Introduction
Preliminary
Interval evidence theory
Interval intuitionistic fuzzy sets
Interval BPA-based intuitionistic fuzzy set method
Green supplier evaluation and selection model
Green supplier evaluation index system
Purpose | First-level indicators | Second-level indicators | Third-level indicators |
---|---|---|---|
Evaluation index system of green suppliers of papermaking enterprises | Supplier operational capability A1 | Product quality B1 | Product quality qualification rate C11 |
Quality control ability C12 | |||
Product cost B2 | Transportation transaction cost C21 | ||
Environmental governance cost C22 | |||
Supplier cooperation capability A2 | Cooperation service capability B3 | Order response delivery capability C31 | |
Outer packaging compliance degree C32 | |||
Cooperation stabilize capability B4 | Leadership attention C41 | ||
Contract performance C42 | |||
Supplier green capability A3 | Green environmental capability B5 | Green production and manufacturing capabilities C51 | |
Green recycling and utilization capacity C52 | |||
Green development capability B6 | Green product development rate C61 | ||
Green technology transformation success rate C62 | |||
Green competitiveness B7 | Green image C71 | ||
Green customer share C72 |
Green supplier selection model
Indicators | Attribute options | Confirmatory question | Confirmation options |
---|---|---|---|
\(Ui\) | \(u_{1}\) | Please select “sure” If you are absolutely sure Please select “hesitate” If you are not completely sure | Sure |
Hesitate | |||
\(\begin{array}{l}
\vdots \\
\vdots
\end{array}\) | \(\begin{array}{l}
\vdots \\
\vdots
\end{array}\) | \(\begin{array}{l}
\vdots \\
\vdots
\end{array}\) | |
\(u_{\text{m}}\) | Please select “sure” If you are absolutely sure Please select “hesitate” If you are not completely sure | Sure | |
Hesitate | |||
Not evaluated |
Evaluation term | Interval intuitionistic fuzzy number | Value |
---|---|---|
Very Poor (VP) | \(\left\langle {\mu _{A}(x) - \alpha \pi_{ A}(x),\upsilon _{A}(x) + \beta \pi _{A}(x)} \right\rangle\) | \(\alpha = 0.10,\quad \beta = 0.90\) |
Poor (P) | \(\left\langle {\mu _{A}(x) - \alpha \pi_{ A}(x),\upsilon_{ A}(x) + \beta \pi _{A}(x)} \right\rangle\) | \(\alpha = 0.30,\quad \beta = 0.70\) |
Medium (M) | \(\left\langle {\mu_{ A}(x) - \alpha \pi _{A}(x),\upsilon_{ A}(x) + \beta \pi_{ A}(x)} \right\rangle\) | \(\alpha = \beta = 0.50\) |
Good (G) | \(\left\langle {\mu _{A}(x) - \alpha \pi _{A}(x),\upsilon_{ A}(x) + \beta \pi_{ A}(x)} \right\rangle\) | \(\alpha = 0.70,\quad \beta = 0.30\) |
Very Good (VG) | \(\left\langle {\mu _{A}(x) - \alpha \pi _{A}(x),\upsilon_{ A}(x) + \beta \pi_{ A}(x)} \right\rangle\) | \(\alpha = 0.90,\quad \beta = 0.10\) |
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Step 1 Form a "typical ranking" of experts.
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Step 2 Obtain overall awareness.
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Step 3 Acquire the evaluation indicator weights.
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Step 1 Establish the interval intuitionistic fuzzy number \(\alpha_ {ij}\) of the evaluation unit \(Z_j\) based on the evaluation indicator attribute \(U_i\).
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Step 2 Use the IIFWA operator to integrate the comprehensive interval intuitionistic fuzzy number \(\beta_{ ij}\) of the evaluation unit \(Z_j\).
Analysis of example
Green supplier evaluation indicators measurement
Indicators | High or strong | Low or weak | Not evaluated | Interval intuitionistic fuzzy number \(\widetilde{\alpha }\) | Evaluation term | Interval intuitionistic fuzzy number \(\alpha\) | ||
---|---|---|---|---|---|---|---|---|
Sure | Hesitate | Sure | Hesitate | |||||
C11 | 206 | 29 | 193 | 21 | 51 | < [0.412, 0.470], [0.386, 0.428] > | M | < [0.361, 0.369], [0.437, 0.529] > |
C12 | 257 | 45 | 133 | 16 | 49 | < [0.514, 0.604], [0.266, 0.298] > | G | < [0.445, 0.450], [0.295, 0.364] > |
C21 | 135 | 19 | 266 | 37 | 43 | < [0.270, 0.308], [0.532, 0.606] > | P | < [0.244, 0.249], [0.592, 0.745] > |
C22 | 211 | 30 | 192 | 28 | 39 | < [0.422, 0.482], [0.384, 0.440] > | M | < [0.383, 0.385], [0.423, 0.537] > |
C31 | 262 | 43 | 132 | 15 | 48 | < [0.524, 0.610], [0.264, 0.294] > | G | < [0.457, 0.462], [0.293, 0.358] > |
C32 | 184 | 47 | 186 | 44 | 39 | < [0.368, 0.462], [0.372, 0.460] > | M | < [0.329, 0.332], [0.411, 0.590] > |
C41 | 260 | 42 | 136 | 14 | 48 | < [0.520, 0.604], [0.272, 0.300] > | G | < [0.453, 0.458], [0.301, 0.362] > |
C42 | 285 | 98 | 85 | 10 | 22 | < [0.570, 0.766], [0.170, 0.190] > | VG | < [0.530, 0.532], [0.174, 0.216] > |
C51 | 145 | 21 | 263 | 36 | 35 | < [0.290, 0.332], [0.526, 0.598] > | P | < [0.269, 0.277], [0.575, 0.727] > |
C52 | 191 | 39 | 197 | 32 | 41 | < [0.382, 0.460], [0.394, 0.458] > | M | < [0.341, 0.348], [0.435, 0.570] > |
C61 | 260 | 37 | 152 | 12 | 39 | < [0.520, 0.594], [0.304, 0.328] > | G | < [0.465, 0.471], [0.327, 0.381] > |
C62 | 261 | 44 | 132 | 16 | 47 | < [0.522, 0.610], [0.264, 0.296] > | G | < [0.456, 0.460], [0.292, 0.360] > |
C71 | 198 | 45 | 183 | 36 | 38 | < [0.396, 0.486], [0.366, 0.438] > | M | < [0.358, 0.367], [0.404, 0.557] > |
C72 | 257 | 48 | 146 | 10 | 39 | < [0.514, 0.610], [0.292, 0.312] > | G | < [0.459, 0.474], [0.315, 0.370] > |
Indicators | V1 | V2 | V3 | V4 |
---|---|---|---|---|
C11 | < [0.361, 0.369], [0.437, 0.529] > | < [0.456, 0.460], [0.292, 0.360] > | < [0.361, 0.367], [0.445, 0.535] > | < [0.450, 0.451], [0.320, 0.373] > |
C12 | < [0.445, 0.450], [0.295, 0.364] > | < [0.321, 0.346], [0.415, 0.572] > | < [0.337, 0.338], [0.431, 0.572] > | < [0.335, 0.336], [0.437, 0.582] > |
C21 | < [0.244, 0.249], [0.592, 0.745] > | < [0.260, 0.265], [0.582, 0.731] > | < [0.256, 0.272], [0.568, 0.736] > | < [0.449, 0.450], [0.299, 0.384] > |
C22 | < [0.383, 0.385], [0.423, 0.537] > | < [0.449, 0.450], [0.297, 0.378] > | < [0.457, 0.464], [0.297, 0.356] > | < [0.249, 0.261], [0.583, 0.743] > |
C31 | < [0.457, 0.462], [0.293, 0.358] > | < [0.329, 0.332], [0.411, 0.590] > | < [0.368, 0.369], [0.458, 0.547] > | < [0.383, 0.386], [0.389, 0.556] > |
C32 | < [0.329, 0.332], [0.411, 0.590] > | < [0.450, 0.452], [0.340, 0.386] > | < [0.449, 0.450], [0.299, 0.384] > | < [0.487, 0.489], [0.297, 0.343] > |
C41 | < [0.453, 0.458], [0.301, 0.362] > | < [0.459, 0.462], [0.315, 0.366] > | < [0.509, 0.511], [0.187, 0.221] > | < [0.359, 0.373], [0.439, 0.529] > |
C42 | < [0.530, 0.532], [0.174, 0.216] > | < [0.348, 0.350], [0.428, 0.574] > | < [0.459, 0.474], [0.315, 0.370] > | < [0.321, 0.323], [0.425, 0.579] > |
C51 | < [0.269, 0.277], [0.575, 0.727] > | < [0.454, 0.455], [0.308, 0.373] > | < [0.367, 0.371], [0.435, 0.531] > | < [0.230, 0.242], [0.580, 0.756] > |
C52 | < [0.341, 0.348], [0.435, 0.570] > | < [0.349, 0.350], [0.415, 0.556] > | < [0.455, 0.456], [0.301,0.366] > | < [0.342, 0.348], [0.434, 0.572] > |
C61 | < [0.465, 0.471], [0.327, 0.381] > | < [0.451, 0.457], [0.275, 0.353] > | < [0.347, 0.349], [0.399, 0.593] > | < [0.366, 0.373], [0.436, 0.523] > |
C62 | < [0.456, 0.460], [0.292, 0.360] > | < [0.244, 0.245], [0.584, 0.769] > | < [0.323, 0.324], [0.457, 0.586] > | < [0.438, 0.446], [0.282, 0.346] > |
C71 | < [0.358, 0.367], [0.404, 0.557] > | < [0.335, 0.336], [0.397, 0.578] > | < [0.449, 0.456], [0.299, 0.362] > | < [0.248, 0.261], [0.582, 0.747] > |
C72 | < [0.459, 0.474], [0.315, 0.370] > | < [0.236, 0.242], [0.614, 0.740] > | < [0.437, 0.441], [0.311, 0.371] > | < [0.334, 0.341], [0.428, 0.575] > |
Green supplier evaluation indicator weights
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Step 1 Form a “typical ranking” of experts.
Expert indicators | D1 | D2 | D3 | D4 | D5 | D6 | D7 | D8 | D9 | D10 |
---|---|---|---|---|---|---|---|---|---|---|
B5 | 1 | 1 | 2 | 1 | 3 | 2 | 1 | 2 | 2 | 1 |
B6 | 2 | 2 | 3 | 2 | 1 | 1 | 3 | 1 | 3 | 2 |
B7 | 3 | 3 | 1 | 3 | 2 | 3 | 2 | 3 | 1 | 3 |
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Step 2 Obtain overall awareness.
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Step 3 Acquire the evaluation indicator weights.
Purpose | First-level indicators | Second-level indicators | Weights | Third-level indicators | Weights |
---|---|---|---|---|---|
Green supplier evaluation indicator weight | A1 | B1 | 0.5453 | C11 | 0.5226 |
C12 | 0.4774 | ||||
B2 | 0.4547 | C21 | 0.4774 | ||
C22 | 0.5226 | ||||
A2 | B3 | 0.5226 | C31 | 0.5679 | |
C32 | 0.4321 | ||||
B4 | 0.4774 | C41 | 0.4547 | ||
C42 | 0.5453 | ||||
A3 | B5 | 0.3615 | C51 | 0.4774 | |
C52 | 0.5226 | ||||
B6 | 0.3560 | C61 | 0.5226 | ||
C62 | 0.4774 | ||||
B7 | 0.2825 | C71 | 0.5000 | ||
C72 | 0.5000 |
Green suppliers indicator attributes comprehensive evaluation
Indicators | V1 | V2 | V3 | V4 |
---|---|---|---|---|
B1 | < [0.403, 0.409], [0.362, 0.443] > | < [0.395, 0.408], [0.345, 0.449] > | < [0.350, 0.353], [0.438, 0.552] > | < [0.398, 0.399], [0.371, 0.461] > |
B2 | < [0.320, 0.323], [0.497, 0.628] > | < [0.366, 0.368], [0.410, 0.518] > | < [0.369, 0.380], [0.405, 0.504] > | < [0.353, 0.358], [0.424, 0.542] > |
B3 | < [0.405, 0.409], [0.339, 0.444] > | < [0.384, 0.387], [0.379, 0.491] > | < [0.405, 0.406], [0.381, 0.469] > | < [0.430, 0.433], [0.346, 0.451] > |
B4 | < [0.497, 0.500], [0.223, 0.273] > | < [0.450, 0.454], [0.286, 0.367] > | < [0.482, 0.491], [0.249, 0.293] > | < [0.339, 0.346], [0.431, 0.556] > |
B5 | < [0.308, 0.315], [0.497, 0.640] > | < [0.401, 0.402], [0.360, 0.459] > | < [0.415, 0.417], [0.359, 0.437] > | < [0.291, 0.299], [0.498, 0.653] > |
B6 | < [0.461, 0.466], [0.310, 0.371] > | < [0.360, 0.364], [0.394, 0.512] > | < [0.336, 0.337], [0.426, 0.590] > | < [0.402, 0.409], [0.354, 0.430] > |
B7 | < [0.411, 0.423], [0.357, 0.454] > | < [0.287, 0.291], [0.494, 0.654] > | < [0.443, 0.448], [0.305, 0.366] > | < [0.292, 0.302], [0.499, 0.655] > |
Indicators | V1 | V2 | V3 | V4 |
---|---|---|---|---|
A1 | < [0.367, 0.371], [0.418, 0.519] > | < [0.382, 0.391], [0.373, 0.479] > | < [0.358, 0.366], [0.423, 0.530] > | < [0.378, 0.381], [0.395, 0.496] > |
A2 | < [0.377, 0.380], [0.366, 0.447] > | < [0.349, 0.352], [0.417, 0.513] > | < [0.372, 0.375], [0.401, 0.469] > | < [0.340, 0.344], [0.449, 0.555] > |
A3 | < [0.418, 0.426], [0.355, 0.451] > | < [0.372, 0.375], [0.386, 0.511] > | < [0.422, 0.425], [0.334, 0.430] > | < [0.350, 0.358], [0.420, 0.546] > |
Green suppliers comprehensive evaluation results fusion
Step 1 The interval Bayesian BPA formed by the first-level indicators interval intuitionistic fuzzy number is normalized.