Algorithms for estimating missing elements of incomplete intuitionistic preference relations

International Journal of Intelligent Systems

Volumn 26, Issue 9, 2011, Pages 787-813

  Xu, Zeshui ^a,b   Cai, Xiaoqiang ^b   Szmidt, Eulalia ^c  

^a Southeast University   (China)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^c SYSTEMS RESEARCH INSTITUTE   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

DECISION MAKING PROCESS; DECISION-MAKING PROBLEM; ESTIMATION ALGORITHM; INTUITIONISTIC FUZZY; MISSING INFORMATION; PREFERENCE RELATION; PROFESSIONAL KNOWLEDGE; REAL PROBLEMS; SOLUTION PROCESS;

DECISION MAKING; ESTIMATION; FUZZY SETS;

ALGORITHMS;

EID: 79960839565     PISSN: 08848173     EISSN: 1098111X     Source Type: Journal    
DOI: 10.1002/int.20494     Document Type: Article

References (58)

1. Herrera F, Herrera-Viedma E, Martínez L,. A fusion approach for managing multi-granularity linguistic term sets in decision making. Fuzzy Sets Syst. 2000; 114: 43-58.
2. Xu ZS,. Intuitionistic preference relations and their application in group decision making. Inform Sci. 2007; 177: 2363-2379.
3. Xu ZS,. An integrated model-based interactive approach to FMAGDM with incomplete preference information. Fuzzy Optim Decis Mak. 2010; 9: 333-357.
4. Xu ZS, Cai XQ,. Nonlinear optimization models for multiple attribute group decision making with intuitionistic fuzzy information. Int J Intell Syst. 2010; 25: 489-513.
5. Yager RR, Xu ZS,. The continuous ordered weighted geometric operator and its application to decision making. Fuzzy Sets Syst. 2006; 157: 1393-1402.
6. Ma J, Fan ZP, Huang LH,. A subjective and objective integrated approach to determine attribute weights. Eur J Oper Res. 1999; 112: 397-404.
7. Wang YM, Parkan C,. Optimal aggregation of fuzzy preference relations with an application to broadband internet service selection. Eur J Oper Res. 2008; 187: 1476-1486. (Pubitemid 350236650)
8. Xu ZS,. Group decision making based on multiple types of linguistic preference relations. Inform Sci. 2008; 178: 452-467.
9. Xu ZS,. A survey of preference relations. Int J Gen Syst. 2007; 36: 179-203.
10. Bustince H, Burillo P, Soria F,. Automorphisms, negations and implication operators. Fuzzy Sets and Systems. 2003; 134: 209-229.
11. Bustince H, Barrenechea E, Pagola M,. Generation of interval-valued fuzzy and Atanassov's intuitionistic fuzzy connectives from fuzzy connectives and from K-alpha operators: laws for conjunctions and disjunctions, amplitude. Int J Intell Syst. 2008; 23: 680-714.
12. Bustince H, Herrera F, Montero J,. Fuzzy sets and their extensions: representation, aggregation and models. Berlin, Germany: Springer-Verlag; 2008.
13. Chiclana F, Herrera F, Herrera-Viedma E,. Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets Syst. 1998; 97: 33-48. (Pubitemid 128654877)
14. Herrera F, Herrera-Viedma E, Chiclana F,. Multiperson decision-making based on multiplicative preference relations. Eur J Oper Res. 2001; 129: 372-385. (Pubitemid 32035361)
15. Herrera F, Herrera-Viedma E, Verdegay JL,. A model of consensus in group decision making under linguistic assessments. Fuzzy Sets Syst. 1996; 78: 73-87. (Pubitemid 126667360)
16. Herrera F, Herrera-Viedma E, Verdegay JL,. Direct approach processes in group decision making using linguistic OWA operators. Fuzzy Sets Syst. 1996; 79: 175-190. (Pubitemid 126667399)
17. Herrera F, Herrera-Viedma E, Verdegay JL,. A rational consensus model in group decision making using linguistic assessments. Fuzzy Sets Syst. 1997; 88: 31-49. (Pubitemid 127699073)
18. Kacprzyk J, Roubens M,. Non-conventional preference relations in decision-making. Berlin, Germany: Springer-Verlag; 1988.
19. Ma J, Fan ZP, Jiang YP, Mao JY,. An optimization approach to multiperson decision making based on different formats of preference information. IEEE Trans Syst Man Cybern A. 2006; 36: 876-889.
20. Ãnüt S, Efendigil T, Kara SS,. A combined fuzzy MCDM approach for selecting shopping center site: an example from Istanbul, Turkey. Expert Syst Appl 2010; 37: 1973-1980.
21. Orlovsky SA,. Decision-making with a fuzzy preference relation. Fuzzy Sets Syst 1978; 1: 155-167.
22. Saaty TL,. The analytic hierarchy process. New York: McGraw-Hill; 1980.
23. Tanino T,. Fuzzy preference orderings in group decision making. Fuzzy Sets Syst. 1984; 12: 117-131. (Pubitemid 14569423)
24. Lootsma FA,. Saaty's priority theory and the nomination of a senior professor in operations research. Eur J Oper Res. 1980; 4: 380-388.
25. van Laarhoven PJM, Pedrycz W,. A fuzzy extension of Saaty's priority theory. Fuzzy Sets Syst. 1983; 11: 199-227.
26. Xu ZS,. A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inform Sci. 2004; 166: 19-30.
27. Xu ZS,. Deviation measures of linguistic preference relations in group decision making. Omega. 2005; 33: 249-254.
28. Xu ZS, Chen J,. Some models for deriving the priority weights from interval fuzzy preference relations. Eur J Oper Res. 2008; 184: 266-280. (Pubitemid 47368918)
29. Xu ZS, Wei CP,. A consistency improving method in the analytic hierarchy process. Eur J Oper Res. 1999; 116: 443-449.
30. Xu ZS,. On compatibility of interval fuzzy preference matrices. Fuzzy Optim Decis Mak. 2004; 3: 217-225.
31. Xu ZS, Cai XQ, Liu SS,. Nonlinear programming model integrating different preference structures. IEEE Trans Syst Man Cybern A. 2011; 41: 169-177.
32. Yager RR, Kacprzyk J,. The ordered weighted averaging operators: Theory and applications. Boston, MA: Kluwer Academic; 1997.
33. Szmidt E, Kacprzyk J,. Using intuitionistic fuzzy sets in group decision making. Control Cybern. 2002; 31: 1037-1053. (Pubitemid 36699124)
34. Szmidt E, Kacprzyk J,. A consensus-reaching process under intuitionistic fuzzy preference relations. Int J Intell Syst. 2003; 18: 837-852.
35. Szmidt E, Kacprzyk J,. A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. Lect Notes Artif Intell. 2004; 3070: 388-393. (Pubitemid 38835852)
36. Xu ZS,. Approaches to multiple attribute decision making with intuitionistic fuzzy preference information. Syst EngâTheory Pract. 2007; 27: 62-71.
37. Xu ZS, Yager RR,. 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. 2009; 8: 123-139.
38. Xu ZS,. A method for estimating criteria weights from intuitionistic preference relations. Fuzzy Inform Eng. 2009; 1: 79-89.
39. Xu ZS, Cai XQ,. Incomplete interval-valued intuitionistic preference relations. Int J Gen Syst. 2009; 38: 871-886.
40. Yager RR,. On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans Syst Man Cybern. 1988; 18: 183-190.
41. Yager RR,. Families and extension of OWA aggregation. Fuzzy Sets Syst. 1993; 59: 125-148.
42. Atanassov K,. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986; 20: 87-96.
43. Szmidt E, Kacprzyk J,. Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst. 2000; 114: 505-518.
44. Szmidt E, Kacprzyk J,. Distances between intuitionistic fuzzy sets: straightforward approaches may not work. In: 3rd Int IEEE Conf on Intelligent Systems (IEEE IS'06), London; 2006. 716-721.
45. Szmidt E, Kacprzyk J,. Some remarks on the Hausdorff distance between Atanassov's intuitionistic fuzzy sets. In: EUROFUSE Workshop'09. Preference Modelling and Decision Analysis, Pamplona, Spain; 2009. 311-316.
46. Szmidt E, Kacprzyk J,. Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst. 2001; 118: 467-477. (Pubitemid 32070574)
47. Szmidt E, Kacprzyk J,. Some problems with entropy measures for the Atanassov intuitionistic fuzzy sets. Lect Notes Artif Intell. 2001; 4578: 291-297.
48. Szmidt E, Kacprzyk J,. A new similarity measure for intuitionistic fuzzy sets: straightforward approaches may not work. In: 2007 IEEE Conf on Fuzzy Systems; 2007. 481-486.
49. Szmidt E, Kacprzyk J,. Amount of information and its reliability in the ranking of Atanassov's intuitionistic fuzzy alternatives. In:, Rakus-Andersson E, Yager R, Ichalkaranje N, Jain L, editors. Recent advances in decision making (Studies in Computational Intelligence). Berlin, Germany: Springer; 2009. 7-19.
50. Szmidt E, Kacprzyk J,. Ranking of intuitionistic fuzzy alternatives in a multi-criteria decision making problem. In: The 28th North American Fuzzy Information Processing Society Ann Conf (NAFIPS2009), Cincinnati, OH; June 2009. 14-17.
51. Szmidt E, Kacprzyk J,. Correlation between intuitionistic fuzzy sets. In:, Hullermeier E, Kruse R, Hoffmann F, editors. Computational intelligence for knowledge-based systems design. Lect Notes Artif Intell 2010;6178: 169-177.
52. Szmidt E, Kukier M,. Atanassov's intuitionistic fuzzy sets in classification of imbalanced and overlapping classes. In:, Chountas P, Petrounias I, Kacprzyk J, editors. Intelligent techniques and tools for novel system architectures (Studies in Computational Intelligence). Berlin, Germany: Springer; 2008. 455-471.
53. Hwang CL, Yoon K,. Multiple attribute decision making: Methods and applications. Berlin, Germany: Springer-Verlag; 1981.
54. Xu ZS,. Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst. 2007; 15: 1179-1187.
55. Xu ZS, Yager RR,. Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst. 2006; 35: 417-433. (Pubitemid 44726498)
56. Xu ZS, Yager RR,. Dynamic intuitionistic fuzzy multi-attribute decision making. Int J Approx Reason. 2008; 48: 246-262. (Pubitemid 351324070)
57. Beliakov G, Bustince H, Goswami DP, Mukherjee UK, Pal NR,. On averaging operators for Atanassov's intuitionistic fuzzy sets. Inform Sci. 2011; 181: 1116-1124.
58. Deschrijver G, Kerre EE,. Aggregation operators in interval-valued fuzzy and Atanassov's intuitionistic fuzzy set theory. In:, Bustince H, Herrera F, Montero J, editors. Fuzzy sets and their extensions: Representation, aggregation and models. Heidelberg, Germany: Springer; 2008. 183-203.