TODIM Method for Picture Fuzzy Multiple Attribute Decision Making

Wei, Guiwu

doi:10.15388/Informatica.2018.181

Informatica

TODIM Method for Picture Fuzzy Multiple Attribute Decision Making

Volume 29, Issue 3 (2018), pp. 555–566

Guiwu Wei

https://doi.org/10.15388/Informatica.2018.181

Pub. online: 1 January 2018 Type: Research Article

Open Access

Received
1 September 2017

Accepted
1 April 2018

Published
1 January 2018

Abstract

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.

References

Abdellaoui, M., Bleichrodt, H., Paraschiv, C. (2017). Loss aversion under prospect theory: a parameter-free measurement. anagement Science, 53, 1659–1674.

Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96.

Atanassov, K. (1989). More on intuitionistic fuzzy sets. Fuzzy Sets and Systems, 33, 37–46.

Atanassov, K. (1994). Operators over interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 64(2), 159–174.

Atanassov, K., Gargov, G. (1989). Interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31, 343–349.

Atanassov, K., Pasi, G., Yager, R.R. (2005). Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. International Journal of Systems Science, 36(14), 859–868.

Bustince, H., Burillo, P. (1995). Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 74(2), 237–244.

Chen, T.Y. (2011). Bivariate models of optimism and pessimism in multi-criteria decision-making based on intuitionistic fuzzy sets. Information Sciences, 181, 2139–2165.

Chen, T.Y. (2014). Interval-valued intuitionistic fuzzy QUALIFLEX method with a likelihood-based comparison approach for multiple criteria decision analysis. nformation Sciences, 261, 149–169.

Chen, T.Y. (2016). An interval-valued intuitionistic fuzzy permutation method with likelihood-based preference functions and its application to multiple criteria decision analysis. Applied Soft Computing, 42, 390–409.

Chen, S.M., Chiou, C.H. (2015). Multiattribute decision making based on interval-valued intuitionistic fuzzy sets, PSO techniques, and evidential reasoning methodology. EEE Transactions on Fuzzy Systems, 23(6), 1905–1916.

Chen, T.Y., Li, C.H. (2011). Determining objective weights with intuitionistic fuzzy entropy measures: a comparative analysis. Information Sciences, 180, 4207–4222.

Chen, L.H., Hung, C.C., Tu, C.C. (2012). Considering the decision maker’s attitudinal character to solve multi-criteria decision-making problems in an intuitionistic fuzzy environ-ment. Knowledge-Based Systems, 361, 29–38.

Cuong, B. (2013). Picture fuzzy sets-first results. Part 1. In: Seminar “Neuro-Fuzzy Systems with Applications”. Institute of Mathematics, Hanoi.

Fan, Z.P., Zhang, X., Chen, F.D., Liu, Y. (2013). Extended TODIM method for hybrid multiple attribute decision making problems. Knowledge-Based Systems, 42, 40–48.

Gao, H., Lu, M., Wei, G.W., Wei, Y. (2018a). Some novel Pythagorean fuzzy interaction aggregation operators in multiple attribute decision making. Fundamenta Informaticae, 159(4), 385–428.

Gao, H., Wei, G.W., Huang, Y.H. (2018b). Dual hesitant bipolar fuzzy Hamacher prioritized aggregation operators in multiple attribute decision making. IEEE Access, 6(1), 11508–11522.

Garg, H. (2016). A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems. Applied Soft Computing, 38, 988–999.

Gomes, L., Lima, M. (1992). TODIM: basics and application to multicriteria ranking of projects with environmental impacts. Foundations of Computing and Decision Sciences, 16, 113–127.

Konwar, N., Debnath, P. (2017). Continuity and Banach contraction principle in intuitionistic fuzzy n-normed linear spaces. Journal of Intelligent and Fuzzy Systems, 33(4), 2363–2373.

Krohling, R.A., Pacheco, A.G.C., Siviero, A.L.T. (2013). IF-TODIM: An intuitionistic fuzzy TODIM to multi-criteria decision making. Knowledge-Based Systems, 53, 142–146.

Li, D.F. (2011). Closeness coefficient based nonlinear programming method for interval-valued intuitionistic fuzzy multiattribute decision making with incomplete preference information. Applied Soft Computing, 11, 3402–3418.

Liu, P.D. (2017a). Multiple attribute decision-making methods based on normal intuitionistic fuzzy interaction aggregation operators. Symmetry, 9(11), 261.

Liu, P.D. (2017b). Some frank aggregation operators for interval-valued intuitionistic fuzzy numbers and their application to group decision making. Multiple-Valued Logic and Soft Computing, 29(1–2), 183–223.

Liu, P.D., Teng, F. (2016). An extended TODIM method for multiple attribute group decision-making based on 2-dimension uncertain linguistic variable. Complexity, 21(5), 20–30.

Liu, H.C., You, J.X., Fan, X.J., Chen, Y.Z. (2014). Site selection in waste management by the VIKOR method using linguistic assessment. Applied Soft Computing, 214, 53–61.

Lourenzutti, R., Krohling, R.A. (2013). A study of TODIM in a intuitionistic fuzzy and random environment. Expert Systems with Applications, 40, 6459–6468.

Merigo, J.M., Casanovas, M. (2009). Induced aggregation operators in decision making with the Dempster–Shafer belief structure. International Journal of Intelligent Systems, 24, 934–954.

Ren, P.J., Xu, Z.S., Gou, X.J. (2016). Pythagorean fuzzy TODIM approach to multi-criteria decision making. Applied Soft Computing, 42, 246–259.

Ronald, R.R. (2015). A note on measuring fuzziness for intuitionistic and interval-valued fuzzy sets. International Journal of General Systems, 44(7–8), 889–901.

Sang, X.Z., Liu, X.W. (2016). An interval type-2 fuzzy sets-based TODIM method and its application to green supplier selection. JORS, 67(5), 722–734.

Singh, P. (2014). Correlation coefficients for picture fuzzy sets. Journal of Intelligent & Fuzzy Systems, 27, 2857–2868.

Son, L. (2015). DPFCM: a novel distributed picture fuzzy clustering method on picture fuzzy sets. Expert System with Applications, 2, 51–66.

Son, L.H. (2016). Generalized picture distance measure and applications to picture fuzzy clustering. Applied Soft Computing, 46, 284–295.

Son, L.H. (2017). Measuring analogousness in picture fuzzy sets: from picture distance measures to picture association measures. FO & DM, 16(3), 359–378.

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.

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.

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.

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.

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.

Thong, P.H., Son, L.H. (2016a). A novel automatic picture fuzzy clustering method based on particle swarm optimization and picture composite cardinality. Knowledge-Based Systems, 109, 48–60.

Thong, P.H., Son, L.H. (2016b). Picture fuzzy clustering: a new computational intelligence method. Soft Computing, 20(9), 3549–3562.

Wang, F.X. (2017). Interval-valued intuitionistic fuzzy ideals of B-algebras. Journal of Intelligent and Fuzzy Systems, 33(4), 2609–2615.

Wang, S.W., Liu, J. (2017). Extension of the TODIM method to intuitionistic linguistic multiple attribute decision making. Symmetry, 9(6), 95.

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.

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. https://doi.org/10.3390/sym10050131.

Wei, G.W. (2016). Picture fuzzy cross-entropy for multiple attribute decision making problems. Journal of Business Economics and Management, 17(4), 491–502.

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.

Wei, G.W. (2017b). Picture uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making. Kybernetes, 46(10), 1777–1800.

Wei, G.W. (2017c). Some cosine similarity measures for picture fuzzy sets and their applications to strategic decision making. Informatica, 28(3), 547–564.

Wei, G.W. (2018a). Picture fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Fundamenta Informaticae, 157(3), 271–320. https://doi.org/10.3233/FI-2018-1628.

Wei, G.W. (2018b). Some similarity measures for picture fuzzy sets and their applications. Iranian Journal of Fuzzy Systems, 15(1), 77–89.

Wei, G.W., Lu, M. (2017). Pythagorean hesitant fuzzy Hamacher aggregation operators in multiple attribute decision making. Journal of Intelligent Systems. https://doi.org/10.1515/jisys-2017-0106.

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.

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.

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.

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. https://doi.org/10.1007/s12652-018-0738-y.

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.

Wei, C.P., Ren, Z.L., Rodríguez, R.M. (2015). A hesitant fuzzy linguistic TODIM method based on a score function. International Journal of Computational Intelligence Systems, 8(4), 701–712.

Wei, G.W., Alsaadi, F.E., Hayat, T., Alsaedi, A. (2016a). Hesitant fuzzy linguistic arithmetic aggregation operators in multiple attribute decision making. Iranian Journal of Fuzzy Systems, 13(4), 1–16.

Wei, G.W., Alsaadi, F.E., Hayat, T., Alsaedi, A. (2016b). Projection models for multiple attribute decision making with picture fuzzy information. International Journal of Machine Learning and Cybernetics. https://doi.org/10.1007/s13042-016-0604-1.

Wei, G.W., Alsaadi, F.E., Hayat, T., Alsaedi, A. (2018a). Bipolar fuzzy Hamacher aggregation operators in multiple attribute decision making. International Journal of Fuzzy System, 20(1), 1–12.

Wei, G.W., Gao, H., Wei, Y. (2018b). Some q-rung orthopair fuzzy heronian mean operators in multiple attribute decision making. International Journal of Intelligent Systems. https://doi.org/10.1002/int.21985.

Wei, G.W., Lu, M., Tang, X.Y., Wei, Y. (2018c). Pythagorean hesitant fuzzy hamacher aggregation operators and their application to multiple attribute decision making. International Journal of Intelligent Systems, 33(6), 1197–1233.

Wu, J., Chiclana, F. (2014). A risk attitudinal ranking method for interval-valued intuitionistic fuzzy numbers based on novel attitudinal expected score and accuracy functions. Applied Soft Computing, 22, 272–286.

Xu, Z.S. (2007). Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems, 15, 1179–1187.

Xu, Z.S., Yager, R.R. (2006). Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems, 35, 417–433.

Ye, J. (2009). Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment. Expert Systems with Applications, 36(2), 899–902.

Ye, J. (2010). Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets. Applied Mathematical Modelling, 34, 3864–3870.

Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8, 338–356.

Zhang, Z.M. (2017). Interval-valued intuitionistic fuzzy Frank aggregation operators and their applications to multiple attribute group decision making. Neural Computing and Applications, 28(6), 1471–1501.

Zhao, X.F., Wei, G.W. (2013). Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making. Knowledge-Based Systems, 37, 472–479.

Zeng, S.Z. (2017). Pythagorean fuzzy multiattribute group decision making with probabilistic information and OWA approach. International Journal of Intelligent Systems, 32(11), 1136–1150.

Zeng, Marqués D. P, S.Z., Zhu, F.C. (2016). A new model for interactive group decision making with intuitionistic fuzzy preference relations. Informatica, 27(4), 911–928.

Biographies

Wei Guiwu

weiguiwu@163.com

G. Wei has an MSc and a PhD degree in applied mathematics from SouthWest Petroleum University, business administration from school of Economics and Management at SouthWest Jiaotong University, China, respectively. From May 2010 to April 2012, he was a postdoctoral researcher with the School of Economics and Management, Tsinghua University, Beijing, China. He is a professor in the School of Business at Sichuan Normal University. He has published more than 100 papers in journals, books and conference proceedings including journals such as Omega, Decision Support Systems, Expert Systems with Applications, Applied Soft Computing, Knowledge and Information Systems, Computers & Industrial Engineering, Knowledge-Based Systems, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, International Journal of Computational Intelligence Systems and Information: An International Interdisciplinary Journal. He has published one book. He has participated in several scientific committees and serves as a reviewer in a wide range of journals including Computers & Industrial Engineering, International Journal of Information Technology and Decision Making, Knowledge-Based Systems, Information Sciences, International Journal of Computational Intelligence Systems and European Journal of Operational Research. He is currently interested in aggregation operators, decision making and computing with words.

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Keywords

multiple attribute decision making (MADM) picture fuzzy sets (PFSs) picture fuzzy numbers (PFNs) TODIM, prospect theory

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