Weak and graded properties of fuzzy relations in the context of aggregation process

Fuzzy Sets and Systems

Volumn 161, Issue 2, 2010, Pages 216-233

  Dudziak, Urszula ^a  

^a UNIVERSITY OF RZESZÓW   (Poland)

Author keywords

Aggregation functions; Fuzzy connectives; Fuzzy relations

Indexed keywords

AGGREGATION FUNCTIONS; AGGREGATION PROCESS; ANTI-SYMMETRIC; BASIC PROPERTIES; FUZZY CONNECTIVES; FUZZY RELATIONS; PARAMETERIZED;

AGGLOMERATION;

EID: 70449726596     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2009.07.002     Document Type: Article

References (43)

1. Bandler W., and Kohout L. Special properties, closures and interiors of crisp and fuzzy relations. Fuzzy Sets Syst. 26 (1988) 317-331
2. Barrett R., and Salles M. Social choice with fuzzy preferences. In: Arrow K.I., et al. (Ed). Handbook of Social Choice and Welfare (2006), North-Holland, Amsterdam 1-19
3. G. Beliakov, A. Pradera, T. Calvo, Aggregation Functions: A Guide for Practitioners, Studies in Fuzziness and Soft Computing, Vol. 221, Springer, Berlin, 2007.
4. Bezdek J.C., and Harris J.D. Fuzzy partitions and relations: an axiomatic basis for clustering. Fuzzy Sets Syst. 1 (1978) 111-127
5. U. Bodenhofer, A similarity-based generalization of fuzzy orderings, Ph.D. Thesis, Universitätsverlag Rudolf Trauner, Linz, 1999.
6. Calvo T., Kolesárová A., Komorniková M., and Mesiar R. Aggregation operators: properties, classes and construction methods. In: Calvo T., et al. (Ed). Aggregation Operators (2002), Physica-Verlag, Heidelberg 3-104
7. Chakraborty M.K., and Das M. On fuzzy equivalence I. Fuzzy Sets Syst. 11 (1983) 185-193
8. Chenggong H. Canonical form of strongly transitive matrices over lattice. Fuzzy Sets Syst. 45 (1992) 219-222
9. Chiclana F., Herrera-Viedma E., Alonso S., and Pereira R.A.M. Preferences and consistency issues in group decision making. In: Bustince H., Herrera F., and Montero J. (Eds). Fuzzy Sets and their Extensions: Representation, Aggregation and Models. Intelligent Systems from Decision Making to Data Mining, Web Intelligence and Computer Vision (2008), Springer, Berlin 219-237
10. Dubois D., and Prade H. Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press, New York
11. Drewniak J. Fuzzy Relation Calculus (1989), Silesian University, Katowice
12. Drewniak J., Drygaś P., and Dudziak U. Domination between multiple operations. In: Hryniewicz O., et al. (Ed). Issues in Soft Computing Decisions and Operations Research (2005), EXIT, Warszawa 149-160
13. Drewniak J., and Dudziak U. Aggregations in classes of fuzzy relations. Ann. Acad. Paed. Cracoviensis 33 Studia Math. 5 (2006) 33-43
14. Dudziak U. Aggregations preserving graded properties of fuzzy relations. In: Atanassov K.T., et al. (Ed). Soft Computing Foundations and Theoretical Aspects (2004), EXIT, Warszawa 191-203
15. Dudziak U. Graded properties of fuzzy relations in aggregation process. J. Electrical Eng. 56 12/s (2005) 56-58
16. Dudziak U. Weak transitivity properties of fuzzy relations and their preservation by operations. J. Electrical Eng. 57 7/s (2006) 74-77
17. U. Dudziak, Preservation of graded properties of fuzzy relations by aggregation functions, in: M. Štěpnička et al. (Eds.), New Dimensions in Fuzzy Logic and Related Technologies, Proc. 5th EUSFLAT Conf., Ostrava, Czech Republic, September 11-14, 2007, Universitas Ostraviensis, Vol. II, 2007, pp. 359-364.
18. Dudziak U. Graded transitivity and aggregation processes. Sci. Bull. Chełm, Sect. Math. Comput. Sci. 1 (2007) 31-39
19. Fishburn P.C. Binary choice probabilities: on the varieties of stochastic transitivity. J. Math. Psych. 10 (1973) 327-352
20. Fodor J., and Roubens M. Fuzzy Preference Modelling and Multicriteria Decision Support (1994), Kluwer Academic Publishers, Dordrecht
21. González L., and Marín A. Weak properties and aggregated extension of fuzzy relations. Fuzzy Sets Syst. 85 (1997) 311-318
22. Grabisch M., Marichal J.-L., Mesiar R., and Pap E. Aggregation Functions (2009), Cambridge University Press, Cambridge
23. Klement E.P., Mesiar R., and Pap E. Triangular Norms (2000), Kluwer Academic Publishers, Dordrecht
24. Kołodziejczyk W. Orlovsky's concepts of decision-making with fuzzy preference relation-further results. Fuzzy Sets Syst. 19 (1986) 11-20
25. Li D.-F. Multiattribute decision making models and method using intuitionistic fuzzy sets. J. Comput. Syst. Sci. 70 (2005) 73-85
26. Mesiar R., and Saminger S. Domination of ordered weighted averaging operators over t-norms. Soft Comput. 8 (2004) 562-570
27. Nakamura K. Preference relations on a set of fuzzy utilities as a basis for decision making. Fuzzy Sets Syst. 20 (1986) 147-162
28. Orlovsky S.A. Decision-making with a fuzzy preference relation. Fuzzy Sets Syst. 1 (1978) 155-167
29. Peneva V., and Popchev I. Aggregation of fuzzy relations. C. R. Acad. Bulgare Sci. 51 9-10 (1998) 41-44
30. Peneva V., and Popchev I. Properties of the aggregation operators related with fuzzy relations. Fuzzy Sets Syst. 139 3 (2003) 615-633
31. Peneva V., and Popchev I. Aggregation of fuzzy preference relations to multicriteria decision making. Fuzzy Optim. Decision Making 6 (2007) 351-365
32. Roubens M., and Vincke P. Preference Modelling (1985), Springer, Berlin
33. Saminger S., Mesiar R., and Bodenhofer U. Domination of aggregation operators and preservation of transitivity. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 10 Suppl. (2002) 11-35
34. Saminger S., De Baets B., and De Meyer H. On the dominance relation between ordinal sums of conjunctors. Kybernetika 42 2 (2006) 337-350
35. Saminger S., Sarkoci P., and De Baets B. The dominance relation on the class of continuous ordinal sum t-norms. In: de Swart H.C.M., Orłowska E., Roubens M., and Schmidt G. (Eds). Theory and Applications of Relational Structures as Knowledge Instruments II, Lecture Notes in Computer Science (2006), Springer, Berlin 337-357
36. Saminger-Platz S., Mesiar R., and Dubois D. Aggregation operators and commuting. IEEE Trans. Fuzzy Syst. 15 6 (2007) 1032-1045
37. Sarkoci P. Domination in the families of Frank and Hamacher t-norms. Kybernetika 41 (2005) 345-356
38. Sarkoci P. Dominance is not transitive on continuous triangular norms. Aequationes Math. 75 (2008) 201-207
39. Schweizer B., and Sklar A. Probabilistic Metric Spaces (1983), North-Holland, Amsterdam
40. Torra V., and Narukawa Y. Modelling Decisions. Information Fusion and Aggregation Operators (2007), Springer, Berlin
41. Venugopalan P. Fuzzy ordered sets. Fuzzy Sets Syst. 46 (1992) 221-226
42. Wang X. An investigation into relations between some transitivity related concepts. Fuzzy Sets Syst. 89 (1997) 257-262
43. Zadeh L.A. Similarity relations and fuzzy orderings. Inform. Sci. 3 (1971) 177-200