Equivalent bipolar fuzzy relations

Fuzzy Sets and Systems

Volumn 161, Issue 2, 2010, Pages 234-253

  Dudziak, Urszula ^a   Pȩkala, Barbara ^a  

^a UNIVERSITY OF RZESZÓW   (Poland)

Author keywords

Atanassov's intuitionistic fuzzy relations; Bipolar fuzzy relations; Fuzzy relations

Indexed keywords

EQUIVALENCE RELATIONS; FUZZY RELATIONS; INTUITIONISTIC FUZZY RELATIONS;

FUZZY SETS;

EID: 70449704301     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2009.06.016     Document Type: Article

References (44)

1. Angelov P.P. Optimization in an intuitionistic fuzzy environment. Fuzzy Sets and Systems 86 (1997) 299-306
2. K.T. Atanassov, Intuitionistic fuzzy sets, VII ITKR's Scientific Session, June 1983, Sofia, Deposed in Central Science-Technical, Library of Bulgarian Academy of Science 1697/84, 1983 (in Bulgarian).
3. K.T. Atanassov, Intuitionistic fuzzy relations, in: Proc. Third Internat. Sympos. Automation and Scientific Instrumentation, Varna, October, Part II, 1984, pp. 56-57.
4. Atanassov K.T. Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20 (1986) 87-96
5. Atanassov K.T., and Gargov G. Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 31 (1989) 343-349
6. Atanassov K.T. Intuitionistic Fuzzy Sets (1999), Physica-Verlag, Heidelberg, New York
7. Bandler W., and Kohout L.J. Special properties, closures and interiors of crisp and fuzzy relations. Fuzzy Sets and Systems 26 (1988) 317-331
8. Benferhat S., Dubois D., Kaci S., and Prade H. Bipolar possibility theory in preference modelling: representation, fusion and optimal solutions. Inf. Fusion 7 1 (2006) 135-150
9. Bhattacharya P. Fuzzy groups: some characterizations. J. Math. Anal. Appl. 128 (1987) 241-252
10. Birkhoff G. Lattice Theory (1967), AMS Collaboration Publication XXV, Providence
11. Burillo P., and Bustince H. Intuitionistic fuzzy relations. Effect of Atanassov's operators on the properties of the intuitionistic fuzzy relations. Math. Soft Comput. 2 (1995) 117-148
12. Bustince H., and Burillo P. Structures on intuitionistic fuzzy relations. Fuzzy Sets and Systems 78 (1996) 293-303
13. Bustince H. Construction of intuitionistic fuzzy relations with predetermined properties. Fuzzy Sets and Systems 109 (2000) 379-403
14. Cacioppo J.T., Gardner W.L., and Berntson G.G. Beyond bipolar conceptualization and measures: the case of attitudes and evaluative spaces. Pers. Soc. Psychol. Rev. 1 (1997) 3-25
15. Cia̧pała T., and Drewniak J. Equivalent fuzzy sets. In: Hryniewicz O., et al. (Ed). Issues in Intelligent Systems (2005), EXIT, Warszawa 19-26
16. Davey B.A., and Pristley H.A. Introduction to Lattices and Orders (1990), Cambridge University Press, Cambridge
17. Dawyndt P., De Meyer H., and De Baets B. The complete linkage clustering algorithm revisited. Soft Comput. 9 (2005) 385-392
18. De Baets B., and De Meyer H. On the existence and construction of T-transitive closures. Inf. Sci. 152 (2003) 167-179
19. De Meyer H., Naessens H., and De Baets B. Algorithms for computing the min-transitive closure and associated partition tree of a symmetric fuzzy relation. Eur. J. Oper. Res. 155 (2004) 226-238
20. G. Deschrijver, E.E. Kerre, A generalization of operators on intuitionistic fuzzy sets using triangular norms and conorms, in: Notes on IFS, Vol. 8, no. 1, 2002, pp. 19-27.
21. Deschrijver G., and Kerre E.E. On the composition of intuitionistic fuzzy relations. Fuzzy Sets and Systems 136 3 (2003) 333-361
22. Deschrijver G., and Kerre E.E. On the relationship between some extensions of fuzzy set theory. Fuzzy Sets and Systems 133 2 (2003) 227-235
23. Deschrijver G., and Kerre E.E. On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision. Inf. Sci. 177 (2007) 1860-1866
24. Drewniak J., and Pȩkala B. Equivalent matrices of fuzzy relations. In: Hryniewicz O., et al. (Ed). Issues in Intelligent Systems (2005), EXIT, Warszawa 39-48
25. Drewniak J., and Dudziak U. Local properties of fuzzy relations. In: Hryniewicz O., et al. (Ed). Issues in Soft Computing. Decisions and Operations Research (2005), EXIT, Warszawa 161-170
26. Dubois D., Gottwald S., Hajek P., Kacprzyk J., and Prade H. Terminological difficulties in fuzzy set theory-the case of "Intuitionistic Fuzzy Sets". Fuzzy Sets and Systems 156 (2005) 485-491
27. Dubois D., and Prade H. An introduction to bipolar representations of information and preference. Int. J. Intell. Syst. 23 8 (2008) 866-877
28. Dudziak U., and Pȩkala B. Equivalent bifuzzy sets. In: Atanassov K., et al. (Ed). Developments in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics. Foundations Vol. I (2008), EXIT, Warszawa 97-105
29. Gerstenkorn T., and Mańko J. Bifuzzy probabilistic sets. Fuzzy Sets and Systems 71 (1995) 207-214
30. T. Gerstenkorn, A. Tepavčević, Lattice valued bifuzzy sets, in: VIII SIGEF Congress (Internat. Assoc. for Fuzzy-set Management and Economy), New Logics for the New Economy, Naples, Italy, September 20-21, 2001. G. Zollo (Ed.), Edizioni Scientifiche Italiane 2001. Extended abstract, Dipartimento di Ingegneria Economico-Gestionale, Universita di Napoli Federico II, pp. 65-68.
31. Gerstenkorn T., and Tepavčević A. Lattice valued intuitionistic fuzzy relations and applications. In: Atanassov K.T., et al. (Ed). Soft Computing Foundations and Theoretical Aspects (2004), EXIT, Warszawa 221-234
32. Lee H.S. An optimal algorithm for computing the max - min transitive closure of a fuzzy similarity matrix. Fuzzy Sets and Systems 123 (2001) 129-136
33. Li D.-F. Multiattribute decision making models and method using intuitionistic fuzzy sets. J. Comput. Syst. Sci. 70 (2005) 73-85
34. Lin L., Yuan X.-H., and Xia Z.-Q. Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets. J. Comput. System Sci. 73 (2007) 84-88
35. Murali V., and Makamba B.B. On an equivalence of fuzzy subgroups I. Fuzzy Sets and Systems 123 (2001) 259-264
36. Murali V. Fuzzy points of equivalent fuzzy subsets. Inf. Sci. 158 (2004) 277-288
37. Naessens H., De Meyer H., and De Baets B. Algorithms for the computation of T-transitive closures. IEEE Trans. Fuzzy Systems 10 (2002) 541-551
38. Pankowska A., and Wygralak M. A general concept of IF-sets with triangular norms. In: Atanassov K., et al. (Ed). Soft Computing Foundations and Theoretical Aspects (2004), EXIT, Warszawa 319-335
39. Šešelja B., and Tepavčević A. A note on natural equivalence relation on fuzzy power set. Fuzzy Sets and Systems 148 (2004) 201-210
40. Wang X., and Kerre E.E. Reasonable properties for the ordering of fuzzy quantities I II. Fuzzy Sets and Systems 118 (2001) 375-385 387-405
41. Warren R.H. Equivalent fuzzy sets. Fuzzy Sets and Systems 6 (1981) 309-312
42. Zadeh L.A. Fuzzy sets. Inf. Control 8 (1965) 338-353
43. Zadeh L.A. Similarity relations and fuzzy orderings. Inf. Sci. 3 (1971) 177-200
44. Zadeh L.A. The concept of a linguistic variable and its application to approximate reasoning-I. Inf. Sci. 8 (1975) 199-249