Introduction
Aftersales performance
Customer satisfaction (CS)
Service quality (SQ)
Financial success (FS)
Perceived service value (PSV)
Customer retention (CR)
Repurchase (RP)
Brand loyalty (BL)
Recommendation (RC)
CS | SQ | FS | PSV | CR | RP | BL | RC | BI | |
---|---|---|---|---|---|---|---|---|---|
t1 | |||||||||
P1 | (0.8, 0.1, 0.1) | (0.8, 0.1, 0.1) | (0.4, 0.5, 0.1) | (0.9, 0.1, 0) | (0.7, 0.2, 0.1) | (0.5, 0.2, 0.3) | (0.7, 0.2, 0.1) | (0.3, 0.1, 0.6) | (0.5, 0.3, 0.2) |
P2 | (0.9, 0.1, 0) | (0.8, 0.1, 0.1) | (0.4, 0.2, 0.4) | (0.9, 0.1, 0) | (0.8, 0.1, 0.1) | (0.5, 0.3, 0.2) | (0.6, 0.2, 0.2) | (0.7, 0.1, 0.2) | (0.3, 0.1, 0.6) |
P3 | (0.1, 0.7, 0.2) | (0.1, 0.7, 0.2) | (0.8, 0.2, 0) | (0.5, 0.2, 0.3) | (0.6, 0.4, 0) | (0.6, 0.2, 0.2) | (0.7, 0.2, 0.1) | (0.9, 0.1, 0) | (0.4, 0.4, 0.2) |
P4 | (0.3, 0.6, 0.1) | (0.8, 0.1, 0.1) | (0.1, 0.6, 0.3) | (0.9, 0.1, 0) | (0.7, 0.2, 0.1) | (0.7, 0.2, 0.1) | (0.5, 0.4, 0.1) | (0.8, 0.2, 0) | (0.4, 0.4, 0.2) |
P5 | (0.4, 0.5, 0.1) | (0.4, 0.1, 0.5) | (0.1, 0.9, 0) | (0.6, 0.2, 0.2) | (0.6, 0.2, 0.2) | (0.4, 0.2, 0.4) | (0.4, 0.3, 0.3) | (0.5, 0.2, 0.3) | (0.6, 0.3, 0.1) |
t2 | |||||||||
P1 | (0.8, 0.1, 0.1) | (0.5, 0.1, 0.4) | (0.7, 0.1, 0.2) | (0.8, 0.1, 0.1) | (0.6, 0.2, 0.2) | (0.9, 0.1, 0) | (0.7, 0.3, 0) | (0.5, 0.2, 0.3) | (0.3, 0.3, 0.4) |
P2 | (0.7, 0.1, 0.2) | (0.1, 0.6, 0.3) | (0.4, 0.4, 0.2) | (0.1, 0.7, 0.2) | (0.3, 0.6, 0.1) | (0.1, 0.2, 0.7) | (0.7, 0.1, 0.2) | (0.3, 0.3, 0.4) | (0.9, 0.1, 0) |
P3 | (0.8, 0.2, 0) | (0.1, 0.8, 0.1) | (0.1, 0.8, 0.1) | (0.2, 0.1, 0.7) | (0.2, 0.7, 0.1) | (0.3, 0.3, 0.4) | (0.8, 0, 0.2) | (0.4, 0.2, 0.4) | (0.5, 0.1, 0.4) |
P4 | (0.5, 0.4, 0.1) | (0.7, 0, 0.3) | (0.5, 0.2, 0.3) | (0.4, 0.2, 0.4) | (0.9, 0, 0.1) | (0.9, 0, 0.1) | (0.8, 0.1, 0.1) | (0.9, 0.1, 0) | (0.4, 0, 0.6) |
P5 | (0.6, 0.2, 0.2) | (0.9, 0, 0.1) | (0.8, 0.1, 0.1) | (0.3, 0.6, 0.1) | (0.1, 0.1, 0.8) | (0.5, 0.4, 0.1) | (0.5, 0.4, 0.1) | (0.8, 0.2, 0) | (0.9, 0.1, 0) |
t3 | |||||||||
P1 | (0.6, 0.1, 0.3) | (0.4, 0.4, 0.2) | (0.3, 0.7, 0) | (0.7, 0.1, 0.2) | (0.9, 0, 0.1) | (0.4, 0.4, 0.2) | (0.8, 0.1, 0.1) | (0.7, 0.2, 0.1) | (0.4, 0.4, 0.2) |
P2 | (0.2, 0.4, 0.4) | (0.5, 0.1, 0.4) | (0.8, 0.2, 0) | (0.9, 0.1, 0) | (0.4, 0.1, 0.5) | (0.6, 0.2, 0.2) | (0.7, 0.2, 0.1) | (0.6, 0.2, 0.2) | (0.6, 0.4, 0) |
P3 | (0.6, 0.1, 0.3) | (0.6, 0.2, 0.2) | (0.3, 0.4, 0.3) | (0.6, 0.3, 0.1) | (0.1, 0.8, 0.1) | (0.6, 0.3, 0.2) | (0.6, 0.1, 0.3) | (0.8, 0.1, 0.1) | (0.5, 0.2, 0.3) |
P4 | (0.7, 0.1, 0.2) | (0.9, 0.1, 0) | (0.6, 0.2, 0.2) | (0.7, 0.2, 0.1) | (0.6, 0.1, 0.3) | (0.8, 0.1, 0.1) | (0.7, 0, 0.3) | (0.5, 0.2, 0.3) | (0.6, 0.3, 0.1) |
P5 | (0.7, 0.1, 0.2) | (0.6, 0.3, 0.1) | (0.9, 0.1, 0) | (0.3, 0.6, 0.1) | (0.7, 0.1, 0.2) | (0.4, 0.4, 0.2) | (0.9, 0, 0.1) | (0.9, 0, 0.1) | (0.5, 0.2, 0.3) |
t4 | |||||||||
P1 | (0.9, 0.1, 0) | (0.9, 0.1, 0) | (0.7, 0.1, 0.2) | (0.6, 0.2, 0.2) | (0.8, 0.1, 0.1) | (0.7, 0.1, 0.2) | (0.6, 0.2, 0.2) | (0.3, 0.6, 0.1) | (0.8, 0, 0.2) |
P2 | (0.2, 0.2, 0.6) | (0.9, 0.1, 0) | (0.2, 0.8, 0) | (0.6, 0.3, 0.1) | (0.6, 0.1, 0.3) | (0.4, 0.4, 0.2) | (0.6, 0.1, 0.3) | (0.6, 0.2, 0.2) | (0.9, 0, 0.1) |
P3 | (0.9, 0.1, 0) | (0.3, 0.6, 0.1) | (0.3, 0.6, 0.1) | (0.3, 0.7, 0) | (0.7, 0.1, 0.2) | (0.5, 0.4, 0.1) | (0.7, 0, 0.3) | (0.7, 0.1, 0.2) | (0.7, 0.1, 0.2) |
P4 | (0.1, 0.1, 0.8) | (0.4, 0.5, 0.1) | (0.2, 0.3, 0.5) | (0.2, 0.1, 0.7) | (0.4, 0.1, 0.5) | (0.5, 0.2, 0.3) | (0.6, 0.3, 0.1) | (0.8, 0.2, 0) | (0.8, 0.2, 0) |
P5 | (0.7, 0.1, 0.2) | (0.4, 0.3, 0.3) | (0.3, 0.6, 0.1) | (0.8, 0.1, 0.1) | (0.1, 0.5, 0.4) | (0.8, 0.2, 0) | (0.8, 0.1, 0.1) | (0.9, 0.1, 0) | (0.5, 0.4, 0.1) |
Brand image (BI)
Dynamic intuitionistic fuzzy multi-attribute decision-making
Preliminaries
CS | SQ | FS | PSV | CR | |
---|---|---|---|---|---|
P1 | (0.813, 0.1, 0.087) | (0.747, 0.152, 0.101) | (0.585, 0.211, 0.204) | (0.722, 0.132, 0.146) | (0.806, 0, 0.194) |
P2 | (0.466, 0.2, 0.334) | (0.73, 0.143, 0.127) | (0.516, 0.4, 0.084) | (0.73, 0.229, 0.041) | (0.529, 0.143, 0.328) |
P3 | (0.783, 0.14, 0.077) | (0.362, 0.464, 0.174) | (0.351, 0.504, 0.145) | (0.412, 0.325, 0.263) | (0.478, 0.316, 0.206) |
P4 | (0.439, 0.158, 0.403) | (0.727, 0, 0.273) | (0.401, 0.263, 0.336) | (0.543, 0.141, 0.316) | (0.654, 0, 0.346) |
P5 | (0.659, 0.135, 0.206) | (0.629, 0, 0.371) | (0.688, 0.255, 0.057) | (0.599, 0.263, 0.138) | (0.403, 0.204, 0.393) |
RP | BL | RC | BI | ||
---|---|---|---|---|---|
P1 | (0.688, 0.162, 0.15) | (0.702, 0.176, 0.122) | (0.492, 0.29, 0.218) | (0.608, 0, 0.392) | |
P2 | (0.434, 0.275, 0.291) | (0.654, 0.132, 0.214) | (0.565, 0.202, 0.233) | (0.816, 0, 0.184) | |
P3 | (0.511, 0.323, 0.166) | (0.698, 0, 0.302) | (0.727, 0.115, 0.158) | (0.585, 0.141, 0.274) | |
P4 | (0.738, 0, 0.262) | (0.673, 0, 0.327) | (0.771, 0.174, 0.055) | (0.658, 0, 0.342) | |
P5 | (0.627, 0.283, 0.09) | (0.782, 0, 0.218) | (0.865, 0, 0.135) | (0.646, 0.239, 0.115) |
Dynamic intuitionistic fuzzy multi-attribute decision-making
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Defining the attributes and evaluating alternatives for the problem.
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Evaluating each alternative i with respect to each attribute j using intuitionistic fuzzy numbers for each period \(t_k\):where \(\mathop {\tilde{I}} _{ij} \left( {t_k } \right) \) is the intuitionistic fuzzy evaluation for alternative \(i=1,2,\ldots ,n\) and attribute \(j=1,2,\ldots ,m\) at period \(t_k\).$$\begin{aligned} {\tilde{I}} _{ij} ({t_k }) =(\mu _{ij} \left( {t_k } \right) ,v_{ij} \left( {t_k } \right) ,\pi _{ij} \left( {t_k}\right) \end{aligned}$$(5)
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Calculating the weight vector for periods \(\omega (t)=\left( {\omega \left( {t_1 } \right) ,\omega \left( {t_2 } \right) ,\ldots ,\omega \left( {t_p } \right) } \right) \) using arithmetic series based method (Xu 2008) where the difference between \(\omega \left( {t_k } \right) \) and \(\omega \left( {t_{k+1} } \right) \) is a constant c:where when all the weights are equal, \(c=0,\eta =\frac{1}{n},\omega \left( {t_k } \right) =\frac{1}{n}(k=1,2,\ldots ,p)\), when \(\omega \left( {t_k } \right) \) is a monotonically increasing sequence, \(c>0\,\mathrm{then}\,\omega \left( {t_k } \right) <\omega \left( {t_{k+1} } \right) ,\) when \(\omega \left( {t_k } \right) \) is a monotonically decreasing sequence \(c<0\,\mathrm{then}\,\omega \left( {t_k } \right) >\omega \left( {t_{k+1} } \right) .\)$$\begin{aligned} \omega \left( {t_{k+1} } \right) -\omega \left( {t_k } \right) =c, \quad \omega \left( {t_k } \right) =\eta +(k-1)c \end{aligned}$$(6)
\(\mathop \sum \nolimits _{j=1}^m \gamma _j (1-v_{ij} )\)
|
\(\mathop \sum \nolimits _{j=1}^m \gamma _j (1+\pi _{ij} )\)
| Closeness coefficient | |
---|---|---|---|
P1 | 0.864 | 1.179 | 0.733 |
P2 | 0.808 | 1.204 | 0.671 |
P3 | 0.741 | 1.196 | 0.620 |
P4 | 0.918 | 1.296 | 0.709 |
P5 | 0.847 | 1.191 | 0.711 |
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Aggregating the Intuitionistic numbers collected at different periods with dynamic weighted fuzzy averaging (DIFWA) operator [41].$$\begin{aligned}&{\widetilde{{DIFWA}}} _{{\omega (t)}}^{{\left( { {\tilde{I}} ({t_1 }), {\tilde{I}} \left( {t_2 }\right) ,\ldots ,\mathop {\tilde{I}} \left( {t_n } \right) } \right) }}\nonumber \\&\quad =\left( 1-\mathop \prod \limits _{k=1}^n \left( {1-\mu _{\mathop {\tilde{I}} \left( {t_k } \right) } } \right) ^{\omega \left( {t_k } \right) },\mathop \prod \limits _{k=1}^n v_{\mathop {\tilde{I}} \left( {t_k } \right) }^{\omega \left( {t_k } \right) } ,\right. \nonumber \\&\qquad \left. \times \mathop \prod \limits _{k=1}^n \left( {1-\mu _{\mathop {\tilde{I}} \left( {t_k } \right) } } \right) ^{\omega \left( {t_k } \right) }-\mathop \prod \limits _{k=1}^n v_{\mathop {\tilde{I}} \left( {t_k } \right) }^{\omega \left( {t_k } \right) } \right) . \end{aligned}$$(7)
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Defining the intuitionistic fuzzy ideal \(Y^{+}=\big ( I_1^+ ,I_2^+ ,\ldots ,I_m^+ \big )^{T}\) and negative ideal solutions \(Y^{+}=\big ( I_1^- ,I_2^- ,\ldots ,I_m^- \big )^{T}\), where \(I_i^+ =(1,0,0)\) is the largest and \(I_i^- =(0,1,0)\) is the smallest Intuitionistic fuzzy numbers.
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Calculating the closeness coefficient of each alternative using Eq. (8) and selecting the alternative with the highest closeness coefficient:where \(i=1,2,\ldots ,n\) and \(w_j \) is the weight of the jth attribute$$\begin{aligned} C_i =\frac{\mathop \sum \nolimits _{j=1}^m w_j (1-v_{ij} )}{\mathop \sum \nolimits _{j=1}^m w_j (1+\pi _{ij} )}, \end{aligned}$$(8)