THE EXTENDED TOPSIS METHOD WITH INTERVAL-VALUED FUZZY SETS AND EXPERIMENTAL ANALYSIS ON SEPARATION MEASURES

Ting-Yu Chen (Taiwan) and Yi-Wen Li (Taiwan)

Received May 26, 2009

References:

[1] M. A. Abo-Sinna and A. H. Amer, Extensions of TOPSIS for multi-objective large-scale nonlinear programming problems, Appl. Math. Comput. 162(1) (2005), 243-256. [2] K. T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems 61(2) (1994), 137-142. [3] K. T. Atanassov, Intuitionistic fuzzy sets, theory and applications, Studies in Fuzziness and Soft Computing, 35, Physica-Verlag, Heidelberg, New York, 1999. [4] H. Bustince, E. Barrenechea, M. Pagola and J. Fernandez, Interval-valued fuzzy sets constructed from matrices: Application to edge detection, Fuzzy Sets and Systems 160 (13) (2009), 1819-1840. [5] C. T. Chen, Extensions of the TOPSIS for group decision-making under fuzzy environment, Fuzzy Sets and Systems 114(1) (2000), 1-9. [6] C. Cornelis, G. Deschrijver and E. E. Kerre, Advances and challenges in interval-valued fuzzy logic, Fuzzy Sets and Systems 157(5) (2006), 622-627. [7] M. Dağdeviren, S. Yavuz and N. Kılınç, Weapon selection using the AHP and TOPSIS methods under fuzzy environment, Expert Systems with Applications 36(4) (2009), 8143-8151. [8] W. L. Gau and D. J. Buehrer, Vague sets, IEEE Trans. Systems Man Cybernet. 23 (1993), 610-614. [9] M. B. Gorzalczany, A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems 21(1) (1987), 1-17. [10] P. Grzegorzewski, Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric, Fuzzy Sets and Systems 148(2) (2004), 319-328. [11] W. L. Hung and M. S. Yang, Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance, Pattern Recognition Letters 25(14) (2004), 1603-1611. [12] C. L. Hwang and K. Yoon, Multiple Attribute Decision Making. Methods and Applications, A state-of-the-art survey, Lecture Notes in Economics and Mathematical Systems, 186, Springer-Verlag, Berlin, New York, 1981. [13] G. R. Jahanshahloo, F. Hosseinzadeh Lotfi and M. Izadikhah, An algorithmic method to extend TOPSIS for decision-making problems with interval data, Appl. Math. Comput. 175 (2006), 1375-1384. [14] N. N. Karnik and J. M. Mendel, Operations on type-2 fuzzy sets, Fuzzy Sets and Systems 122(2) (2001), 327-348. [15] Z. Liang and P. Shi, Similarity measures on intuitionistic fuzzy sets, Pattern Recognition Letters 24 (2003), 2687-2693. [16] Y. H. Lin, P. C. Lee and H. I. Ting, Dynamic multi-attribute decision making model with grey number evaluations, Expert Systems with Applications 35 (2008), 1638-1644. [17] I. Mahdavi, N. Mahdavi-Amiri, A. Heidarzade and R. Nourifar, Designing a model of fuzzy TOPSIS in multiple criteria decision making, Appl. Math. Comput. 206 (2008), 607-617. [18] H. B. Mitchell, On the Dengfeng-Chuntian similarity measure and its application to pattern recognition, Pattern Recognition Letters 24(16) (2003), 3101-3104. [19] S. Opricovic and G. H. Tzeng, Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS, European J. Oper. Res. 156 (2004), 445-455. [20] R. Sambuc, Fonctions Φ-floues, Application a l’aide au diagnostic en pathologie thyroidienne, Ph.D. Thesis, University of Marseille, France, 1975. [21] E. Szmidt and J. Kacprzyk, Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems 114 (2000), 505-518. [22] I. B. Türksen, Interval valued fuzzy sets based on normal forms, Fuzzy Sets and Systems 20(2) (1986), 191-210. [23] I. B. Türksen, Interval-valued fuzzy sets and compensatory, Fuzzy Sets and Systems 51(3) (1992), 295-307. [24] İ. B. Türkşen and T. Bilgiç, Interval valued strict preference with Zadeh triples, Fuzzy multiple criteria decision making, Fuzzy Sets and Systems 78(2) (1996), 183-195. [25] I. K. Vlachos and G. D. Sergiadis, Subsethood, entropy and cardinality for interval-valued fuzzy sets – An algebraic derivation, Fuzzy Sets and Systems 158(12) (2007), 1384-1396. [26] T. C. Wang and H. D. Lee, Developing a fuzzy TOPSIS approach based on subjective weights and objective weights, Expert Systems with Applications 36 (2009), 8980-8985. [27] G. Wang and X. Li, The applications of interval-valued fuzzy numbers and interval-distribution numbers, Fuzzy Sets and Systems 98(3) (1998), 331-335. [28] W. Wang and X. Xin, Distances measure between intuitionistic fuzzy sets, Pattern Recognition Letters 26(1) (2005), 2053-2069. [29] H. Y. Wu, G. H. Tzeng and Y. H. Chem, A fuzzy MCDM approach for evaluating banking performance based on balanced scorecard, Expert Systems with Application 36 (2009), 10135-10147. [30] Z.-S. Xu and J. Chen, An interactive method for fuzzy multiple attribute group decision making, Inform. Sci. 177(1) (2007), 248-263. [31] T. Yang, M.-C. Chen and C.-C. Hung, Multiple attribute decision-making methods for the dynamic operator allocation problem, Math. Comput. Simulation 73(5) (2007), 285-299. [32] T. Yang and C. C. Hung, Multiple-attribute decision making methods for plant layout design problem, Robotics and Computer-Integrated Manufacturing 23(1) (2007), 126-137. [33] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I, Inform. Sci. 8 (1975), 199-249.

Keywords and phrases: interval-valued fuzzy set, multiple attribute decision analysis, TOPSIS, experimental analysis, separation measure.