TODIM method for picture fuzzy multiple attribute decision making. (English) Zbl 1485.91071
Summary: For this article, we shall expand the TODIM model to the MADM with the picture fuzzy numbers (PFNs). Firstly, the concept, comparative method and distance of PFNs are introduced and the traditional TODIM model is presented. Then, the expanded TODIM model is developed to solve MADM problems with PFNs. Finally, a numerical example is given to verify the proposed approach.
MSC:
| 91B06 | Decision theory |
| 90B50 | Management decision making, including multiple objectives |
| 91B86 | Mathematical economics and fuzziness |
Keywords:
multiple attribute decision making (MADM); picture fuzzy sets (PFSs); picture fuzzy numbers (PFNs); TODIM; prospect theoryReferences:
| [1] | Abdellaoui, M., Bleichrodt, H., Paraschiv, C. (2017). Loss aversion under prospect theory: a parameter-free measurement.Manag. Sci., 53, 1659-1674. |
| [2] | Atanassov, K. (1986). Intuitionistic fuzzy sets.Fuzzy Sets and Systems, 20, 87-96. · Zbl 0631.03040 |
| [3] | Atanassov, K. (1989). More on intuitionistic fuzzy sets.Fuzzy Sets and Systems, 33, 37-46. · Zbl 0685.03037 |
| [4] | Atanassov, K. (1994). Operators over interval-valued intuitionistic fuzzy sets.Fuzzy Sets and Systems, 64(2), 159-174. · Zbl 0844.04001 |
| [5] | Atanassov, K., Gargov, G. (1989). Interval-valued intuitionistic fuzzy sets.Fuzzy Sets and Systems, 31, 343-349. · Zbl 0674.03017 |
| [6] | Son, L. (2015). DPFCM: a novel distributed picture fuzzy clustering method on picture fuzzy sets.Expert System with Applications, 2, 51-66. |
| [7] | Son, L.H. (2016). Generalized picture distance measure and applications to picture fuzzy clustering.Appl. Soft Comput., 46, 284-295. |
| [8] | Son, L.H. (2017). Measuring analogousness in picture fuzzy sets: from picture distance measures to picture association measures.FO & DM, 16(3), 359-378. · Zbl 1428.03067 |
| [9] | Son, L.H., Thong, P.H. (2017). Some novel hybrid forecast methods based on picture fuzzy clustering for weather nowcasting from satellite image sequences.Applied Intelligence, 46(1), 1-15. |
| [10] | Song, Y.F., Wang, X.D. (2017). A new similarity measure between intuitionistic fuzzy sets and the positive definiteness of the similarity matrix.Pattern Analysis and Applications, 20(1), 215-226. · Zbl 1425.68368 |
| [11] | Son, L.H., Viet, P.V., Hai, P.V. (2017). Picture inference system: a new fuzzy inference system on picture fuzzy set.Applied Intelligence, 46(3), 652-669. |
| [12] | Tang, X.Y., Wei, G.W. (2018). Models for green supplier selection in green supply chain management with Pythagorean 2-tuple linguistic information.IEEE Access, 6, 18042-18060. |
| [13] | Thong, N.T. (2015). HIFCF: An effective hybrid model between picture fuzzy clustering and intuitionistic fuzzy recommender systems for medical diagnosis.Expert Systems with Applications, 42(7), 3682-3701. |
| [14] | Thong, P.H., Son, L.H. (2016a). A novel automatic picture fuzzy clustering method based on particle swarm optimization and picture composite cardinality.Knowl.-Based Syst., 109, 48-60. |
| [15] | Thong, P.H., Son, L.H. (2016b). Picture fuzzy clustering: a new computational intelligence method.Soft Comput., 20(9), 3549-3562. · Zbl 1370.68257 |
| [16] | Wang, F.X. (2017). Interval-valued intuitionistic fuzzy ideals of B-algebras.Journal of Intelligent and Fuzzy Systems, 33(4), 2609-2615. · Zbl 1377.06007 |
| [17] | Wang, S.W., Liu, J. (2017). Extension of the TODIM method to intuitionistic linguistic multiple attribute decision making.Symmetry, 9(6), 95. · Zbl 1423.90125 |
| [18] | Wang, J., Wang, J.Q., Zhang, H.Y. (2016). A likelihood-based TODIM approach based on multi-hesitant fuzzy linguistic information for evaluation in logistics outsourcing.Computers & Industrial Engineering, 99, 287- 299. |
| [19] | Wang, J., Wei, G.W., Wei, Y. (2018). Models for Green supplier selection with some 2-tuple linguistic neutrosophic number Bonferroni mean operators.Symmetry, 10(5), 131. doi:10.3390/sym10050131. |
| [20] | Wei, G.W. (2016). Picture fuzzy cross-entropy for multiple attribute decision making problems.Journal of Business Economics and Management, 17(4), 491-502. |
| [21] | Wei, G.W. (2017a). Picture fuzzy aggregation operators and their application to multiple attribute decision making.Journal of Intelligent and Fuzzy Systems, 33(2), 713-724. · Zbl 1376.91081 |
| [22] | Wei, G.W. (2017b). Picture uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making.Kybernetes, 46(10), 1777-1800. |
| [23] | Wei, G.W. (2017c). Some cosine similarity measures for picture fuzzy sets and their applications to strategic decision making.Informatica, 28(3), 547-564. · Zbl 1398.03200 |
| [24] | Wei, G.W. (2018a). Picture fuzzy Hamacher aggregation operators and their application to multiple attribute decision making.Fundamenta Informaticae, 157(3), 271-320. doi:10.3233/FI-2018-1628. · Zbl 1390.68684 |
| [25] | Wei, G.W. (2018b). Some similarity measures for picture fuzzy sets and their applications.Iranian Journal of Fuzzy Systems, 15(1), 77-89. · Zbl 1398.03201 |
| [26] | Wei, G.W., Lu, M. (2017). Pythagorean hesitant fuzzy Hamacher aggregation operators in multiple attribute decision making.Journal of Intelligent Systems. doi:10.1515/jisys-2017-0106. · Zbl 1443.91119 |
| [27] | Wei, G.W., Lu, M. (2018a). Pythagorean fuzzy Maclaurin symmetric mean operators in multiple attribute decision making.International Journal of Intelligent Systems, 33(5), 1043-1070. |
| [28] | Wei, G.W., Lu, M. (2018b). Pythagorean fuzzy power aggregation operators in multiple attribute decision making.International Journal of Intelligent Systems, 33(1), 169-186. |
| [29] | Wei, G.W., Wei, Y. (2018). Similarity measures of Pythagorean fuzzy sets based on cosine function and their applications.International Journal of Intelligent Systems, 33(3), 634-652. |
| [30] | Wei, G.W., Zhang, Z.P. (2018). Some single-valued neutrosophic bonferroni power aggregation operators in multiple attribute decision making.Journal of Ambient Intelligence and Humanized Computing. doi:10.1007/s12652-018-0738-y. |
| [31] | Wei, G.W., Zhao, X.F. (2012). Some induced correlated aggregating operators with intuitionistic fuzzy information and their application to multiple attribute group decision making.Expert Systems with Applications, 39 (2), 2026-2034. |
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