_2,q_2,0)\) | (0.8, 0.7) | (0.7, 0.6) | (0.5, 0.3) | (0.7, 0.6) | (0.9, 0.2) |
\((e_2,q_3,0)\) | (0.5, 0.8) | (0.9, 0.5) | (0.8, 0.6) | (0.9, 0.6) | (0.8, 0.7) |
\((e_3,q_1,0)\) | (0.5, 0.7) | (0.7, 0.8) | (0.5, 0.4) | (0.9, 0.1) | (0.7, 0.6) |
\((e_3,q_2,0)\) | (0.9, 0.3) | (0.5, 0.4) | (0.6, 0.8) | (0.5, 0.6) | (0.9, 0.3) |
\((e_3,q_3,0)\) | (0.9, 0.1) | (0.6, 0.6) | (0.9, 0.4) | (0.8, 0.4) | (0.2, 0.9) |
\((e_4,q_1,0)\) | (0.5, 0.4) | (0.8, 0.5) | (0.7, 0.2) | (0.5, 0.6) | (0.8, 0.3) |
\((e_4,q_2,0)\) | (0.8, 0.4) | (0.9, 0.3) | (0.6, 0.2) | (0.7, 0.5) | (0.5, 0.8) |
\((e_4,q_3,0)\) | (0.7, 0.6) | (0.8, 0.3) | (0.5, 0.8) | (0.5, 0.7) | (0.8, 0.1) |
\((\lambda ,A)^c\)
|
\(p_1\)
|
\(p_2\)
|
\(p_3\)
|
\(p_4\)
|
\(p_5\)
|
---|---|---|---|---|---|
\((\lnot e_1,q_1,1)\)
| (0.7, 0.5) | (0.4, 0.8) | (0.6, 0.7) | (0.8, 0.4) | (0.4, 0.6) |
\((\lnot e_1,q_2,1)\)
| (0.3, 0.9) | (0.9, 0.4) | (0.7, 0.5) | (0.7, 0.4) | (0.5, 0.7) |
\((\lnot e_1,q_3,1)\)
| (0.7, 0.8) | (0.8, 0.4) | (0.6, 0.7) | (0.6, 0.4) | (0.9, 0.4) |
\((\lnot e_2,q_1,1)\)
| (0.7, 0.5) | (0.4, 0.7) | (0.4, 0.8) | (0.6, 0.4) | (0.7, 0.6) |
\((\lnot e_2,q_2,1)\)
| (0.5, 0.6) | (0.6, 0.4) | (0.4, 0.8) | (0.4, 0.5) | (0.2, 0.9) |
\((\lnot e_2,q_3,1)\)
| (0.7, 0.5) | (0.4, 0.8) | (0.5, 0.6) | (0.6, 0.4) | (0.7, 0.8) |
\((\lnot e_3,q_1,1)\)
| (0.4, 0.8) | (0.4, 0.9) | (0.6, 0.7) | (0.4, 0.8) | (0.6, 0.4) |
\((\lnot e_3,q_2,1)\)
| (0.5, 0.7) | (0.6, 0.6) | (0.5, 0.8) | (0.5, 0.7) | (0.6, 0.3) |
\((\lnot e_3,q_3,1)\)
| (0.4, 0.8) | (0.5, 0.4) | (0.5, 0.7) | (0.6, 0.5) | (0.7, 0.6) |
\((\lnot e_4,q_1,1)\)
| (0.6, 0.5) | (0.7, 0.8) | (0.9, 0.4) | (0.5, 0.4) | (0.3, 0.7) |
\((\lnot e_4,q_2,1)\)
| (0.9, 0.2) | (0.2, 0.8) | (0.5, 0.6) | (0.3, 0.7) | (0.6, 0.4) |
\((\lnot e_4,q_3,1)\)
| (0.4, 0.8) | (0.4, 0.6) | (0.3, 0.8) | (0.7, 0.4) | (0.2, 0.9) |
\((\lnot e_1,q_1,0)\)
| (0.9, 0.5) | (0.6, 0.8) | (0.2, 0.9) | (0.5, 0.5) | (0.1, 0.9) |
\((\lnot e_1,q_2,0)\)
| (0.5, 0.6) | (0.4, 0.8) | (0.4, 0.5) | (0.3, 0.9) | (0.4, 0.5) |
\((\lnot e_1,q_3,0)\)
| (0.7, 0.8) | (0.4, 0.9) | (0.8, 0.7) | (0.7, 0.5) | (0.7, 0.4) |
\((\lnot e_2,q_1,0)\)
| (0.8, 0.6) | (0.8, 0.5) | (0.3, 0.9) | (0.4, 0.8) | (0.6, 0.7) |
\((\lnot e_2,q_2,0)\)
| (0.7, 0.8) | (0.6, 0.7) | (0.3, 0.5) | (0.6, 0.7) | (0.2, 0.9) |
\((\lnot e_2,q_3,0)\)
| (0.8, 0.5) | (0.5, 0.9) | (0.6, 0.8) | (0.6, 0.9) | (0.7, 0.8) |
\((\lnot e_3,q_1,0)\)
| (0.7, 0.5) | (0.8, 0.7) | (0.4, 0.5) | (0.1, 0.9) | (0.6, 0.7) |
\((\lnot e_3,q_2,0)\)
| (0.3, 0.9) | (0.4, 0.5) | (0.8, 0.6) | (0.6, 0.5) | (0.3, 0.9) |
\((\lnot e_3,q_3,0)\)
| (0.1, 0.9) | (0.6, 0.6) | (0.4, 0.9) | (0.4, 0.8) | (0.9, 0.2) |
\((\lnot e_4,q_1,0)\)
| (0.4, 0.5) | (0.5, 0.8) | (0.2, 0.7) | (0.6, 0.5) | (0.3, 0.8) |
\((\lnot e_4,q_2,0)\)
| (0.4, 0.8) | (0.3, 0.9) | (0.2, 0.6) | (0.5, 0.7) | (0.8, 0.5) |
\((\lnot e_4,q_3,0)\)
| (0.6, 0.7) | (0.3, 0.8) | (0.8, 0.5) | (0.7, 0.5) | (0.1, 0.8) |
\((\lambda ,A)\)
|
\(p_1\)
|
\(p_2\)
|
\(p_3\)
|
\(p_4\)
|
\(p_5\)
|
---|---|---|---|---|---|
\((e_1,q_1,1)\)
| (0.5, 0.7) | (0.8, 0.4) | (0.7, 0.6) | (0.4, 0.8) | (0.6, 0.4) |
\((e_1,q_2,1)\)
| (0.9, 0.3) | (0.4, 0.9) | (0.5, 0.7) | (0.4, 0.7) | (0.7, 0.5) |
\((e_1,q_3,1)\)
| (0.8, 0.7) | (0.4, 0.8) | (0.7, 0.6) | (0.4, 0.6) | (0.4, 0.9) |
\((e_2,q_1,1)\)
| (0.5, 0.7) | (0.7, 0.4) | (0.8, 0.4) | (0.4, 0.6) | (0.6, 0.7) |
\((e_2,q_2,1)\)
| (0.6, 0.5) | (0.4, 0.6) | (0.8, 0.4) | (0.5, 0.4) | (0.9, 0.2) |
\((e_2,q_3,1)\)
| (0.5, 0.7) | (0.8, 0.4) | (0.6, 0.5) | (0.4, 0.6) | (0.8, 0.7) |
\((e_3,q_1,1)\)
| (0.8, 0.4) | (0.9, 0.4) | (0.7, 0.6) | (0.8, 0.4) | (0.4, 0.6) |
\((e_3,q_2,1)\)
| (0.7, 0.5) | (0.6, 0.6) | (0.8, 0.5) | (0.7, 0.5) | (0.3, 0.6) |
\((e_3,q_3,1)\)
| (0.8, 0.4) | (0.4, 0.5) | (0.7, 0.5) | (0.5, 0.6) | (0.6, 0.7) |
\((e_4,q_1,1)\)
| (0.5, 0.6) | (0.8, 0.7) | (0.4, 0.9) | (0.4, 0.5) | (0.7, 0.3) |
\((e_4,q_2,1)\)
| (0.2, 0.9) | (0.8, 0.2) | (0.6, 0.5) | (0.7, 0.3) | (0.4, 0.6) |
\((e_4,q_3,1)\)
| (0.8, 0.4) | (0.6, 0.4) | (0.8, 0.3) | (0.4, 0.7) | (0.9, 0.2) |
\((e_1,q_1,0)\)
| (0.5, 0.9) | (0.8, 0.6) | (0.9, 0.2) | (0.5, 0.5) | (0.9, 0.1) |
\((e_1,q_2,0)\)
| (0.6, 0.5) | (0.8, 0.4) | (0.5, 0.4) | (0.9, 0.3) | (0.5, 0.4) |
\((e_1,q_3,0)\)
| (0.8, 0.7) | (0.9, 0.4) | (0.7, 0.8) | (0.5, 0.7) | (0.4, 0.7) |
\((e_2,q_1,0)\)
| (0.6, 0.8) | (0.5, 0.8) | (0.9, 0.3) | (0.8, 0.4) | (0.7, 0.6) |
\((e_2,q_2,0)\)
| (0.8, 0.7) | (0.7, 0.6) | (0.5, 0.3) | (0.7, 0.6) | (0.9, 0.2) |
\((e_2,q_3,0)\)
| (0.5, 0.8) | (0.9, 0.5) | (0.8, 0.6) | (0.9, 0.6) | (0.8, 0.7) |
\((e_3,q_1,0)\)
| (0.5, 0.7) | (0.7, 0.8) | (0.5, 0.4) | (0.9, 0.1) | (0.7, 0.6) |
\((e_3,q_2,0)\)
| (0.9, 0.3) | (0.5, 0.4) | (0.6, 0.8) | (0.5, 0.6) | (0.9, 0.3) |
\((e_3,q_3,0)\)
| (0.9, 0.1) | (0.6, 0.6) | (0.9, 0.4) | (0.8, 0.4) | (0.2, 0.9) |
\((e_4,q_1,0)\)
| (0.5, 0.4) | (0.8, 0.5) | (0.7, 0.2) | (0.5, 0.6) | (0.8, 0.3) |
\((e_4,q_2,0)\)
| (0.8, 0.4) | (0.9, 0.3) | (0.6, 0.2) | (0.7, 0.5) | (0.5, 0.8) |
\((e_4,q_3,0)\)
| (0.7, 0.6) | (0.8, 0.3) | (0.5, 0.8) | (0.5, 0.7) | (0.8, 0.1) |
\((\zeta ,B)\)
|
\(p_1\)
|
\(p_2\)
|
\(p_3\)
|
\(p_4\)
|
\(p_5\)
|
---|---|---|---|---|---|
\((e_1,q_1,1)\)
| (0.8, 0.2) | (0.9, 0.3) | (0.8, 0.1) | (0.2, 0.9) | (0.6, 0.5) |
\((e_1,q_2,1)\)
| (0.4, 0.9) | (0.3, 0.7) | (0.8, 0.4) | (0.6, 0.5) | (0.4, 0.7) |
\((e_1,q_3,1)\)
| (0.5, 0.8) | (0.7, 0.5) | (0.5, 0.4) | (0.7, 0.8) | (0.6, 0.5) |
\((e_2,q_1,1)\)
| (0.6, 0.6) | (0.8, 0.2) | (0.7, 0.4) | (0.5, 0.7) | (0.9, 0.3) |
\((e_2,q_2,1)\)
| (0.8, 0.3) | (0.9, 0.3) | (0.6, 0.7) | (0.6, 0.4) | (0.5, 0.8) |
\((e_2,q_3,1)\)
| (0.9, 0.1) | (0.5, 0.4) | (0.4, 0.7) | (0.2, 0.9) | (0.6, 0.7) |
\((e_3,q_1,1)\)
| (0.8, 0.7) | (0.9, 0.4) | (0.6, 0.6) | (0.5, 0.4) | (0.5, 0.5) |
\((e_3,q_2,1)\)
| (0.5, 0.4) | (0.7, 0.6) | (0.8, 0.5) | (0.6, 0.5) | (0.9, 0.3) |
\((e_3,q_3,1)\)
| (0.6, 0.2) | (0.5, 0.8) | (0.7, 0.5) | (0.8, 0.4) | (0.7, 0.6) |
\((e_4,q_1,1)\)
| (0.8, 0.3) | (0.7, 0.3) | (0.4, 0.8) | (0.6, 0.5) | (0.8, 0.2) |
\((e_4,q_2,1)\)
| (0.4, 0.6) | (0.8, 0.7) | (0.6, 0.5) | (0.5, 0.4) | (0.3, 0.6) |
\((e_4,q_3,1)\)
| (0.8, 0.4) | (0.4, 0.7) | (0.6, 0.7) | (0.3, 0.6) | (0.4, 0.9) |
\((e_1,q_1,0)\)
| (0.6, 0.3) | (0.5, 0.8) | (0.2, 0.9) | (0.6, 0.7) | (0.5, 0.5) |
\((e_1,q_2,0)\)
| (0.5, 0.4) | (0.8, 0.3) | (0.6, 0.5) | (0.8, 0.3) | (0.2, 0.9) |
\((e_1,q_3,0)\)
| (0.7, 0.6) | (0.9, 0.1) | (0.4, 0.7) | (0.6, 0.4) | (0.7, 0.6) |
\((e_2,q_1,0)\)
| (0.5, 0.7) | (0.4, 0.6) | (0.8, 0.2) | (0.5, 0.8) | (0.5, 0.4) |
\((e_2,q_2,0)\)
| (0.8, 0.1) | (0.5, 0.4) | (0.3, 0.7) | (0.5, 0.5) | (0.6, 0.3) |
\((e_2,q_3,0)\)
| (0.9, 0.2) | (0.3, 0.6) | (0.6, 0.6) | (0.7, 0.6) | (0.8, 0.1) |
\((e_3,q_1,0)\)
| (0.5, 0.4) | (0.7, 0.6) | (0.9, 0.4) | (0.8, 0.2) | (0.7, 0.5) |
\((e_3,q_2,0)\)
| (0.7, 0.3) | (0.6, 0.3) | (0.5, 0.6) | (0.3, 0.7) | (0.2, 0.9) |
\((e_3,q_3,0)\)
| (0.6, 0.7) | (0.2, 0.9) | (0.4, 0.7) | (0.9, 0.1) | (0.6, 0.5) |
\((e_4,q_1,0)\)
| (0.5, 0.7) | (0.8, 0.2) | (0.9, 0.1) | (0.8, 0.3) | (0.4, 0.7) |
\((e_4,q_2,0)\)
| (0.8, 0.4) | (0.3, 0.6) | (0.4, 0.7) | (0.5, 0.7) | (0.9, 0.3) |
\((e_4,q_3,0)\)
| (0.6, 0.7) | (0.5, 0.7) | (0.8, 0.4) | (0.6, 0.4) | (0.6, 0.6) |
\((\lambda ,A)\Cup (\zeta ,B)\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) |
---|---|---|---|---|---|
\((e_1,q_1,1)\) | (0.8, 0.2) | (0.9, 0.3) | (0.8, 0.1) | (0.4, 0.8) | (0.6, 0.4) |
\((e_1,q_2,1)\) | (0.9, 0.3) | (0.4, 0.7) | (0.8, 0.4) | (0.6, 0.5) | (0.7, 0.5) |
\((e_1,q_3,1)\) | (0.8, 0.7) | (0.7, 0.5) | (0.7, 0.4) | (0.7, 0.6) | (0.6, 0.5) |
\((e_2,q_1,1)\) | (0.6, 0.6) | (0.8, 0.2) | (0.8, 0.4) | (0.5, 0.6) | (0.9, 0.3) |
\((e_2,q_2,1)\) | (0.8, 0.3) | (0.9, 0.3) | (0.8, 0.4) | (0.6, 0.4) | (0.9, 0.2) |
\((e_2,q_3,1)\) | (0.9, 0.1) | (0.8, 0.4) | (0.6, 0.5) | (0.4, 0.6) | (0.8, 0.7) |
\((e_3,q_1,1)\) | (0.8, 0.4) | (0.9, 0.4) | (0.7, 0.6) | (0.8, 0.4) | (0.5, 0.5) |
\((e_3,q_2,1)\) | (0.7, 0.4) | (0.7, 0.6) | (0.8, 0.5) | (0.7, 0.5) | (0.9, 0.3) |
\((e_3,q_3,1)\) | (0.8, 0.2) | (0.5, 0.5) | (0.7, 0.5) | (0.8, 0.4) | (0.7, 0.6) |
\((e_4,q_1,1)\) | (0.8, 0.3) | (0.8, 0.3) | (0.4, 0.8) | (0.6, 0.5) | (0.8, 0.2) |
\((e_4,q_2,1)\) | (0.4, 0.6) | (0.8, 0.2) | (0.6, 0.5) | (0.7, 0.3) | (0.4, 0.6) |
\((e_4,q_3,1)\) | (0.8, 0.4) | (0.6, 0.4) | (0.8, 0.3) | (0.4, 0.6) | (0.9, 0.2) |
\((e_1,q_1,0)\) | (0.6, 0.3) | (0.8, 0.6) | (0.9, 0.2) | (0.6, 0.5) | (0.9, 0.1) |
\((e_1,q_2,0)\) | (0.6, 0.4) | (0.8, 0.3) | (0.6, 0.4) | (0.9, 0.3) | (0.5, 0.4) |
\((e_1,q_3,0)\) | (0.8, 0.6) | (0.9, 0.1) | (0.7, 0.7) | (0.6, 0.4) | (0.7, 0.6) |
\((e_2,q_1,0)\) | (0.6, 0.7) | (0.5, 0.6) | (0.9, 0.2) | (0.8, 0.4) | (0.7, 0.4) |
\((e_2,q_2,0)\) | (0.8, 0.1) | (0.7, 0.4) | (0.5, 0.3) | (0.7, 0.5) | (0.9, 0.2) |
\((e_2,q_3,0)\) | (0.9, 0.2) | (0.9, 0.5) | (0.8, 0.6) | (0.9, 0.6) | (0.8, 0.1) |
\((e_3,q_1,0)\) | (0.5, 0.4) | (0.7, 0.6) | (0.9, 0.4) | (0.9, 0.1) | (0.7, 0.5) |
\((e_3,q_2,0)\) | (0.9, 0.3) | (0.6, 0.3) | (0.6, 0.6) | (0.5, 0.6) | (0.9, 0.3) |
\((e_3,q_3,0)\) | (0.9, 0.1) | (0.6, 0.6) | (0.9, 0.4) | (0.9, 0.7) | (0.6, 0.5) |
\((e_4,q_1,0)\) | (0.5, 0.4) | (0.8, 0.2) | (0.9, 0.1) | (0.8, 0.3) | (0.8, 0.3) |
\((e_4,q_2,0)\) | (0.8, 0.4) | (0.9, 0.3) | (0.6, 0.2) | (0.7, 0.5) | (0.9, 0.3) |
\((e_4,q_3,0)\) | (0.7, 0.6) | (0.8, 0.3) | (0.8, 0.4) | (0.6, 0.4) | (0.8, 0.1) |
\((\lambda ,A)\Cap (\zeta ,B)\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) |
---|---|---|---|---|---|
\((e_1,q_1,1)\) | (0.5, 0.7) | (0.8, 0.4) | (0.7, 0.6) | (0.9, 0.8) | (0.6, 0.5) |
\((e_1,q_2,1)\) | (0.4, 0.9) | (0.3, 0.9) | (0.5, 0.7) | (0.4, 0.7) | (0.4, 0.7) |
\((e_1,q_3,1)\) | (0.5, 0.8) | (0.4, 0.7) | (0.5, 0.6) | (0.4, 0.8) | (0.4, 0.9) |
\((e_2,q_1,1)\) | (0.5, 0.7) | (0.7, 0.4) | (0.7, 0.4) | (0.4, 0.7) | (0.6, 0.7) |
\((e_2,q_2,1)\) | (0.6, 0.5) | (0.4, 0.6) | (0.6, 0.7) | (0.5, 0.4) | (0.5, 0.8) |
\((e_2,q_3,1)\) | (0.5, 0.7) | (0.5, 0.4) | (0.4, 0.7) | (0.2, 0.9) | (0.6, 0.7) |
\((e_3,q_1,1)\) | (0.8, 0.7) | (0.9, 0.4) | (0.6, 0.6) | (0.5, 0.4) | (0.5, 0.5) |
\((e_3,q_2,1)\) | (0.5, 0.5) | (0.6, 0.6) | (0.8, 0.5) | (0.6, 0.5) | (0.3, 0.6) |
\((e_3,q_3,1)\) | (0.6, 0.2) | (0.4, 0.5) | (0.7, 0.5) | (0.5, 0.4) | (0.6, 0.6) |
\((e_4,q_1,1)\) | (0.5, 0.6) | (0.7, 0.7) | (0.4, 0.9) | (0.4, 0.5) | (0.7, 0.3) |
\((e_4,q_2,1)\) | (0.2, 0.9) | (0.8, 0.7) | (0.6, 0.5) | (0.5, 0.4) | (0.3, 0.6) |
\((e_4,q_3,1)\) | (0.8, 0.4) | (0.4, 0.7) | (0.6, 0.7) | (0.3, 0.7) | (0.4, 0.9) |
\((e_1,q_1,0)\) | (0.5, 0.9) | (0.5, 0.8) | (0.2, 0.9) | (0.5, 0.7) | (0.5, 0.5) |
\((e_1,q_2,0)\) | (0.5, 0.5) | (0.8, 0.4) | (0.5, 0.5) | (0.8, 0.3) | (0.2, 0.9) |
\((e_1,q_3,0)\) | (0.7, 0.7) | (0.4, 0.4) | (0.4, 0.8) | (0.5, 0.7) | (0.4, 0.7) |
\((e_2,q_1,0)\) | (0.5, 0.8) | (0.4, 0.8) | (0.8, 0.3) | (0.5, 0.8) | (0.5, 0.6) |
\((e_2,q_2,0)\) | (0.8, 0.7) | (0.5, 0.6) | (0.3, 0.7) | (0.5, 0.6) | (0.6, 0.3) |
\((e_2,q_3,0)\) | (0.5, 0.8) | (0.3, 0.6) | (0.6, 0.6) | (0.7, 0.6) | (0.8, 0.7) |
\((e_3,q_1,0)\) | (0.5, 0.7) | (0.7, 0.8) | (0.9, 0.4) | (0.8, 0.2) | (0.7, 0.6) |
\((e_3,q_2,0)\) | (0.7, 0.3) | (0.5, 0.4) | (0.5, 0.8) | (0.3, 0.7) | (0.2, 0.9) |
\((e_3,q_3,0)\) | (0.6, 0.7) | (0.2, 0.9) | (0.4, 0.7) | (0.8, 0.7) | (0.2, 0.9) |
\((e_4,q_1,0)\) | (0.5, 0.7) | (0.8, 0.5) | (0.7, 0.2) | (0.5, 0.6) | (0.4, 0.7) |
\((e_4,q_2,0)\) | (0.8, 0.4) | (0.3, 0.6) | (0.4, 0.7) | (0.5, 0.7) | (0.5, 0.8) |
\((e_4,q_3,0)\) | (0.6, 0.7) | (0.5, 0.7) | (0.5, 0.8) | (0.5, 0.7) | (0.6, 0.6) |
\((\lambda ,A)\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) |
---|---|---|---|---|---|
\((e_1,q_1,1)\) | (0.5, 0.7) | (0.8, 0.4) | (0.7, 0.6) | (0.4, 0.8) | (0.6, 0.4) |
\((e_2,q_1,1)\) | (0.5, 0.7) | (0.7, 0.4) | (0.8, 0.4) | (0.4, 0.6) | (0.6, 0.7) |
\((e_2,q_2,1)\) | (0.6, 0.5) | (0.4, 0.6) | (0.8, 0.4) | (0.5, 0.4) | (0.9, 0.2) |
\((e_2,q_3,1)\) | (0.5, 0.7) | (0.8, 0.4) | (0.6, 0.5) | (0.4, 0.6) | (0.8, 0.7) |
\((e_3,q_1,1)\) | (0.6, 0.7) | (0.9, 0.3) | (0.6, 0.5) | (0.6, 0.6) | (0.4, 0.7) |
\(( \zeta ,B)\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) |
---|---|---|---|---|---|
\((e_3,q_3,1)\) | (0.6, 0.2) | (0.5, 0.8) | (0.7, 0.5) | (0.8, 0.4) | (0.7, 0.6) |
\((e_3,q_1,0)\) | (0.8, 0.7) | (0.9, 0.4) | (0.6, 0.6) | (0.5, 0.4) | (0.5, 0.5) |
\((e_2,q_2,1)\) | (0.8, 0.3) | (0.9, 0.3) | (0.6, 0.7) | (0.6, 0.4) | (0.5, 0.8) |
\((e_1,q_3,1)\) | (0.5, 0.8) | (0.7, 0.5) | (0.5, 0.4) | (0.7, 0.8) | (0.6, 0.5) |
\(( \lambda ,A) \wedge (\zeta ,B )\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) |
---|---|---|---|---|---|
\(\big ((e_1,q_1,1),(e_3,q_3,1)\big )\) | (0.5, 0.7) | (0.5, 0.8) | (0.7, 0.6) | (0.4, 0.8) | (0.6, 0.6) |
\(\big ((e_1,q_1,1),(e_3,q_1,0)\big )\) | (0.5, 0.7) | (0.8, 0.4) | (0.6, 0.6) | (0.4, 0.8) | (0.5, 0.5) |
\(\big ((e_1,q_1,1),(e_2,q_2,1)\big )\) | (0.5, 0.7) | (0.8, 0.4) | (0.6, 0.7) | (0.4, 0.8) | (0.5, 0.8) |
\(\big ((e_1,q_1,1),(e_1,q_3,1)\big )\) | (0.5, 0.8) | (0.7, 0.5) | (0.5, 0.6) | (0.4, 0.8) | (0.6, 0.5) |
\(\big ((e_2,q_1,1),(e_3,q_3,1)\big )\) | (0.5, 0.7) | (0.5, 0.8) | (0.7, 0.5) | (0.4, 0.6) | (0.6, 0.7) |
\(\big ((e_2,q_1,1),(e_3,q_1,0)\big )\) | (0.5, 0.7) | (0.7, 0.4) | (0.6, 0.6) | (0.4, 0.6) | (0.5, 0.7) |
\(\big ((e_2,q_1,1),(e_2,q_2,1)\big )\) | (0.5, 0.7) | (0.7, 0.4) | (0.6, 0.7) | (0.4, 0.6) | (0.5, 0.8) |
\(\big ((e_2,q_1,1),(e_1,q_3,1)\big )\) | (0.5, 0.8) | (0.7, 0.5) | (0.5, 0.4) | (0.4, 0.8) | (0.6, 0.7) |
\(\big ((e_2,q_2,1),(e_3,q_3,1)\big )\) | (0.6, 0.5) | (0.4, 0.8) | (0.7, 0.5) | (0.5, 0.4) | (0.7, 0.6) |
\(\big ((e_2,q_2,1),(e_3,q_1,0)\big )\) | (0.6, 0.7) | (0.4, 0.6) | (0.6, 0.6) | (0.5, 0.4) | (0.5, 0.5) |
\(\big ((e_2,q_2,1),(e_2,q_2,1)\big )\) | (0.6, 0.5) | (0.4, 0.6) | (0.6, 0.7) | (0.5, 0.4) | (0.5, 0.8) |
\(\big ((e_2,q_2,1),(e_1,q_3,1)\big )\) | (0.5, 0.8) | (0.4, 0.6) | (0.5, 0.4) | (0.5, 0.8) | (0.6, 0.5) |
\(\big ((e_2,q_3,1),(e_3,q_3,1)\big )\) | (0.5, 0.7) | (0.5, 0.8) | (0.6, 0.5) | (0.4, 0.6) | (0.7, 0.7) |
\(\big ((e_2,q_3,1),(e_3,q_1,0)\big )\) | (0.5, 0.7) | (0.8, 0.4) | (0.6, 0.6) | (0.4, 0.6) | (0.5, 0.7) |
\(\big ((e_2,q_3,1),(e_2,q_2,1)\big )\) | (0.5, 0.7) | (0.8, 0.4) | (0.6, 0.7) | (0.4, 0.6) | (0.5, 0.8) |
\(\big ((e_2,q_3,1),(e_1,q_3,1)\big )\) | (0.5, 0.8) | (0.7, 0.5) | (0.5, 0.5) | (0.4, 0.8) | (0.6, 0.7) |
\(\big ((e_3,q_1,1),(e_3,q_3,1)\big )\) | (0.6, 0.7) | (0.5, 0.8) | (0.6, 0.5) | (0.6, 0.6) | (0.4, 0.7) |
\(\big ((e_3,q_1,1),(e_3,q_1,0)\big )\) | (0.6, 0.7) | (0.9, 0.4) | (0.6, 0.6) | (0.5, 0.6) | (0.4, 0.7) |
\(\big ((e_3,q_1,1),(e_2,q_2,1)\big )\) | (0.6, 0.7) | (0.9, 0.3) | (0.6, 0.7) | (0.6, 0.6) | (0.4, 0.8) |
\(\big ((e_3,q_1,1),(e_1,q_3,1)\big )\) | (0.5, 0.8) | (0.7, 0.5) | (0.5, 0.5) | (0.6, 0.8) | (0.4, 0.7) |
\((\lambda ,A)\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) |
---|---|---|---|---|---|
\((e_1,q_1,1)\) | (0.5, 0.7) | (0.8, 0.4) | (0.7, 0.6) | (0.4, 0.8) | (0.6, 0.4) |
\((e_2,q_1,1)\) | (0.5, 0.7) | (0.7, 0.4) | (0.8, 0.4) | (0.4, 0.6) | (0.6, 0.7) |
\((e_2,q_2,1)\) | (0.6, 0.5) | (0.4, 0.6) | (0.8, 0.4) | (0.5, 0.4) | (0.9, 0.2) |
\((e_2,q_3,1)\) | (0.5, 0.7) | (0.8, 0.4) | (0.6, 0.5) | (0.4, 0.6) | (0.8, 0.7) |
\((e_3,q_1,1)\) | (0.6, 0.7) | (0.9, 0.3) | (0.6, 0.5) | (0.6, 0.6) | (0.4, 0.7) |
\(( \zeta ,B)\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) |
---|---|---|---|---|---|
\((e_3,q_3,1)\) | (0.6, 0.2) | (0.5, 0.8) | (0.7, 0.5) | (0.8, 0.4) | (0.7, 0.6) |
\((e_3,q_1,0)\) | (0.8, 0.7) | (0.9, 0.4) | (0.6, 0.6) | (0.5, 0.4) | (0.5, 0.5) |
\((e_2,q_2,1)\) | (0.8, 0.3) | (0.9, 0.3) | (0.6, 0.7) | (0.6, 0.4) | (0.5, 0.8) |
\((e_1,q_3,1)\) | (0.5, 0.8) | (0.7, 0.5) | (0.5, 0.4) | (0.7, 0.8) | (0.6, 0.5) |
\(( \lambda ,A) \vee (\zeta ,B )\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) |
---|---|---|---|---|---|
\(\big ((e_1,q_1,1),(e_3,q_3,1)\big )\) | (0.6, 0.2) | (0.8, 0.4) | (0.7, 0.5) | (0.8, 0.4) | (0.7, 0.4) |
\(\big ((e_1,q_1,1),(e_3,q_1,0)\big )\) | (0.8, 0.7) | (0.9, 0.4) | (0.7, 0.6) | (0.5, 0.4) | (0.6, 0.4) |
\(\big ((e_1,q_1,1),(e_2,q_2,1)\big )\) | (0.8, 0.3) | (0.9, 0.3) | (0.7, 0.6) | (0.6, 0.4) | (0.6, 0.4) |
\(\big ((e_1,q_1,1),(e_1,q_3,1)\big )\) | (0.5, 0.7) | (0.8, 0.4) | (0.7, 0.4) | (0.7, 0.8) | (0.6, 0.4) |
\(\big ((e_2,q_1,1),(e_3,q_3,1)\big )\) | (0.6, 0.2) | (0.7, 0.4) | (0.8, 0.4) | (0.8, 0.4) | (0.7, 0.6) |
\(\big ((e_2,q_1,1),(e_3,q_1,0)\big )\) | (0.8, 0.7) | (0.9, 0.4) | (0.8, 0.4) | (0.5, 0.4) | (0.6, 0.5) |
\(\big ((e_2,q_1,1),(e_2,q_2,1)\big )\) | (0.8, 0.3) | (0.9, 0.3) | (0.8, 0.4) | (0.6, 0.4) | (0.6, 0.7) |
\(\big ((e_2,q_1,1),(e_1,q_3,1)\big )\) | (0.5, 0.7) | (0.7, 0.4) | (0.8, 0.4) | (0.7, 0.6) | (0.6, 0.5) |
\(\big ((e_2,q_2,1),(e_3,q_3,1)\big )\) | (0.6, 0.2) | (0.5, 0.6) | (0.8, 0.4) | (0.8, 0.4) | (0.9, 0.2) |
\(\big ((e_2,q_2,1),(e_3,q_1,0)\big )\) | (0.8, 0.5) | (0.9, 0.4) | (0.8, 0.4) | (0.5, 0.4) | (0.9, 0.2) |
\(\big ((e_2,q_2,1),(e_2,q_2,1)\big )\) | (0.8, 0.3) | (0.9, 0.3) | (0.8, 0.4) | (0.6, 0.4) | (0.9, 0.2) |
\(\big ((e_2,q_2,1),(e_1,q_3,1)\big )\) | (0.6, 0.5) | (0.7, 0.5) | (0.8, 0.4) | (0.7, 0.4) | (0.9, 0.2) |
\(\big ((e_2,q_3,1),(e_3,q_3,1)\big )\) | (0.6, 0.2) | (0.8, 0.4) | (0.7, 0.5) | (0.8, 0.4) | (0.8, 0.6) |
\(\big ((e_2,q_3,1),(e_3,q_1,0)\big )\) | (0.8, 0.7) | (0.9, 0.4) | (0.6, 0.5) | (0.5, 0.4) | (0.8, 0.5) |
\(\big ((e_2,q_3,1),(e_2,q_2,1)\big )\) | (0.8, 0.3) | (0.9, 0.3) | (0.6, 0.5) | (0.6, 0.4) | (0.8, 0.7) |
\(\big ((e_2,q_3,1),(e_1,q_3,1)\big )\) | (0.5, 0.7) | (0.8, 0.4) | (0.6, 0.4) | (0.7, 0.6) | (0.8, 0.5) |
\(\big ((e_3,q_1,1),(e_3,q_3,1)\big )\) | (0.6, 0.2) | (0.9, 0.3) | (0.7, 0.5) | (0.8, 0.4) | (0.7, 0.6) |
\(\big ((e_3,q_1,1),(e_3,q_1,0)\big )\) | (0.8, 0.7) | (0.9, 0.3) | (0.6, 0.5) | (0.6, 0.4) | (0.5, 0.5) |
\(\big ((e_3,q_1,1),(e_2,q_2,1)\big )\) | (0.8, 0.3) | (0.9, 0.3) | (0.6, 0.5) | (0.6, 0.4) | (0.5, 0.7) |
\(\big ((e_3,q_1,1),(e_1,q_3,1)\big )\) | (0.6, 0.7) | (0.9, 0.3) | (0.6, 0.4) | (0.7, 0.6) | (0.6, 0.5) |
4 Application to MCGDM under FFSES
4.1 A case study: selection of most suitable solar panel system
\((\lambda ,A)_1\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) | \(p_6\) | \(p_7\) | \(p_8\) | \(p_9\) |
---|---|---|---|---|---|---|---|---|---|
\((e_1,q_1,1)\) | (0.3, 0.9) | (0.7, 0.6) | (0.8, 0.5) | (0.6, 0.5) | (0.7, 0.6) | (0.8, 0.5) | (0.7, 0.5) | (0.9, 0.2) | (0.9, 0.4) |
\((e_1,q_2,1)\) | (0.8, 0.7) | (0.7, 0.3) | (0.9, 0.2) | (0.6, 0.2) | (0.5, 0.4) | (0.7, 0.7) | (0.6, 0.3) | (0.9, 0.2) | (0.7, 0.6) |
\((e_1,q_3,1)\) | (0.8, 0.5) | (0.9, 0.4) | (0.6, 0.5) | (0.8, 0.5) | (0.7, 0.5) | (0.7, 0.6) | (0.5, 0.4) | (0.7, 0.3) | (0.9, 0.4) |
\((e_2,q_1,1)\) | (0.7, 0.4) | (0.6, 0.5) | (0.5, 0.4) | (0.8, 0.7) | (0.9, 0.2) | (0.5, 0.4) | (0.8, 0.7) | (0.6, 0.3) | (0.6, 0.5) |
\((e_2,q_2,1)\) | (0.7, 0.4) | (0.8, 0.2) | (0.6, 0.6) | (0.4, 0.9) | (0.8, 0.5) | (0.5, 0.4) | (0.6, 0.3) | (0.5, 0.4) | (0.7, 0.6) |
\((e_2,q_3,1)\) | (0.6, 0.4) | (0.8, 0.4) | (0.9, 0.3) | (0.7, 0.6) | (0.4.0.8) | (0.6, 0.4) | (0.7, 0.5) | (0.6, 0.5) | (0.5, 0.7) |
\((e_3,q_1,1)\) | (0.8, 0.7) | (0.6, 0.8) | (0.9, 0.4) | (0.8, 0.6) | (0.2, 0.9) | (0.6, 0.8) | (0.9, 0.3) | (0.5, 0.4) | (0.8, 0.7) |
\((e_3,q_2,1)\) | (0.8, 0.4) | (0.5, 0.7) | (0.8, 0.1) | (0.9, 0.4) | (0.9, 0.1) | (0.7, 0.6) | (0.9, 0.1) | (0.6, 0.5) | (0.8, 0.4) |
\((e_3,q_3,1)\) | (0.8, 0.2) | (0.9, 0.3) | (0.8, 0.1) | (0.2, 0.9) | (0.6, 0.5) | (0.4, 0.7) | (0.6, 0.5) | (0.8, 0.4) | (0.3, 0.7) |
\((e_4,q_1,1)\) | (0.5, 0.8) | (0.7, 0.5) | (0.5, 0.4) | (0.7, 0.8) | (0.6, 0.5) | (0.7, 0.8) | (0.5, 0.4) | (0.7, 0.5) | (0.6, 0.5) |
\((e_4,q_2,1)\) | (0.6, 0.7) | (0.8, 0.4) | (0.5, 0.7) | (0.6, 0.4) | (0.9, 0.3) | (0.4, 0.7) | (0.5, 0.7) | (0.3, 0.6) | (0.5, 0.7) |
\((e_4,q_3,1)\) | (0.6, 0.7) | (0.2, 0.9) | (0.4, 0.7) | (0.9, 0.1) | (0.5, 0.4) | (0.6, 0.3) | (0.7, 0.5) | (0.4, 0.6) | (0.9, 0.2) |
\((e_5,q_1,1)\) | (0.9, 0.3) | (0.3, 0.7) | (0.7, 0.5) | (0.8, 0.2) | (0.9, 0.3) | (0.5, 0.4) | (0.9, 0.4) | (0.7, 0.6) | (0.5, 0.8) |
\((e_5,q_2,1)\) | (0.5, 0.4) | (0.7, 0.6) | (0.5, 0.7) | (0.8, 0.1) | (0.9, 0.2) | (0.5, 0.4) | (0.7, 0.3) | (0.6, 0.7) | (0.5, 0.7) |
\((e_5,q_3,1)\) | (0.5, 0.4) | (0.8, 0.3) | (0.6, 0.5) | (0.8, 0.3) | (0.2, 0.9) | (0.6, 0.7) | (0.3, 0.6) | (0.5, 0.4) | (0.2, 0.9) |
\((e_6,q_1,1)\) | (0.5, 0.8) | (0.8, 0.4) | (0.7, 0.5) | (0.9, 0.4) | (0.3, 0.6) | (0.4, 0.7) | (0.8, 0.2) | (0.9, 0.3) | (0.6, 0.7) |
\((e_6,q_2,1)\) | (0.8, 0.5) | (0.7, 0.4) | (0.9, 0.1) | (0.6, 0.4) | (0.5, 0.4) | (0.2, 0.9) | (0.8, 0.4) | (0.9, 0.2) | (0.5, 0.4) |
\((e_6,q_3,1)\) | (0.8, 0.7) | (0.5, 0.7) | (0.9, 0.3) | (0.5, 0.4) | (0.8, 0.4) | (0.7, 0.6) | (0.5, 0.8) | (0.2, 0.9) | (0.8, 0.3) |
\((e_7,q_1,1)\) | (0.8, 0.4) | (0.6, 0.3) | (0.8, 0.3) | (0.9, 0.3) | (0.5, 0.8) | (0.5, 0.3) | (0.4, 0.7) | (0.5, 0.4) | (0.7, 0.8) |
\((e_7,q_2,1)\) | (0.7, 0.5) | (0.8, 0.2) | (0.9, 0.3) | (0.8, 0.4) | (0.9, 0.4) | (0.7, 0.6) | (0.5, 0.6) | (0.8, 0.3) | (0.7, 0.2) |
\((e_7,q_3,1)\) | (0.5, 0.6) | (0.7, 0.4) | (0.9, 0.5) | (0.7, 0.6) | (0.6, 0.3) | (0.8, 0.2) | (0.9, 0.3) | (0.8, 0.3) | (0.7, 0.6) |
\((e_8,q_1,1)\) | (0.8, 0.2) | (0.9, 0.3) | (0.8, 0.7) | (0.7, 0.3) | (0.9, 0.1) | (0.8, 0.4) | (0.7, 0.3) | (0.8, 0.3) | (0.6, 0.4) |
\((e_8,q_2,1)\) | (0.9, 0.3) | (0.4, 0.7) | (0.7, 0.5) | (0.8, 0.2) | (0.9, 0.3) | (0.8, 0.4) | (0.7, 0.6) | (0.8, 0.3) | (0.7, 0.4) |
\((e_8,q_3,1)\) | (0.8, 0.4) | (0.7, 0.3) | (0.9, 0.1) | (0.6, 0.4) | (0.3, 0.9) | (0.4, 0.8) | (0.7, 0.2) | (0.6, 0.5) | (0.7, 0.6) |
\((e_9,q_1,1)\) | (0.6, 0.4) | (0.8, 0.4) | (0.9, 0.2) | (0.8, 0.1) | (0.7, 0.5) | (0.9, 0.3) | (0.8, 0.1) | (0.6, 0.5) | (0.7, 0.4) |
\((e_9,q_2,1)\) | (0.8, 0.3) | (0.5, 0.7) | (0.9, 0.2) | (0.5, 0.4) | (0.9, 0.3) | (0.8, 0.4) | (0.7, 0.5) | (0.9, 0.4) | (0.9, 0.5) |
\((e_9,q_3,1)\) | (0.8, 0.4) | (0.6, 0.5) | (0.7, 0.6) | (0.8, 0.5) | (0.4, 0.7) | (0.9, 0.2) | (0.5, 0.3) | (0.8, 0.6) | (0.3, 0.8) |
\((e_{10},q_1,1)\) | (0.6, 0.7) | (0.8, 0.1) | (0.9, 0.2) | (0.5, 0.4) | (0.8, 0.4) | (0.7, 0.6) | (0.6, 0.2) | (0.7, 0.5) | (0.7, 0.4) |
\((e_{10},q_2,1)\) | (0.7, 0.5) | (0.8, 0.3) | (0.5, 0.4) | (0.7, 0.6) | (0.8, 0.4) | (0.9, 0.1) | (0.3, 0.7) | (0.2, 0.9) | (0.8, 0.4) |
\((e_{10},q_3,1)\) | (0.9, 0.3) | (0.5, 0.8) | (0.6, 0.7) | (0.7, 0.6) | (0.2, 0.9) | (0.7, 0.5) | (0.4, 0.6) | (0.9, 0.1) | (0.7, 0.6) |
\((e_{11},q_1,1)\) | (0.9, 0.3) | (0.5, 0.4) | (0.7, 0.6) | (0.5, 0.8) | (0.7, 0.3) | (0.6, 0.4) | (0.5, 0.7) | (0.3, 0.6) | (0.4, 0.7) |
\((e_{11},q_2,1)\) | (0.4, 0.9) | (0.7, 0.6) | (0.8, 0.4) | (0.5, 0.7) | (0.8, 0.4) | (0.7, 0.5) | (0.7, 0.8) | (0.8, 0.2) | (0.5, 0.8) |
\((e_{11},q_3,1)\) | (0.4, 0.7) | (0.5, 0.8) | (0.8, 0.3) | (0.9, 0.1) | (0.4, 0.6) | (0.5, 0.4) | (0.7, 0.3) | (0.2, 0.9) | (0.8, 0.2) |
\((e_{12},q_1,1)\) | (0.7, 0.4) | (0.6, 0.7) | (0.4, 0.7) | (0.8, 0.5) | (0.4, 0.7) | (0.6, 0.3) | (0.9, 0.1) | (0.6, 0.7) | (0.8, 0.1) |
\((e_{12},q_2,1)\) | (0.9, 0.3) | (0.8, 0.4) | (0.6, 0.5) | (0.8, 0.3) | (0.5, 0.8) | (0.6, 0.4) | (0.9, 0.4) | (0.6, 0.5) | (0.2, 0.9) |
\((e_{12},q_3,1)\) | (0.7, 0.5) | (0.8, 0.4) | (0.6, 0.5) | (0.3, 0.9) | (0.8, 0.1) | (0.6, 0.3) | (0.4, 0.9) | (0.6, 0.7) | (0.8, 0.4) |
\((\lambda ,A)_0\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) | \(p_6\) | \(p_7\) | \(p_8\) | \(p_9\) |
---|---|---|---|---|---|---|---|---|---|
\((e_1,q_1,0)\) | (0.8, 0.3) | (0.5, 0.4) | (0.7, 0.7) | (0.6, 0.3) | (0.9, 0.2) | (0.7, 0.6) | (0.6, 0.5) | (0.3, 0.9) | (0.8, 0.1) |
\((e_1,q_2,0)\) | (0.6, 0.2) | (0.7, 0.5) | (0.7, 0.4) | (0.8, 0.3) | (0.5, 0.7) | (0.9, 0.2) | (0.5, 0.4) | (0.9, 0.3) | (0.8, 0.4) |
\((e_1,q_3,0)\) | (0.8, 0.4) | (0.7, 0.3) | (0.9, 0.1) | (0.6, 0.4) | (0.3, 0.9) | (0.4, 0.8) | (0.7, 0.2) | (0.6, 0.5) | (0.7, 0.6) |
\((e_2,q_1,0)\) | (0.7, 0.4) | (0.6, 0.2) | (0.7, 0.3) | (0.9, 0.1) | (0.7, 0.5) | (0.8, 0.3) | (0.9, 0.1) | (0.4, 0.6) | (0.9, 0.3) |
\((e_2,q_2,0)\) | (0.7, 0.6) | (0.6, 0.5) | (0.4, 0.7) | (0.5, 0.8) | (0.8, 0.3) | (0.9, 0.1) | (0.4, 0.6) | (0.5, 0.4) | (0.7, 0.3) |
\((e_2,q_3,0)\) | (0.2, 0.9) | (0.8, 0.2) | (0.8, 0.4) | (0.6, 0.3) | (0.7, 0.5) | (0.7, 0.6) | (0.6, 0.5) | (0.8, 0.4) | (0.6, 0.5) |
\((e_3,q_1,0)\) | (0.3, 0.9) | (0.8, 0.1) | (0.6, 0.3) | (0.4, 0.9) | (0.6, 0.7) | (0.8, 0.4) | (0.9, 0.1) | (0.3, 0.7) | (0.2, 0.9) |
\((e_3,q_2,0)\) | (0.7, 0.5) | (0.8, 0.3) | (0.7, 0.6) | (0.6, 0.5) | (0.4, 0.7) | (0.5, 0.4) | (0.7, 0.6) | (0.6, 0.4) | (0.7, 0.3) |
\((e_3,q_3,0)\) | (0.8, 0.4) | (0.6, 0.7) | (0.8, 0.4) | (0.7, 0.5) | (0.9, 0.1) | (0.8, 0.4) | (0.6, 0.5) | (0.8, 0.1) | (0.6, 0.4) |
\((e_4,q_1,0)\) | (0.7, 0.4) | (0.5, 0.7) | (0.8, 0.1) | (0.9, 0.4) | (0.9, 0.1) | (0.7, 0.6) | (0.9, 0.1) | (0.6, 0.5) | (0.9, 0.4) |
\((e_4,q_2,0)\) | (0.9, 0.2) | (0.7, 0.3) | (0.6, 0.4) | (0.5, 0.7) | (0.3, 0.6) | (0.4, 0.7) | (0.5, 0.2) | (0.7, 0.6) | (0.2, 0.9) |
\((e_4,q_3,0)\) | (0.4, 0.7) | (0.9, 0.1) | (0.2, 0.9) | (0.5, 0.4) | (0.6, 0.3) | (0.9, 0.2) | (0.6, 0.7) | (0.7, 0.5) | (0.4, 0.6) |
\((e_5,q_1,0)\) | (0.3, 0.7) | (0.7, 0.5) | (0.8, 0.2) | (0.9, 0.3) | (0.5, 0.4) | (0.9, 0.4) | (0.7, 0.6) | (0.5, 0.8) | (0.9, 0.3) |
\((e_5,q_2,0)\) | (0.5, 0.4) | (0.7, 0.6) | (0.5, 0.7) | (0.8, 0.1) | (0.9, 0.2) | (0.5, 0.4) | (0.7, 0.3) | (0.6, 0.7) | (0.5, 0.7) |
\((e_5,q_3,0)\) | (0.6, 0.7) | (0.3, 0.6) | (0.5, 0.4) | (0.2, 0.9) | (0.5, 0.4) | (0.8, 0.3) | (0.6, 0.5) | (0.8, 0.3) | (0.2, 0.9) |
\((e_6,q_1,0)\) | (0.5, 0.8) | (0.8, 0.4) | (0.7, 0.5) | (0.9, 0.4) | (0.3, 0.6) | (0.4, 0.7) | (0.8, 0.2) | (0.9, 0.3) | (0.6, 0.7) |
\((e_6,q_2,0)\) | (0.9, 0.2) | (0.8, 0.5) | (0.7, 0.4) | (0.9, 0.1) | (0.6, 0.4) | (0.5, 0.4) | (0.8, 0.4) | (0.5, 0.4) | (0.9, 0.3) |
\((e_6,q_3,0)\) | (0.5, 0.8) | (0.8, 0.7) | (0.5, 0.7) | (0.9, 0.3) | (0.5, 0.4) | (0.8, 0.4) | (0.7, 0.6) | (0.2, 0.9) | (0.8, 0.3) |
\((e_7,q_1,0)\) | (0.3, 0.6) | (0.5, 0.3) | (0.8, 0.4) | (0.6, 0.3) | (0.8, 0.3) | (0.5, 0.4) | (0.7, 0.8) | (0.9, 0.3) | (0.4, 0.7) |
\((e_7,q_2,0)\) | (0.8, 0.4) | (0.9, 0.4) | (0.7, 0.2) | (0.7, 0.5) | (0.8, 0.2) | (0.9, 0.3) | (0.7, 0.6) | (0.5, 0.6) | (0.8, 0.3) |
\((e_7,q_3,0)\) | (0.6, 0.3) | (0.8, 0.2) | (0.5, 0.6) | (0.7, 0.4) | (0.9, 0.5) | (0.7, 0.6) | (0.9, 0.3) | (0.8, 0.3) | (0.7, 0.6) |
\((e_8,q_1,0)\) | (0.9, 0.1) | (0.8, 0.4) | (0.7, 0.3) | (0.8, 0.3) | (0.6, 0.4) | (0.8, 0.2) | (0.9, 0.3) | (0.8, 0.7) | (0.7, 0.3) |
\((e_8,q_2,0)\) | (0.9, 0.3) | (0.7, 0.4) | (0.8, 0.4) | (0.9, 0.3) | (0.4, 0.7) | (0.7, 0.5) | (0.8, 0.2) | (0.7, 0.6) | (0.8, 0.3) |
\((e_8,q_3,0)\) | (0.7, 0.2) | (0.6, 0.5) | (0.7, 0.6) | (0.3, 0.9) | (0.4, 0.8) | (0.8, 0.4) | (0.7, 0.3) | (0.9, 0.1) | (0.6, 0.4) |
\((e_9,q_1,0)\) | (0.9, 0.2) | (0.8, 0.1) | (0.7, 0.5) | (0.9, 0.3) | (0.8, 0.1) | (0.6, 0.5) | (0.7, 0.4) | (0.6, 0.4) | (0.8, 0.4) |
\((e_9,q_2,0)\) | (0.8, 0.4) | (0.7, 0.5) | (0.9, 0.4) | (0.9, 0.5) | (0.8, 0.3) | (0.5, 0.7) | (0.9, 0.2) | (0.5, 0.4) | (0.9, 0.3) |
\((e_9,q_3,0)\) | (0.6, 0.5) | (0.9, 0.2) | (0.5, 0.3) | (0.8, 0.6) | (0.3, 0.8) | (0.4, 0.7) | (0.7, 0.5) | (0.5, 0.7) | (0.9, 0.2) |
\((e_{10},q_1,0)\) | (0.8, 0.3) | (0.5, 0.8) | (0.6, 0.4) | (0.9, 0.4) | (0.6, 0.5) | (0.2, 0.9) | (0.9, 0.3) | (0.4, 0.7) | (0.7, 0.5) |
\((e_{10},q_2,0)\) | (0.7, 0.5) | (0.8, 0.3) | (0.5, 0.4) | (0.7, 0.6) | (0.8, 0.4) | (0.9, 0.1) | (0.3, 0.7) | (0.2, 0.9) | (0.8, 0.4) |
\((e_{10},q_3,0)\) | (0.2, 0.9) | (0.5, 0.7) | (0.5, 0.5) | (0.5, 0.5) | (0.8, 0.4) | (0.5, 0.5) | (0.8, 0.3) | (0.2, 0.9) | (0.8, 0.4) |
\((e_{11},q_1,0)\) | (0.5, 0.5) | (0.6, 0.6) | (0.8, 0.5) | (0.6, 0.5) | (0.3, 0.6) | (0.6, 0.2) | (0.4, 0.5) | (0.7, 0.5) | (0.5, 0.4) |
\((e_{11},q_2,0)\) | (0.6, 0.6) | (0.5, 0.6) | (0.7, 0.7) | (0.4, 0.9) | (0.4, 0.5) | (0.7, 0.3) | (0.2, 0.9) | (0.8, 0.7) | (0.6, 0.5) |
\((e_{11},q_3,0)\) | (0.5, 0.4) | (0.3, 0.6) | (0.8, 0.4) | (0.4, 0.7) | (0.6, 0.7) | (0.3, 0.7) | (0.4, 0.9) | (0.5, 0.9) | (0.5, 0.8) |
\((e_{12},q_1,0)\) | (0.8, 0.4) | (0.9, 0.1) | (0.3, 0.7) | (0.7, 0.6) | (0.6, 0.5) | (0.4, 0.7) | (0.5, 0.8) | (0.6, 0.4) | (0.7, 0.3) |
\((e_{12},q_2,0)\) | (0.3, 0.9) | (0.8, 0.1) | (0.6, 0.3) | (0.4, 0.9) | (0.7, 0.6) | (0.5, 0.7) | (0.8, 0.4) | (0.7, 0.4) | (0.6, 0.7) |
\((e_{12},q_3,0)\) | (0.6, 0.2) | (0.5, 0.4) | (0.7, 0.7) | (0.6, 0.3) | (0.9, 0.2) | (0.5, 0.6) | (0.8, 0.3) | (0.7, 0.2) | (0.9, 0.1) |
\((\lambda ,A)_1\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) | \(p_6\) | \(p_7\) | \(p_8\) | \(p_9\) |
---|---|---|---|---|---|---|---|---|---|
\((e_1,q_1,1)\) | − 0.702 | 0.127 | 0.387 | 0.091 | 0.127 | 0.387 | 0.218 | 0.721 | 0.665 |
\((e_1,q_2,1)\) | 0.169 | 0.316 | 0.721 | 0.208 | 0.061 | 0 | 0.189 | 0.721 | 0.127 |
\((e_1,q_3,1)\) | 0.387 | 0.665 | 0.091 | 0.387 | 0.218 | 0.127 | 0.061 | 0.316 | 0.665 |
\((e_2,q_1,1)\) | 0.279 | 0.091 | 0.061 | 0.169 | 0.721 | 0.061 | 0.169 | 0.189 | 0.091 |
\((e_2,q_2,1)\) | 0.279 | 0.504 | 0 | − 0.665 | 0.387 | 0.061 | 0.189 | 0.061 | 0.127 |
\((e_2,q_3,1)\) | 0.152 | 0.448 | 0.702 | 0.127 | − 0.448 | 0.152 | 0.218 | 0.091 | − 0.218 |
\((e_3,q_1,1)\) | 0.169 | − 0.296 | 0.665 | 0.296 | − 0.721 | − 0.296 | 0.702 | 0.061 | 0.169 |
\((e_3,q_2,1)\) | 0.448 | − 0.218 | 0.511 | 0.665 | 0.728 | 0.127 | 0.728 | 0.091 | 0.448 |
\((e_3,q_3,1)\) | 0.504 | 0.702 | 0.511 | − 0.721 | 0.091 | − 0.279 | 0.091 | 0.448 | − 0.316 |
\((e_4,q_1,1)\) | − 0.387 | 0.218 | 0.061 | − 0.169 | 0.091 | − 0.169 | 0.061 | 0.218 | 0.091 |
\((e_4,q_2,1)\) | − 0.127 | 0.448 | − 0.218 | 0.152 | 0.702 | − 0.279 | − 0.218 | − 0.189 | − 0.218 |
\((e_4,q_3,1)\) | − 0.127 | − 0.721 | − 0.279 | 0.728 | 0.061 | 0.189 | 0.218 | − 0.152 | 0.721 |
\((e_5,q_1,1)\) | 0.702 | − 0.316 | 0.218 | 0.504 | 0.702 | 0.061 | 0.665 | 0.127 | − 0.387 |
\((e_5,q_2,1)\) | 0.061 | 0.127 | − 0.218 | 0.511 | 0.721 | 0.061 | 0.316 | − 0.127 | − 0.218 |
\((e_5,q_3,1)\) | 0.061 | 0.485 | 0.091 | 0.485 | − 0.721 | − 0.127 | − 0.189 | 0.061 | − 0.721 |
\((e_6,q_1,1)\) | − 0.387 | 0.448 | 0.218 | 0.665 | − 0.189 | − 0.279 | 0.504 | 0.702 | − 0.127 |
\((e_6,q_2,1)\) | 0.387 | 0.279 | 0.728 | 0.152 | 0.061 | − 0.721 | 0.448 | 0.721 | 0.061 |
\((e_6,q_3,1)\) | 0.169 | − 0.218 | 0.702 | 0.061 | 0.448 | 0.127 | − 0.387 | − 0.721 | 0.485 |
\((e_7,q_1,1)\) | 0.448 | 0.189 | 0.485 | 0.702 | − 0.387 | 0.098 | − 0.279 | 0.061 | − 0.169 |
\((e_7,q_2,1)\) | 0.218 | 0.504 | 0.702 | 0.448 | 0.665 | 0.127 | − 0.091 | 0.485 | 0.335 |
\((e_7,q_3,1)\) | − 0.091 | 0.279 | 0.604 | 0.127 | 0.189 | 0.504 | 0.702 | 0.485 | 0.127 |
\((e_8,q_1,1)\) | 0.504 | 0.702 | 0.169 | 0.316 | 0.728 | 0.448 | 0.316 | 0.485 | 0.152 |
\((e_8,q_2,1)\) | 0.702 | − 0.279 | 0.218 | 0.504 | 0.702 | 0.448 | 0.127 | 0.485 | 0.279 |
\((e_8,q_3,1)\) | 0.448 | 0.316 | 0.728 | 0.152 | − 0.702 | − 0.448 | 0.335 | 0.091 | 0.127 |
\((e_9,q_1,1)\) | 0.152 | 0.448 | 0.721 | 0.511 | 0.218 | 0.702 | 0.511 | 0.091 | 0.279 |
\((e_9,q_2,1)\) | 0.485 | − 0.218 | 0.721 | 0.061 | 0.702 | 0.448 | 0.218 | 0.665 | 0.604 |
\((e_9,q_3,1)\) | 0.448 | 0.091 | 0.127 | 0.387 | − 0.279 | 0.721 | 0.098 | 0.296 | − 0.485 |
\((e_{10},q_1,1)\) | − 0.127 | 0.511 | 0.721 | 0.061 | 0.448 | 0.127 | 0.208 | 0.218 | 0.279 |
\((e_{10},q_2,1)\) | 0.218 | 0.485 | 0.061 | 0.127 | 0.448 | 0.728 | − 0.316 | − 0.721 | 0.448 |
\((e_{10},q_3,1)\) | 0.702 | − 0.387 | − 0.127 | 0.127 | − 0.721 | 0.218 | − 0.152 | 0.728 | 0.127 |
\((e_{11},q_1,1)\) | 0.702 | 0.061 | 0.127 | − 0.387 | 0.316 | 0.152 | − 0.218 | − 0.189 | − 0.279 |
\((e_{11},q_2,1)\) | − 0.665 | 0.127 | 0.448 | − 0.218 | 0.448 | 0.218 | − 0.169 | 0.504 | − 0.387 |
\((e_{11},q_3,1)\) | − 0.279 | − 0.387 | 0.485 | 0.728 | − 0.152 | 0.061 | 0.316 | − 0.721 | 0.504 |
\((e_{12},q_1,1)\) | 0.279 | − 0.127 | − 0.279 | 0.387 | − 0.279 | 0.189 | 0.728 | − 0.127 | 0.511 |
\((e_{12},q_2,1)\) | 0.702 | 0.448 | 0.091 | 0.485 | − 0.387 | 0.152 | 0.665 | 0.091 | − 0.721 |
\((e_{12},q_3,1)\) | 0.218 | 0.448 | 0.091 | − 0.702 | 0.511 | 0.189 | − 0.665 | − 0.127 | 0.448 |
\(a_j=\sum _i p_{ij}\) | \(a_1=7.101\) | \(a_2=6.3\) | \(a_3=11.045\) | \(a_4=7.462\) | \(a_5=5.508\) | \(a_6=3.837\) | \(a_7=6.317\) | \(a_8=6.139\) | \(a_9=3.624\) |
\((\lambda ,A)_0\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) | \(p_6\) | \(p_7\) | \(p_8\) | \(p_9\) |
---|---|---|---|---|---|---|---|---|---|
\((e_1,q_1,0)\) | 0.485 | 0.061 | 0 | 0.189 | 0.721 | 0.127 | 0.091 | − 0.702 | 0.511 |
\((e_1,q_2,0)\) | 0.208 | 0.218 | 0.279 | 0.485 | − 0.218 | 0.721 | 0.061 | 0.702 | 0.448 |
\((e_1,q_3,0)\) | 0.448 | 0.316 | 0.728 | 0.152 | − 0.702 | − 0.448 | 0.335 | 0.091 | 0.127 |
\((e_2,q_1,0)\) | 0.279 | 0.208 | 0.316 | 0.728 | 0.218 | 0.485 | 0.728 | − 0.152 | 0.702 |
\((e_2,q_2,0)\) | 0.127 | 0.091 | − 0.279 | − 0.387 | 0.485 | 0.728 | − 0.152 | 0.061 | 0.316 |
\((e_2,q_3,0)\) | − 0.721 | 0.504 | 0.448 | 0.189 | 0.218 | 0.127 | 0.091 | 0.448 | 0.091 |
\((e_3,q_1,0)\) | − 0.702 | 0.511 | 0.189 | − 0.665 | − 0.127 | 0.448 | 0.728 | − 0.316 | − 0.721 |
\((e_3,q_2,0)\) | 0.218 | 0.485 | 0.127 | 0.091 | − 0.279 | 0.061 | 0.127 | 0.152 | 0.316 |
\((e_3,q_3,0)\) | 0.448 | − 0.127 | 0.448 | 0.218 | 0.728 | 0.448 | 0.091 | 0.511 | 0.152 |
\((e_4,q_1,0)\) | 0.279 | − 0.218 | 0.511 | 0.665 | 0.728 | 0.127 | 0.728 | 0.091 | 0.665 |
\((e_4,q_2,0)\) | 0.721 | 0.316 | 0.152 | − 0.218 | − 0.189 | − 0.279 | 0.117 | 0.127 | − 0.721 |
\((e_4,q_3,0)\) | − 0.279 | 0.728 | − 0.721 | 0.061 | 0.189 | 0.721 | − 0.127 | 0.218 | − 0.152 |
\((e_5,q_1,0)\) | − 0.316 | 0.218 | 0.504 | 0.702 | 0.061 | 0.665 | 0.127 | − 0.387 | 0.702 |
\((e_5,q_2,0)\) | 0.061 | 0.127 | − 0.218 | 0.511 | 0.721 | 0.061 | 0.316 | − 0.127 | − 0.218 |
\((e_5,q_3,0)\) | − 0.127 | − 0.189 | 0.061 | − 0.721 | 0.061 | 0.485 | 0.091 | 0.485 | − 0.721 |
\((e_6,q_1,0)\) | − 0.387 | 0.448 | 0.218 | 0.665 | − 0.189 | − 0.279 | 0.504 | 0.702 | − 0.127 |
\((e_6,q_2,0)\) | 0.721 | 0.387 | 0.279 | 0.728 | 0.152 | 0.061 | 0.448 | 0.061 | 0.702 |
\((e_6,q_3,0)\) | − 0.387 | 0.169 | − 0.218 | 0.702 | 0.061 | 0.448 | 0.127 | − 0.721 | 0.485 |
\((e_7,q_1,0)\) | − 0.189 | 0.098 | 0.448 | 0.189 | 0.485 | 0.061 | − 0.169 | 0.702 | − 0.279 |
\((e_7,q_2,0)\) | 0.448 | 0.665 | 0.335 | 0.218 | 0.504 | 0.702 | 0.127 | − 0.091 | 0.485 |
\((e_7,q_3,0)\) | 0.189 | 0.504 | − 0.091 | 0.279 | 0.604 | 0.127 | 0.702 | 0.485 | 0.127 |
\((e_8,q_1,0)\) | 0.728 | 0.448 | 0.316 | 0.485 | 0.152 | 0.504 | 0.702 | 0.169 | 0.316 |
\((e_8,q_2,0)\) | 0.702 | 0.279 | 0.448 | 0.702 | − 0.279 | 0.218 | 0.504 | 0.127 | 0.485 |
\((e_8,q_3,0)\) | 0.335 | 0.091 | 0.127 | − 0.702 | − 0.448 | 0.448 | 0.316 | 0.728 | 0.152 |
\((e_9,q_1,0)\) | 0.721 | 0.511 | 0.218 | 0.702 | 0.511 | 0.091 | 0.279 | 0.152 | 0.448 |
\((e_9,q_2,0)\) | 0.448 | 0.218 | 0.665 | 0.604 | 0.485 | − 0.218 | 0.721 | 0.061 | 0.702 |
\((e_9,q_3,0)\) | 0.091 | 0.721 | 0.098 | 0.296 | − 0.485 | − 0.279 | 0.218 | − 0.218 | 0.721 |
\((e_{10},q_1,0)\) | 0.485 | − 0.387 | 0.152 | 0.665 | 0.091 | − 0.721 | 0.702 | − 0.279 | 0.218 |
\((e_{10},q_2,0)\) | 0.218 | 0.485 | 0.061 | 0.127 | 0.448 | 0.728 | − 0.316 | − 0.721 | 0.448 |
\((e_{10},q_3,0)\) | − 0.721 | − 0.218 | 0 | 0 | 0.448 | 0 | 0.485 | − 0.721 | 0.448 |
\((e_{11},q_1,0)\) | 0 | 0 | 0.387 | 0.091 | − 0.189 | 0.208 | − 0.061 | 0.218 | 0.061 |
\((e_{11},q_2,0)\) | 0 | − 0.091 | 0 | − 0.665 | − 0.061 | 0.316 | − 0.721 | 0.169 | 0.091 |
\((e_{11},q_3,0)\) | 0.061 | − 0.189 | 0.448 | − 0.279 | − 0.127 | − 0.316 | − 0.665 | − 0.604 | − 0.387 |
\((e_{12},q_1,0)\) | 0.448 | 0.728 | − 0.316 | 0.127 | 0.091 | − 0.279 | − 0.387 | 0.152 | 0.316 |
\((e_{12},q_2,0)\) | − 0.702 | 0.511 | 0.189 | − 0.665 | 0.127 | − 0.218 | 0.448 | 0.279 | − 0.127 |
\((e_{12},q_3,0)\) | 0.208 | 0.061 | 0 | 0.189 | 0.721 | − 0.091 | 0.485 | 0.335 | 0.728 |
\(b_j=\sum _i p_{ij}\) | \(b_1= 4.546\) | \(b_2=8.688\) | \(b_3=6.030\) | \(b_4=6.458\) | \(b_5=4.935\) | \(b_6=5.988\) | \(b_7=7.801\) | \(b_8= 2.187\) | \(b_9=7.510\) |
\(a_j=\sum _i p_{ij}\) | \(b_j=\sum _i p_{ij}\) | \(z_j=a_j-b_j\) |
---|---|---|
\(a_1=7.101\) | \(b_1=4.546\) | \(z_1=2.555\) |
\(a_2=6.300\) | \(b_2=8.688\) | \(z_2=-2.388\) |
\(a_3=11.045\) | \(b_3=6.030\) | \(z_3=5.015\) |
\(a_4=7.462\) | \(b_4=6.458\) | \(z_4=1.004\) |
\(a_5=5.508\) | \(b_5=4.935\) | \(z_5=0.573\) |
\(a_6=3.837\) | \(b_6=5.988\) | \(z_6=-2.151\) |
\(a_7=6.317\) | \(b_7=7.801\) | \(z_7=-1.484\) |
\(a_8=6.139\) | \(b_8=2.187\) | \(z_8=3.952\) |
\(a_9=3.624\) | \(b_9=7.510\) | \(z_9=-3.886\) |
Experts | \(e_1\) | \(e_2\) | \(e_3\) | \(e_4\) | \(e_5\) | \(e_6\) | \(e_7\) | \(e_8\) | \(e_9\) | \(e_{10}\) | \(e_{11}\) | \(e_{12}\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(q_1\) | 0.05 | 0.02 | 0.23 | 0.11 | 0.09 | 0.12 | 0.03 | 0.04 | 0.06 | 0.07 | 0.14 | 0.04 |
\(q_2\) | 0.15 | 0.07 | 0.13 | 0.07 | 0.04 | 0.10 | 0.02 | 0.01 | 0.08 | 0.09 | 0.13 | 0.11 |
\(q_3\) | 0.10 | 0.05 | 0.17 | 0.08 | 0.07 | 0.09 | 0.01 | 0.03 | 0.05 | 0.04 | 0.19 | 0.12 |
\((\lambda ,A)_1\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) | \(p_6\) | \(p_7\) | \(p_8\) | \(p_9\) |
---|---|---|---|---|---|---|---|---|---|
\((e_1,q_1,1)\) | − 0.0351 | 0.0064 | 0.0194 | 0.0046 | 0.0064 | 0.0194 | 0.0109 | 0.0360 | 0.0333 |
\((e_1,q_2,1)\) | 0.0254 | 0.0474 | 0.1082 | 0.0312 | 0.0092 | 0 | 0.0284 | 0.1082 | 0.0191 |
\((e_1,q_3,1)\) | 0.0387 | 0.0665 | 0.0091 | 0.0387 | 0.0218 | 0.0127 | 0.0061 | 0.0316 | 0.0665 |
\((e_2,q_1,1)\) | 0.0056 | 0.0018 | 0.0012 | 0.0034 | 0.0144 | 0.0012 | 0.0034 | 0.0038 | 0.0018 |
\((e_2,q_2,1)\) | 0.0195 | 0.0353 | 0 | − 0.0466 | 0.0271 | 0.0043 | 0.0132 | 0.0043 | 0.0089 |
\((e_2,q_3,1)\) | 0.0076 | 0.0224 | 0.0351 | 0.0064 | − 0.0224 | 0.0076 | 0.0109 | 0.0046 | − 0.0109 |
\((e_3,q_1,1)\) | 0.0389 | − 0.0681 | 0.1530 | 0.0681 | − 0.1658 | − 0.0681 | 0.1615 | 0.0140 | 0.0389 |
\((e_3,q_2,1)\) | 0.0582 | − 0.0283 | 0.0664 | 0.0865 | 0.0946 | 0.0165 | 0.0946 | 0.0118 | 0.0582 |
\((e_3,q_3,1)\) | 0.0857 | 0.1193 | 0.0869 | − 0.1226 | 0.0155 | − 0.0474 | 0.0155 | 0.0762 | − 0.0537 |
\((e_4,q_1,1)\) | − 0.0426 | 0.0240 | 0.0067 | − 0.0186 | 0.0100 | − 0.0186 | 0.0067 | 0.0240 | 0.0100 |
\((e_4,q_2,1)\) | − 0.0089 | 0.0314 | − 0.0153 | 0.0106 | 0.0491 | − 0.0195 | − 0.0153 | − 0.0132 | − 0.0153 |
\((e_4,q_3,1)\) | − 0.0102 | − 0.0577 | − 0.0223 | 0.0582 | 0.0049 | 0.0151 | 0.0174 | − 0.0122 | 0.0577 |
\((e_5,q_1,1)\) | 0.0632 | − 0.0284 | 0.0196 | 0.0454 | 0.0632 | 0.0055 | 0.0599 | 0.0114 | − 0.0348 |
\((e_5,q_2,1)\) | 0.0024 | 0.0051 | − 0.0087 | 0.0204 | 0.0288 | 0.0024 | 0.0126 | − 0.0051 | − 0.0087 |
\((e_5,q_3,1)\) | 0.0043 | 0.0340 | 0.0064 | 0.0340 | − 0.0505 | − 0.0089 | − 0.0132 | 0.0043 | − 0.0505 |
\((e_6,q_1,1)\) | − 0.0464 | 0.0538 | 0.0262 | 0.0798 | − 0.0227 | − 0.0335 | 0.0605 | 0.0842 | − 0.0152 |
\((e_6,q_2,1)\) | 0.0387 | 0.0279 | 0.0728 | 0.0152 | 0.0061 | − 0.0721 | 0.0448 | 0.0721 | 0.0061 |
\((e_6,q_3,1)\) | 0.0152 | − 0.0196 | 0.0632 | 0.0055 | 0.0403 | 0.0114 | − 0.0348 | − 0.0649 | 0.0436 |
\((e_7,q_1,1)\) | 0.0134 | 0.0057 | 0.0145 | 0.0211 | − 0.0116 | 0.0029 | − 0.0084 | 0.0018 | − 0.0051 |
\((e_7,q_2,1)\) | 0.0044 | 0.0101 | 0.0140 | 0.0090 | 0.0133 | 0.0025 | − 0.0018 | 0.0097 | 0.0067 |
\((e_7,q_3,1)\) | − 0.0009 | 0.0028 | 0.0060 | 0.0013 | 0.0019 | 0.0050 | 0.0070 | 0.0049 | 0.0013 |
\((e_8,q_1,1)\) | 0.0202 | 0.0281 | 0.0068 | 0.0126 | 0.0291 | 0.0179 | 0.0126 | 0.0194 | 0.0061 |
\((e_8,q_2,1)\) | 0.0070 | − 0.0028 | 0.0022 | 0.0050 | 0.0070 | 0.0045 | 0.0013 | 0.0049 | 0.0028 |
\((e_8,q_3,1)\) | 0.0134 | 0.0095 | 0.0218 | 0.0046 | − 0.0211 | − 0.0134 | 0.0101 | 0.0027 | 0.0038 |
\((e_9,q_1,1)\) | 0.0091 | 0.0269 | 0.0433 | 0.0307 | 0.0131 | 0.0421 | 0.0307 | 0.0055 | 0.0167 |
\((e_9,q_2,1)\) | 0.0388 | − 0.0174 | 0.0577 | 0.0049 | 0.0562 | 0.0358 | 0.0174 | 0.0532 | 0.0483 |
\((e_9,q_3,1)\) | 0.0224 | 0.0046 | 0.0064 | 0.0194 | − 0.0140 | 0.0360 | 0.0049 | 0.0148 | − 0.0243 |
\((e_{10},q_1,1)\) | − 0.0089 | 0.0358 | 0.0505 | 0.0043 | 0.0314 | 0.0089 | 0.0146 | 0.0153 | 0.0195 |
\((e_{10},q_2,1)\) | 0.0196 | 0.0436 | 0.0055 | 0.0114 | 0.0403 | 0.0655 | − 0.0284 | − 0.0649 | 0.0403 |
\((e_{10},q_3,1)\) | 0.0281 | − 0.0155 | − 0.0051 | 0.0051 | − 0.0288 | 0.0087 | − 0.0061 | 0.0291 | 0.0051 |
\((e_{11},q_1,1)\) | 0.0983 | 0.0085 | 0.0178 | − 0.0542 | 0.0442 | 0.0213 | − 0.0305 | − 0.0265 | − 0.0391 |
\((e_{11},q_2,1)\) | − 0.0865 | 0.0165 | 0.0582 | − 0.0283 | 0.0582 | 0.0283 | − 0.0220 | 0.0655 | − 0.0503 |
\((e_{11},q_3,1)\) | − 0.0530 | − 0.0735 | 0.0921 | 0.1383 | − 0.0289 | 0.0116 | 0.0600 | − 0.1370 | 0.0958 |
\((e_{12},q_1,1)\) | 0.0112 | − 0.0051 | − 0.0112 | 0.0155 | − 0.0112 | 0.0076 | 0.0291 | − 0.0051 | 0.0204 |
\((e_{12},q_2,1)\) | 0.0772 | 0.0493 | 0.0100 | 0.0534 | − 0.0426 | 0.0167 | 0.0732 | 0.0100 | − 0.0793 |
\((e_{12},q_3,1)\) | 0.0262 | 0.0538 | 0.0109 | − 0.0842 | 0.0613 | 0.0227 | − 0.0798 | − 0.0152 | 0.0538 |
\({\mathfrak {a}}_j=\sum _i p_{ij}\) | \({\mathfrak {a}}_1=0.5002\) | \({\mathfrak {a}}_2=0.4537\) | \({\mathfrak {a}}_3=1.0292\) | \({\mathfrak {a}}_4=0.4897\) | \({\mathfrak {a}}_5=0.3280\) | \({\mathfrak {a}}_6=0.1528\) | \({\mathfrak {a}}_7=0.5669\) | \({\mathfrak {a}}_8=0.3792\) | \({\mathfrak {a}}_9=0.2775\) |
\((\lambda ,A)_0\) | \(p_1\) | \(p_2\) | \(p_3\) | \(p_4\) | \(p_5\) | \(p_6\) | \(p_7\) | \(p_8\) | \(p_9\) |
---|---|---|---|---|---|---|---|---|---|
\((e_1,q_1,0)\) | 0.0243 | 0.0031 | 0 | 0.0095 | 0.0360 | 0.0064 | 0.0046 | − 0.0351 | 0.0256 |
\((e_1,q_2,0)\) | 0.0312 | 0.0327 | 0.0419 | 0.0727 | − 0.0327 | 0.1082 | 0.0092 | 0.1053 | 0.0672 |
\((e_1,q_3,0)\) | 0.0448 | 0.0316 | 0.0728 | 0.0152 | − 0.0702 | − 0.0448 | 0.0335 | 0.0091 | 0.0127 |
\((e_2,q_1,0)\) | 0.0056 | 0.0042 | 0.0063 | 0.0146 | 0.0044 | 0.0097 | 0.0146 | − 0.0030 | 0.0140 |
\((e_2,q_2,0)\) | 0.0089 | 0.0064 | − 0.0195 | − 0.0271 | 0.0340 | 0.0510 | − 0.0106 | 0.0043 | 0.0221 |
\((e_2,q_3,0)\) | 0.0360 | 0.0252 | 0.0224 | 0.0095 | 0.0109 | 0.0064 | 0.0046 | 0.0224 | 0.0046 |
\((e_3,q_1,0)\) | − 0.1615 | 0.1175 | 0.0435 | − 0.1530 | − 0.0292 | 0.1030 | 0.1674 | − 0.0727 | − 0.1658 |
\((e_3,q_2,0)\) | 0.0283 | 0.0630 | 0.0165 | 0.0118 | − 0.0363 | 0.0079 | 0.0165 | 0.0198 | 0.0411 |
\((e_3,q_3,0)\) | 0.0762 | − 0.0216 | 0.0762 | 0.0371 | 0.1238 | 0.0762 | 0.0155 | 0.0869 | 0.0258 |
\((e_4,q_1,0)\) | 0.0307 | − 0.0240 | 0.0562 | 0.0732 | 0.0801 | 0.0140 | 0.0801 | 0.0100 | 0.0732 |
\((e_4,q_2,0)\) | 0.0505 | 0.0221 | 0.0106 | − 0.0153 | − 0.0132 | − 0.0195 | 0.0082 | 0.0089 | − 0.0505 |
\((e_4,q_3,0)\) | − 0.0223 | 0.0582 | − 0.0577 | 0.0049 | 0.0151 | 0.0577 | − 0.0102 | 0.0174 | − 0.0122 |
\((e_5,q_1,0)\) | − 0.0284 | 0.0196 | 0.0454 | 0.0632 | 0.0055 | 0.0599 | 0.0114 | − 0.0348 | 0.0632 |
\((e_5,q_2,0)\) | 0.0024 | 0.0051 | − 0.0087 | 0.0204 | 0.0288 | 0.0024 | 0.0126 | − 0.0051 | − 0.0087 |
\((e_5,q_3,0)\) | − 0.0089 | − 0.0132 | 0.0043 | − 0.0505 | 0.0043 | 0.0340 | 0.0064 | 0.0340 | − 0.0505 |
\((e_6,q_1,0)\) | − 0.0464 | 0.0538 | 0.0262 | 0.0798 | − 0.0227 | − 0.0335 | 0.0605 | 0.0842 | − 0.0152 |
\((e_6,q_2,0)\) | 0.0721 | 0.0387 | 0.0279 | 0.0728 | 0.0152 | 0.0061 | 0.0448 | 0.0061 | 0.0702 |
\((e_6,q_3,0)\) | − 0.0348 | 0.0152 | − 0.0196 | 0.0632 | 0.0055 | 0.0403 | 0.0114 | − 0.0649 | 0.0436 |
\((e_7,q_1,0)\) | − 0.0057 | 0.0029 | 0.0134 | 0.0057 | 0.0145 | 0.0018 | − 0.0051 | 0.0211 | − 0.0084 |
\((e_7,q_2,0)\) | 0.0090 | 0.0133 | 0.0067 | 0.0044 | 0.0101 | 0.0140 | 0.0025 | − 0.0018 | 0.0097 |
\((e_7,q_3,0)\) | 0.0019 | 0.0050 | − 0.0009 | 0.0028 | 0.0060 | 0.0013 | 0.0070 | 0.0049 | 0.0013 |
\((e_8,q_1,0)\) | 0.0291 | 0.0179 | 0.0126 | 0.0194 | 0.0061 | 0.0202 | 0.0281 | 0.0068 | 0.0126 |
\((e_8,q_2,0)\) | 0.0070 | 0.0028 | 0.0045 | 0.0070 | − 0.0028 | 0.0022 | 0.0050 | 0.0013 | 0.0049 |
\((e_8,q_3,0)\) | 0.0101 | 0.0027 | 0.0038 | − 0.0211 | − 0.0134 | 0.0134 | 0.0095 | 0.0218 | 0.0046 |
\((e_9,q_1,0)\) | 0.0433 | 0.0307 | 0.0131 | 0.0421 | 0.0307 | 0.0055 | 0.0167 | 0.0091 | 0.0269 |
\((e_9,q_2,0)\) | 0.0358 | 0.0174 | 0.0532 | 0.0483 | 0.0388 | − 0.0174 | 0.0577 | 0.0049 | 0.0562 |
\((e_9,q_3,0)\) | 0.0046 | 0.0360 | 0.0049 | 0.0148 | − 0.0243 | − 0.0140 | 0.0109 | − 0.0109 | 0.0360 |
\((e_{10},q_1,0)\) | 0.0340 | − 0.0271 | 0.0106 | 0.0466 | 0.0064 | − 0.0505 | 0.0491 | − 0.0195 | 0.0153 |
\((e_{10},q_2,0)\) | 0.0196 | 0.0436 | 0.0055 | 0.0114 | 0.0403 | 0.0655 | − 0.0284 | − 0.0649 | 0.0403 |
\((e_{10},q_3,0)\) | − 0.0288 | − 0.0087 | 0 | 0 | 0.0179 | 0 | 0.0194 | − 0.0288 | 0.0179 |
\((e_{11},q_1,0)\) | 0 | 0 | 0.0542 | 0.0127 | − 0.0265 | 0.0291 | − 0.0085 | 0.0305 | 0.0085 |
\((e_{11},q_2,0)\) | 0 | − 0.0118 | 0 | − 0.0865 | − 0.0079 | 0.0411 | − 0.0937 | 0.0220 | 0.0118 |
\((e_{11},q_3,0)\) | 0.0116 | − 0.0359 | 0.0851 | − 0.0530 | − 0.0241 | − 0.0600 | − 0.1264 | − 0.1148 | − 0.0735 |
\((e_{12},q_1,0)\) | 0.0179 | 0.0291 | − 0.0126 | 0.0051 | 0.0036 | − 0.0112 | − 0.0155 | 0.0061 | 0.0126 |
\((e_{12},q_2,0)\) | − 0.0772 | 0.0562 | 0.0208 | − 0.0732 | 0.0140 | − 0.0240 | 0.0493 | 0.0307 | − 0.0140 |
\((e_{12},q_3,0)\) | 0.0250 | 0.0073 | 0 | 0.0227 | 0.0865 | -0.0109 | 0.0582 | 0.0402 | 0.0874 |
\({\mathfrak {b}}_j=\sum _i p_{ij}\) | \({\mathfrak {b}}_1=0.2456\) | \({\mathfrak {b}}_2=0.6192\) | \({\mathfrak {b}}_3=0.6194\) | \({\mathfrak {b}}_4=0.3113\) | \({\mathfrak {b}}_5=0.3352\) | \({\mathfrak {b}}_6=0.4913\) | \({\mathfrak {b}}_7=0.5162\) | \({\mathfrak {b}}_8=0.1512\) | \({\mathfrak {b}}_9=0.4105\) |
\({\mathfrak {a}}_j=\sum _i p_{ij}\) | \({\mathfrak {b}}_j=\sum _i p_{ij}\) | \({\mathfrak {z}}_j={\mathfrak {a}}_j-{\mathfrak {b}}_j\) |
---|---|---|
\({\mathfrak {a}}_1=0.5002\) | \({\mathfrak {b}}_1=0.2456\) | \({\mathfrak {z}}_1=0.2546\) |
\({\mathfrak {a}}_2=0.4537\) | \({\mathfrak {b}}_2=0.6192\) | \({\mathfrak {z}}_2=-0.1655\) |
\({\mathfrak {a}}_3=1.0292\) | \({\mathfrak {b}}_3=0.6194\) | \({\mathfrak {z}}_3=0.4098\) |
\({\mathfrak {a}}_4=0.4897\) | \({\mathfrak {b}}_4=0.3113\) | \({\mathfrak {z}}_4=0.1784\) |
\({\mathfrak {a}}_5=0.3280\) | \({\mathfrak {b}}_5=0.3352\) | \({\mathfrak {z}}_5=-0.0072\) |
\({\mathfrak {a}}_6=0.1528\) | \({\mathfrak {b}}_6=0.4913\) | \({\mathfrak {z}}_6=-0.3385\) |
\({\mathfrak {a}}_7=0.5669\) | \({\mathfrak {b}}_7=0.5162\) | \({\mathfrak {z}}_7=0.0507\) |
\({\mathfrak {a}}_8=0.3792\) | \({\mathfrak {b}}_8=0.1512\) | \({\mathfrak {z}}_8=0.228\) |
\({\mathfrak {a}}_9=0.2775\) | \({\mathfrak {b}}_9=0.410\) | \({\mathfrak {z}}_9=-0.1325\) |
5 Sensitivity analysis
5.1 Advantages of the model initiated in this work
5.2 Comparison with existing models
Objects | FSESs (Alkhazaleh and Salleh 2014) | Proposed FFSESs |
---|---|---|
\(p_1\) | 2.5 | 2.555 |
\(p_2\) | − 0.4 | − 2.388 |
\(p_3\) | 2.5 | 5.015 |
\(p_4\) | 0.7 | 1.004 |
\(p_5\) | − 0.2 | 0.573 |
\(p_6\) | − 0.3 | − 2.151 |
\(p_7\) | − 1 | − 1.484 |
\(p_8\) | 1.1 | 3.952 |
\(p_9\) | − 1.1 | − 3.886 |
Models | Ranking order | Best option |
---|---|---|
FSESs (Alkhazaleh and Salleh 2014) | \(p_{3}=p_{1}>p_{8}>p_{4}>p_5>p_6>p_{2}>p_7>p_{9}\) | \(p_3\) |
Proposed FFSESs | \(p_{3}>p_{8}>p_1>p_{4}>p_5>p_7>p_{6}>p_2>p_{9}\) | \(p_3\) |
Models | \(u_1\) | \(u_2\) | \(u_3\) | Ranking order | Best option |
---|---|---|---|---|---|
IFSESs (Broumi and Smarandache 2015) | 0.20 | 1.45 | − 0.55 | \(u_{2}>u_{1}>u_{3}\) | \(u_2\) |
Proposed FFSESs | − 0.20 | 2.36 | − 0.98 | \(u_{2}>u_{1}>u_{3}\) | \(u_2\) |
5.3 Limitations of the model initiated in this paper
-
The competency of the proposed model is limited to address the two-dimensional obscure information, that is, it fails if in a situation, we consider membership value 0.7 and non-membership value 0.9, since \(0.7^3+0.9^3=1.072\nless 1\).
-
Another limitation of the proposed hybrid model is the occurrence of large sets of alternatives, parameters and experts in several MCGDM problems, because the computational speed may be handicapped by the increase in available information. Like proposed model there are several existing mathematical tools involving this deficiency which can be easily control with a suitable code of developed method via different mathematical software such as MATLAB, MAPLE, etc.
-
Moreover, there may be observed a variation in the ranking order of optimal or sub-optimal objects when any existing parameters (or objects) are removed or new parameters (or objects) are added in a MCGDM problem. It happens due to the autonomous behavior of objects and parameters.