Introduction
References | Inf. types | Decision-makers’ weights | Attributes’ weights | Correlation between attributes | Methods of utility degree | Applications |
---|---|---|---|---|---|---|
Ali (2021) [57] | SFNs | Subjective assessment | CRITIC | No | Division operation | Illustrative example |
Ecer et al. (2021) [58] | IFNs | Subjective assessment | Closeness coefficient | No | Division operation | Insurance assessment |
Stevic et al. (2021) [59] | RNs and FNs | Assumed | Rough PIPRECIA | No | Division operation | Evaluation sustainable production |
Boral et al. (2021) [60] | IT2FNs | Assumed | AHP | No | Division operation | Failure analysis |
Deveci et al. (2021) [61] | IRNs | Assumed | BWM | No | Division operation | Offshore wind farm site selection |
Ali (2021) [56] | q-ROFNs | Subjective assessment | CRITIC | No | Division operation | Municipal solid waste site selection |
Fan et al. (2021) [62] | DNs | Distance-based method | BWM | No | Division operation | Failure analysis |
Gong et al. (2021) [63] | IT2FNs | Assumed | BWM | No | Division operation | Renewable energy |
Puska et al. (2021) [64] | TFNs | Assumed | FUCOM | No | Division operation | Tourism potential evaluation |
Pamucar et al. (2021) [65] | SVNFNs | Assumed | Fuzzy FUCOM | No | Euclidean distance | Alternative fuel vehicles evaluation |
Saha et al. (2022) [66] | DPLEs | Distance-based method | FUCOM | No | Division operation | Learning management system selection |
Simic et al. (2022) [67] | FFNs | Assumed | ITARA | No | Division operation | locating for HCW |
Proposed method | TSULNs | Similarity measure | MDM | Yes (HM) | Generalized distance | Investment decision for CGB platform |
Preliminaries
Some notions of T-spherical uncertain linguistic sets
The TSUL-weighted AOs and TSULHM AOs
The TSUL-weighted AOs
The TSULHM AOs
A novel MAGDM framework based on TSUL-MARCOS
Calculate expert weights based on TSUL similarity
Calculate attribute weights based on MDM
Rank the alternatives by extended MARCOS
A case study
Platforms | Brand birthplace | Description |
---|---|---|
1Xingsheng (h1) | Changsha | As a well-known brand of community e-commerce, Xingsheng provides vegetables and fruits, meat, poultry, and aquatic products, rice, flour, grain and oil, daily necessities, and other selected commodities. Xingsheng relies on community convenience stores, through the “pre-sale + self-pickup” model to provide services for residents |
2Meituan (h2) | Beijing | The social group-buying business of Meituan adopts the mode of “pre-order + self-pickup” to select cost-effective vegetables, fruits, meat, poultry and eggs, drinks and snacks, household kitchen and toilet, instant frozen food, grain, oil and seasoning, and other products for residents in the community |
3Duoduo (h3) | Shanghai | Duoduo is the community group buying launched by PDD in August 2020. It adopts the semi-pre-purchase mode of “online order + offline self-pickup” and provides food buying service through PDD APP or Wechat grogram |
4Nicetuan (h4) | Beijing | Nicetuan provides urban community families with fresh and delicious ingredients and daily necessities through the Wechat program, to bring convenient and fresh purchasing services for social families |
5Jingxi (h5) | Beijing | Jingxi is a community O2O group-buying service platform. Relying on the Jingdong supply chain system ensures that consumers can place orders on the same day and pick them up the next day. It also guarantees the daily supply of rice, flour, oil, meat, poultry, eggs and milk, fresh vegetables and fruits, epidemic prevention and elimination, leisure snacks, and other daily necessities for community residents |
E | H | a1 | a2 | a3 | a4 | a5 | a6 |
---|---|---|---|---|---|---|---|
e1 | h1 | ([s5,s6], (0.7,0.4,0.3)) | ([s6,s7], (0.6,0.4,0.5)) | ([s3,s5], (0.5,0.4,0.2)) | ([s2,s4], (0.6,0.5,0.4)) | ([s7,s8], (0.5,0.5,0.4)) | ([s5,s6], (0.8,0.3,0.7)) |
h2 | ([s6,s8], (0.8,0.1,0.4)) | ([s2,s3], (0.7,0.3,0.4)) | ([s4,s7], (0.4,0.4,0.4)) | ([s1,s3], (0.5,0.8,0.3)) | ([s6,s7], (0.6,0.2,0.3)) | ([s4,s6], (0.4,0.1,0.7)) | |
h3 | ([s2,s5], (0.6,0.7,0.5)) | ([s2,s3], (0.8,0.1,0.2)) | ([s4,s6], (0.3,0.5,0.6)) | ([s2,s3], (0.3,0.6,0.7)) | ([s3,s5], (0.8,0.4,0.4)) | ([s6,s7], (0.9,0.3,0.6)) | |
h4 | ([s4,s5], (0.5,0.3,0.8)) | ([s5,s6], (0.6,0.3,0.3)) | ([s3,s5], (0.7,0.5,0.1)) | ([s5,s6], (0.5,0.4,0.2)) | ([s4,s5], (0.5,0.2,0.8)) | ([s2,s4], (0.5,0.6,0.2)) | |
h5 | ([s6,s7], (0.8,0.3,0.3)) | ([s5,s7], (0.7,0.4,0.5)) | ([s0,s3], (0.8,0.3,0.4)) | ([s6,s7], (0.7,0.5,0.1)) | ([s2,s4], (0.8,0.1,0.2)) | ([s3,s4], (0.5,0.2,0.4)) | |
e2 | h1 | ([s5,s7], (0.5,0.2,0.3)) | ([s5,s6], (0.8,0.2,0.2)) | ([s6,s7], (0.4,0.6,0.7)) | ([s2,s3], (0.5,0.4,0.6)) | ([s0,s1], (0.7,0.5,0.4)) | ([s1,s3], (0.4,0.7,0.5)) |
h2 | ([s2,s4], (0.6,0.3,0.5)) | ([s4,s6], (0.4,0.3,0.5)) | ([s6,s8], (0.6,0.4,0.3)) | ([s1,s4], (0.8,0.4,0.6)) | ([s2,s3], (0.6,0.2,0.7)) | ([s6,s7], (0.6,0.8,0.2)) | |
h3 | ([s1,s3], (0.7,0.4,0.2)) | ([s1,s3], (0.8,0.1,0.1)) | ([s5,s6], (0.6,0.3,0.8)) | ([s0,s3], (0.7,0.3,0.3)) | ([s1,s3], (0.8,0.4,0.2)) | ([s3,s4], (0.9,0.5,0.2)) | |
h4 | ([s2,s3], (0.5,0.3,0.8)) | ([s4,s6], (0.5,0.7,0.7)) | ([s3,s5], (0.6,0.4,0.5)) | ([s2,s3], (0.6,0.4,0.8)) | ([s2,s4], (0.7,0.2,0.6)) | ([s2,s3], (0.5,0.6,0.2)) | |
h5 | ([s3,s4], (0.6,0.4,0.5)) | ([s5,s6], (0.6,0.3,0.2)) | ([s4,s5], (0.4,0.4,0.7)) | ([s1,s2], (0.7,0.5,0.3)) | ([s4,s6], (0.8,0.2,0.1)) | ([s6,s7], (0.7,0.4,0.3)) | |
e3 | h1 | ([s6,s7], (0.8,0.3,0.5)) | ([s5,s7], (0.8,0.7,0.1)) | ([s4,s6], (0.8,0.3,0.2)) | ([s1,s3], (0.8,0.4,0.3)) | ([s3,s4], (0.8,0.3,0.5)) | ([s1,s3], (0.6,0.6,0.1)) |
h2 | ([s5,s7], (0.6,0.2,0.6)) | ([s2,s3], (0.5,0.2,0.7)) | ([s1,s2], (0.6,0.6,0.6)) | ([s6,s7], (0.4,0.5,0.8)) | ([s0,s2], (0.8,0.6,0.1)) | ([s4,s5], (0.8,0.5,0.5)) | |
h3 | ([s4,s5], (0.7,0.5,0.4)) | ([s4,s5], (0.7,0.8,0.2)) | ([s5,s7], (0.4,0.5,0.8)) | ([s1,s3], (0.6,0.4,0.2)) | ([s2,s3], (0.5,0.2,0.4)) | ([s4,s5], (0.7,0.2,0.4)) | |
h4 | ([s4,s5], (0.6,0.7,0.5)) | ([s3,s5], (0.2,0.6,0.4)) | ([s0,s3], (0.5,0.5,0.3)) | ([s3,s4], (0.5,0.3,0.1)) | ([s5,s6], (0.8,0.4,0.3)) | ([s5,s6], (0.5,0.1,0.2)) | |
h5 | ([s2,s3], (0.4,0.1,0.7)) | ([s3,s4], (0.8,0.3,0.5)) | ([s1,s2], (0.7,0.2,0.4)) | ([s4,s6], (0.6,0.2,0.7)) | ([s1,s3], (0.9,0.1,0.4)) | ([s4,s6], (0.9,0.4,0.5)) |
Decision process
H | a1 | a2 | a3 | a4 | a5 | a6 |
---|---|---|---|---|---|---|
hAAI | ([s2.386,s4.366], (0.537, 0.514, 0.691)) | ([s2.417,s3.715], (0.500, 0.492, 0.513)) | ([s1.737,s3.378], (0.463, 0.468, 0.723)) | ([s1.017,s3.000], (0.540, 0.538, 0.531)) | ([s2.001,s4.3663.707], (0.692, 0.421, 0.520)) | ([s2.479,s4.109], (0.500, 0.518, 0.392)) |
h1 | ([s5.344,s6.718], (0.695, 0.284, 0.352)) | ([s5.392,s6.715], (0.750, 0.380, 0.224)) | ([s4.411,s6.052], (0.649, 0.407, 0.289)) | ([s1.674,s3.388], (0.675, 0.429, 0.417)) | ([s4.064,s5.406], (0.705, 0.421, 0.431)) | ([s2.479,s4.109], (0.648, 0.518, 0.323)) |
h2 | ([s4.537,s6.774], (0.690, 0.185, 0.492)) | ([s2.732,s4.221], (0.578, 0.264, 0.513)) | ([s3.924,s6.466], (0.549, 0.461, 0.461)) | ([s3.273,s5.123], (0.644, 0.538, 0.531)) | ([s3.141,s4.502], (0.692, 0.289, 0.281)) | ([s4.867,s4.867], (0.665, 0.371, 0.392)) |
h3 | ([s2.386,s4.366], (0.673, 0.514, 0.334)) | ([s2.417,s3.715], (0.774, 0.192, 0.159)) | ([s4.671,s6.399], (0.463, 0.430, 0.723)) | ([s1.017,s3.000], (0.594, 0.412, 0.342)) | ([s2.001,s3.707], (0.741, 0.317, 0.312)) | ([s4.397,s5.457], (0.860, 0.317, 0.348)) |
h4 | ([s3.351,s4.366], (0.537, 0.391, 0.691)) | ([s4.114,s5.717], (0.500, 0.492, 0.434)) | ([s2.080,s4.387], (0.617, 0.468, 0.236)) | ([s3.440,s4.476], (0.540, 0.363, 0.254)) | ([s3.768,s5.066], (0.705, 0.252, 0.520)) | ([s3.189,s4.485], (0.500, 0.331, 0.200)) |
h5 | ([s3.973,s5.069], (0.662, 0.236, 0.471)) | ([s4.459,s5.957], (0.715, 0.333, 0.370)) | ([s1.737,s3.378], (0.701, 0.283, 0.472)) | ([s4.008,s5.477], (0.671, 0.366, 0.282)) | ([s2.507,s4.570], (0.843, 0.128, 0.197)) | ([s4.638,s6.001], (0.806, 0.195, 0.257)) |
hAI | ([s5.344,s6.774], (0.695, 0.185, 0.334)) | ([s5.392,s6.715], (0.774, 0.192, 0.159)) | ([s4.671,s6.466], (0.701, 0.283, 0.236)) | ([s4.008,s5.447], (0.675, 0.363, 0.254)) | ([s4.064,s5.406], (0.843,0.128, 0.194)) | ([s4.867,s6.162], (0.860, 0.195, 0.200)) |
Sensitivity investigation
q | f(K1) | f(K2) | f(K3) | f(K4) | f(K5) | Rankings |
---|---|---|---|---|---|---|
q = 3 | 0.08233 | 0.08101 | 0.07698 | 0.07727 | 0.07114 | h1 > h2 > h4 > h3 > h5 |
q = 4 | 0.06985 | 0.07272 | 0.07019 | 0.07241 | 0.06548 | h2 > h4 > h3 > h1 > h5 |
q = 5 | 0.05846 | 0.06216 | 0.06271 | 0.06584 | 0.06057 | h4 > h3 > h2 > h5 > h1 |
q = 6 | 0.05050 | 0.05362 | 0.05629 | 0.06032 | 0.05682 | h4 > h5 > h3 > h2 > h1 |
q = 7 | 0.04576 | 0.04777 | 0.05128 | 0.05634 | 0.05418 | h4 > h5 > h3 > h2 > h1 |
q = 8 | 0.04294 | 0.04405 | 0.04742 | 0.05356 | 0.05233 | h4 > h5 > h3 > h2 > h1 |
q = 9 | 0.04128 | 0.04180 | 0.04454 | 0.05164 | 0.05107 | h4 > h5 > h3 > h2 > h1 |
q = 10 | 0.04033 | 0.04048 | 0.04242 | 0.05033 | 0.05022 | h4 > h5 > h3 > h2 > h1 |
φ | f(K1) | f(K2) | f(K3) | f(K4) | f(K5) | Rankings |
---|---|---|---|---|---|---|
1 | 0.08233 | 0.08101 | 0.07698 | 0.07727 | 0.07114 | h1 > h2 > h4 > h3 > h5 |
2 | 0.08113 | 0.08019 | 0.07641 | 0.07631 | 0.07092 | h1 > h2 > h3 > h4 > h5 |
5 | 0.08045 | 0.07964 | 0.07594 | 0.07564 | 0.07092 | h1 > h2 > h3 > h4 > h5 |
10 | 0.08040 | 0.07959 | 0.07592 | 0.07551 | 0.07105 | h1 > h2 > h3 > h4 > h5 |
50 | 0.08025 | 0.07962 | 0.07614 | 0.07536 | 0.07097 | h1 > h2 > h3 > h4 > h5 |
100 | 0.08029 | 0.07951 | 0.07600 | 0.07533 | 0.07109 | h1 > h2 > h3 > h4 > h5 |
200 | 0.08029 | 0.07951 | 0.07600 | 0.07533 | 0.07108 | h1 > h2 > h3 > h4 > h5 |
500 | 0.08035 | 0.07947 | 0.07599 | 0.07533 | 0.07122 | h1 > h2 > h3 > h4 > h5 |
σ and ρ | f(K1) | f(K2) | f(K3) | f(K4) | f(K5) | Rankings |
---|---|---|---|---|---|---|
0, 1 | 0.06514 | 0.07453 | 0.06872 | 0.06875 | 0.04785 | h2 > h4 > h3 > h1 > h5 |
1, 0 | 0.06234 | 0.09096 | 0.08996 | 0.08269 | 0.08840 | h2 > h3 > h5 > h4 > h1 |
1, 1 | 0.08233 | 0.08101 | 0.07698 | 0.07727 | 0.07114 | h1 > h2 > h4 > h3 > h5 |
1, 3 | 0.08171 | 0.08198 | 0.07837 | 0.07900 | 0.05873 | h2 > h1 > h4 > h3 > h5 |
3,1 | 0.07479 | 0.08793 | 0.08683 | 0.08397 | 0.08045 | h2 > h3 > h4 > h5 > h1 |
3, 3 | 0.07981 | 0.08332 | 0.08302 | 0.08166 | 0.06982 | h2 > h3 > h4 > h1 > h5 |
3, 5 | 0.08077 | 0.08843 | 0.08218 | 0.08328 | 0.06290 | h2 > h4 > h3 > h1 > h5 |
5, 3 | 0.07509 | 0.08612 | 0.08672 | 0.08468 | 0.07466 | h3 > h2 > h4 > h1 > h5 |
5, 5 | 0.07692 | 0.08896 | 0.08454 | 0.08405 | 0.06837 | h2 > h3 > h4 > h1 > h5 |
5, 7 | 0.08702 | 0.09436 | 0.08269 | 0.08569 | 0.06340 | h2 > h1 > h4 > h3 > h5 |
7, 5 | 0.07316 | 0.08934 | 0.08531 | 0.08493 | 0.07158 | h2 > h3 > h4 > h1 > h5 |
7, 7 | 0.08444 | 0.09285 | 0.08330 | 0.08622 | 0.06704 | h2 > h4 > h1 > h3 > h5 |
10, 10 | 0.09142 | 0.09830 | 0.08124 | 0.08826 | 0.06535 | h2 > h1 > h4 > h3 > h5 |
Comparative study
Approaches | Results | Rankings |
---|---|---|
q-ROULWGHM [76] | Cannot be calculated | No |
PULWA [30] | Cannot be calculated | No |
PULWG [30] | Cannot be calculated | No |
PULWBM [31] | Cannot be calculated | No |
PULWGBM [31] | Cannot be calculated | No |
Lt-SF-ARAS [77] | Cannot be calculated | No |
TSUL-MARCOS | f(K1) = 0.0823; f(K2) = 0.0810; f(K3) = 0.0770; f(K4) = 0.0773; f(K5) = 0.0711 | h1 > h2 > h4 > h3 > h5 |
C1 | C2 | C3 | C4 | |
---|---|---|---|---|
P1 | ([s3,s4], (0.53, 0.33, 0.09)) | ([s5,s7], (0.89, 0.08, 0.03)) | ([s2,s3], (0.42, 0.35, 0.18)) | ([s3,s4], (0.08, 0.89, 0.02)) |
P2 | ([s2,s3], (0.73, 0.12, 0.08)) | ([s2,s3], (0.13, 0.64, 0.21)) | ([s4,s6], (0.03, 0.82, 0.13)) | ([s4,s5], (0.73, 0.15, 0.08)) |
P3 | ([s4,s5], (0.91, 0.03, 0.02)) | ([s4,s6], (0.07, 0.09, 0.05)) | ([s5,s6], (0.04, 0.85, 0.10)) | ([s6,s7], (0.68, 0.26, 0.06)) |
P4 | ([s3,s5], (0.85,0.09, 0.05)) | ([s6,s7], (0.74, 0.16, 0.10)) | ([s4,s5], (0.02, 0.89, 0.05)) | ([s5,s6], (0.08, 0.84, 0.06)) |
P5 | ([s2,s3], (0.90, 0.05, 0.02)) | ([s5,s6], (0.68, 0.08, 0.21)) | ([s3,s4], (0.05, 0.87, 0.06)) | ([s4,s6], (0.13, 0.75, 0.09)) |
Approaches | Results | Rankings | |
---|---|---|---|
q-ROULWGHM [76] | Cannot be calculated | No | |
PULWA [30] | sc(p1) = [s2.29, s2.97]; sc(p2) = [s1.39, s2.09]; sc(p3) = [s2.33, s3.54]; sc(p4) = [s1.46, s2.59]; sc(p5) = [s1.69, s2.63] | P3 > P1 > P5 > P4 > P2 | |
PULWG [30] | sc(p1) = [s1.54,s2.25]; sc(p2) = [s1.06, s1.66]; sc(p3) = [s1.77, s2.71]; sc(p4) = [s0.97, s1.96]; sc(p5) = [s1.21, s2.09] | P3 > P1 > P5 > P4 > P2 | |
PULWBM [31] | sc(p1) = [s0.57, s0.79]; sc(p2) = [s0.67, s0.94]; sc(p3) = [s1.02,s 1.25]; sc(p4) = [s0.90, s1.15]; sc(p5) = [s0.67, s0.94] | P3 > P4 > P5 > P2 > P1 | |
PULWGBM [31] | sc(p1) = [s1.11, s1.21]; sc(p2) = [s1.12, s1.22]; sc(p3) = [s1.28, s1.35]; sc(p4) = [s1.25, s1.33]; sc(p5) = [s1.16, s1.27] | P3 > P4 > P5 > P2 > P1 | |
Lt-SF-ARAS [77] | Cannot be calculated | No | |
Proposed method | q = 1 | f(K1) = 0.085, f(K2) = 0.065, f(K3) = 0.132, f(K4) = 0.141, f(K5) = 0.099 | P4 > P3 > P5 > P1 > P2 |
q = 2 | f(K1) = 0.160, f(K2) = 0.136, f(K3) = 0.199, f(K4) = 0.221, f(K5) = 0.167 | P4 > P3 > P5 > P1 > P2 | |
q = 3 | f(K1) = 0.173, f(K2) = 0.150, f(K3) = 0.219, f(K4) = 0.232, f(K5) = 0.172 | P4 > P3 > P1 > P5 > P2 |
Methods | Alternatives | xi | Ki+ | Ki− | f(Ki+) | f(Ki−) | f(Ki) | Ranking |
---|---|---|---|---|---|---|---|---|
Traditional MAROCS | hAAI | s0.360 | – | – | – | – | – | – |
h1 | s0.841 | s1.130 | s2.339 | s0.674 | s0.326 | s0.976 | 1 | |
h2 | s0.841 | s1.130 | s2.339 | s0.674 | s0.326 | s0.976 | 1 | |
h3 | s0.653 | s0.877 | s1.815 | s0.674 | s0.326 | s0.758 | 3 | |
hAI | s0.745 | – | – | – | – | – | – | |
Improved MARCOS | hAAI | ([s0.858,s1.627], (0.419, 0.559, 0.574)) | – | – | – | – | – | – |
h1 | ([s1.645,s2.620], (0.509, 0.465, 0.551)) | 0.203 | 0.150 | 0.424 | 0.576 | 0.114 | 1 | |
h2 | ([s1.653,s2.672], (0.509, 0.503, 0.455)) | 0.150 | 0.167 | 0.527 | 0.473 | 0.105 | 2 | |
h3 | ([s1.067,s1.860], (0.447,0.565, 0.459)) | 0.241 | 0.078 | 0.244 | 0.756 | 0.072 | 3 | |
hAI | ([s2.160,s3.200], (0.537,0.422, 0.370)) | – | – | – | – | – | – |