Abstract
Xu and Chen (J Syst Sci Syst Eng 17:432–445, 2008) introduced a new decision-making technique called the ordered weighted distance (OWD) measure, having been proved useful for the treatment of situation where the available information is represented in exact numerical values. In this paper, we consider the situations with intuitionistic fuzzy and interval-valued intuitionistic information, and develop some intuitionistic fuzzy weighted distance measures such as intuitionistic fuzzy ordered weighted distance (IFOWD) measure, interval-valued intuitionistic fuzzy ordered weighted distance (IVIFOWD) measure, intuitionistic fuzzy hybrid weighted distance (IFHWD) measure and interval-valued intuitionistic fuzzy hybrid weighted distance (IVIFHWD) measure. These developed weighted distance measures are very suitable to deal with the situation where the input data are represented in intuitionistic fuzzy numbers or interval-lvalued intuitionistic fuzzy numbers. Then we present a consensus reaching process for group decision making with intuitionistic fuzzy preference information based on the developed distance measures. Finally, a practical application of he developed approach to the problem of evaluating university faculty for tenure and promotion is given.
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References
Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20: 87–96
Atanassov K, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31: 343–349
Atanassov K, Pasi G, Yager RR (2005) Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. Int J Syst Sci 36: 859–868
Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. Springer, Berlin
Bogart KP (1975) Preference structures II: distances between asymetric relations. SIAM Journal of Applied Mathematics 29: 254–262
Bolton J, Gader P, Wilson JN (2008) Choquet integral as a distance measure. IEEE Trans Fuzzy Syst 16: 1107–1110
Boran FE, Genc S, Kurt M, Akay D (2009) A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Syst Appl 36: 11363–11368
Bryson N, Mobolurin A (1995) An action learning evaluation procedure for multiple criteria decision making problems. Eur J Oper Res 96: 379–386
Chen SJ, Chen SM (2003) A new method for handling multi-criteria fuzzy decision-making problems using FN-IOWA operators. Cybern Syst 34: 109–137
Cheng CH, Wang JW, Wu MC (2009) OWA-weighted based clustering method for classification problem. Expert Syst Appl 36: 4988–4995
Hamming RW (1950) Error-detecting and error-correcting codes. Bell Syst Tech J 29: 147–160
Herrera-Viedma E, Chiclana F, Herrera F, Alonso S (2007) Group decision making model with incomplete fuzzy preference relations based on additive consistency. IEEE Trans Syst Man Cybern B 37: 176–189
Kacprzyk J (1997) Multistage Fuzzy Control: A model-based approach to control and decision-making. Wiley, Chichester
Karayiannis N (2000) Soft learning vector quantization and clustering algorithms based on ordered weighted aggregation operators. IEEE Trans Neural Netw 11: 1093–1105
Kaufmann A (1975) Introduction to the theory of fuzzy subsets. Academic Press, New York
Liu X (2008) A general model of parameterized OWA aggregation with given orness level. Int J Approx Reason 48: 598–627
Liu PD (2009) A novel method for hybrid multiple attribute decision making. Knowl Based Syst 22: 388–391
Merigó JM, Casanovas M (2010) Decision making with distance measures and linguistic aggregation operators. Int J Fuzzy Syst 12: 190–198
Merigó JM, Casanovas M (2011a) Decision making with distance measures and induced aggregation operators. Comput Ind Eng 60: 66–76
Merigó JM, Casanovas M (2011b) The uncertain induced quasi-arithmetic OWA operator. Int J Intell Syst 26: 1–24
Merigó JM, Gil-Lafuente AM (2008) Using the OWA operator in the Minkowski distance. Int J Electr Comput Eng 3: 149–157
Merigó JM, Gil-Lafuente AM (2010) New decision making techniques and their application in the selection of financial products. Inf Sci 180: 2085–2094
Szmidt E, Kacprzyk J (2000) Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst 114: 505–518
Szmidt E, Kacprzyk J (2002) Using intuitonistic fuzzy sets in group making. Control Cybern 31: 1017–1053
Szmidt E, Kacprzyk J (2003) A consensus-reaching process under intuitionistic fuzzy preference relations. Int J Intell Syst 18: 837–852
Tan CQ, Chen XH (2010) Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making. Expert Syst Appl 37: 149–157
Wang P (2009) Qos-aware web services selection with intuitionistic fuzzy set under consumer’s vague perception. Expert Syst Appl 36: 4460–4466
Wei GW (2008) Maximizing deviation method for multiple attribute decision making in intuitionistic fuzzy setting. Knowl Based Syst 21: 833–836
Wei GW (2009) Uncertain linguistic hybrid geometric mean operator and its application to group decision making under uncertain linguistic environment. Int J Uncertain Fuzziness Knowl Based Syst 17: 251–267
Wei GW (2010a) Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Appl Soft Comput 10: 423–431
Wei GW (2010b) GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting. Knowl Based Syst 23: 243–247
Wei GW, Zhao X, Lin R (2010) Some induced aggregating operators with fuzzy number intuitionistic fuzzy information and their applications to group decision making. Int J Comput Intell Syst 3: 84–95
Xu ZS (2005) An overview of methods for determining OWA weights. Int J Intell Syst 20: 843–865
Xu ZS (2007a) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15: 1179–1187
Xu ZS (2007b) Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optim Decis Mak 6: 109–121
Xu ZS (2007c) Multi-person multi-attribute decision making models under intuitionistic fuzzy environment. Fuzzy Optim Decis Mak 6: 221–236
Xu ZS (2007d) Intuitionistic preference relations and their application in group decision making. Info Sci 177: 2363–2379
Xu ZS (2007e) Models for multiple attribute decision making with intuitionistic fuzzy information. Int J Uncertain Fuzziness Knowl Based Syst 15: 285–297
Xu ZS (2007f) Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control Decis 22: 215–219
Xu ZS (2008) Dependent uncertain ordered weighted averaging operators. Info Fusion 9: 310–316
Xu ZS (2010a) A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Info Sci 180: 181–190
Xu ZS (2010b) A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making. Group Decis Negotiat 19: 57–76
Xu ZS, Cai XQ (2009) Incomplete interval-valued intuitionistic preference relations. Int J Gen Syst 38: 871–886
Xu ZS, Cai XQ (2010) Nonlinear optimization models for multiple attribute group decision making with intuitionistic fuzzy information. Int J Intell Syst 25: 489–513
Xu ZS, Chen J (2007) An approach to group decision making based on interval-valued intuitionistic judgment matrices. Syst Eng Theory Pract 27: 126–133
Xu ZS, Chen J (2008) Ordered weighted distance measure. J Syst Sci Syst Eng 17: 432–445
Xu ZS, Xia M (2010) Induced generalized intuitionistic fuzzy operators. Knowledge-Based Systems in press,
Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35: 417–433
Xu ZS, Yager RR (2008) Dynamic intuitionistic fuzzy multiple attribute decision making. Int J Approx Reason 48: 246–262
Xu ZS, Yager RR (2009) Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim Decis Mak 8: 123–139
Yager RR (1988) On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans Syst Man Cybern B 18: 183–190
Yager RR (2003) Induced aggregation operators. Fuzzy Sets Syst 137: 59–69
Yager RR (2007) Centered OWA operators. Soft Comput 11: 631–639
Yager RR (2009a) Weighted maximum entropy OWA aggregation with applications to decision making under risk. IEEE Trans Syst Man Cybern A 39: 555–564
Yager RR (2009b) Prioritized OWA aggregation. Fuzzy Optim Decis Mak 8: 245–262
Yager RR (2010) Norms induced from OWA operators. IEEE Trans Fuzzy Syst 18: 57–66
Ye J (2009) Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment. Expert Syst Appl 36: 6899–6902
Ye J (2010) Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment. Eur J Oper Res 205: 202–204
Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning, Part-I. Info Sci 8: 199–249
Zarghami M, Szidarovszky F (2009) Revising the OWA operator for fuzzy stochastic multi criteria decision making. Eur J Oper Res 198: 259–265
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Zeng, S. Some Intuitionistic Fuzzy Weighted Distance Measures and Their Application to Group Decision Making. Group Decis Negot 22, 281–298 (2013). https://doi.org/10.1007/s10726-011-9262-6
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DOI: https://doi.org/10.1007/s10726-011-9262-6