Uniform fuzzy relations and fuzzy functions

Fuzzy Sets and Systems

Volumn 160, Issue 8, 2009, Pages 1054-1081

  Ćirić, Miroslav ^a   Ignjatović, Jelena ^a   Bogdanović, Stojan ^a  

^a UNIVERSITY OF NI   (Serbia)

Author keywords

Complete residuated lattice; Fuzzy equivalence; Fuzzy partition; Fuzzy relation; Partial fuzzy function; Perfect fuzzy function; Uniform fuzzy relation

Indexed keywords

COMPLETE RESIDUATED LATTICE; FUZZY EQUIVALENCE; FUZZY PARTITION; FUZZY RELATION; PARTIAL FUZZY FUNCTION; PERFECT FUZZY FUNCTION; UNIFORM FUZZY RELATION;

FUZZY CONTROL;

EID: 60949094094     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2008.07.006     Document Type: Article

References (35)

1. Bandler W., and Kohout L.J. Fuzzy relational products as a tool for analysis and synthesis of the behaviour of complex natural and artificial systems. In: Wang S.K., and Chang P.P. (Eds). Fuzzy Sets: Theory and Application to Policy Analysis and Information Systems (1980), Plenum Press, New York 341-367
2. Bělohlávek R. Fuzzy Relational Systems: Foundations and Principles (2002), Kluwer, New York
3. Cerruti U., and Höhle U. An approach to uncertainty using algebras over a monoidal closed category. Rend. Circ. Mat. Palermo (2) 12 Suppl. (1986) 47-63
4. Ćirić M., Ignjatović J., and Bogdanović S. Fuzzy equivalence relations and their equivalence classes. Fuzzy Sets and Systems 158 (2007) 1295-1313
5. De Baets B., and Kerre E. The cutting of compositions. Fuzzy Sets and Systems 62 (1994) 295-309
6. De Baets B., and Mesiar R. T-partitions. Fuzzy Sets and Systems 97 (1998) 211-223
7. De Cock M., and Kerre E.E. Fuzzy modifiers based on fuzzy relations. Inform. Sci. 160 (2004) 173-199
8. Demirci M. Fuzzy functions and their fundamental properties. Fuzzy Sets and Systems 106 (1999) 239-246
9. Demirci M. Vague groups. J. Math. Anal. Appl. 230 (1999) 142-156
10. Demirci M. Fuzzy functions and their applications. J. Math. Anal. Appl. 252 (2000) 495-517
11. Demirci M. Gradation of being fuzzy function. Fuzzy Sets and Systems 119 (2001) 383-392
12. Demirci M. Construction of fuzzy functions based on fuzzy equalities. Soft Comput. 7 (2003) 199-207
13. Demirci M. Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations. Part I: fuzzy functions and their applications. Internat. J. Gen. Systems 32 (2003) 123-155
14. Demirci M. Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations. Part II: vague algebraic notions. Internat. J. Gen. Systems 32 (2003) 157-175
15. Demirci M. Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations. Part III: constructions of vague algebraic notions and vague arithmetic operations. Internat. J. Gen. Systems 32 (2003) 177-201
16. Demirci M. On many-valued partitions and many valued equivalence relations. Internat. J. Uncertainty Fuzziness Knowledge-Based Systems 11 (2003) 235-253
17. Demirci M. A theory of vague lattices based on many-valued equivalence relations-I: general representation results. Fuzzy Sets and Systems 151 (2005) 437-472
18. Demirci M., and Recasens J. Fuzzy groups, fuzzy functions and fuzzy equivalence relations. Fuzzy Sets and Systems 144 (2004) 441-458
19. Höhle U. Quotients with respect to similarity relations. Fuzzy Sets and Systems 27 (1988) 31-44
20. Höhle U. Commutative, residuated ℓ-monoids. In: Höhle U., and Klement E.P. (Eds). Non-Classical Logics and Their Applications to Fuzzy Subsets (1995), Kluwer Academic Publishers, Boston, Dordrecht 53-106
21. Höhle U. On the fundamentals of fuzzy set theory. J. Math. Anal. Appl. 201 (1996) 786-826
22. J. Ignjatović, M. Ćirić, S. Bogdanović, Fuzzy homomorphisms of algebras, Fuzzy Sets and Systems, to appear.
23. Klawonn F. Fuzzy points, fuzzy relations and fuzzy functions. In: Novâk V., and Perfilieva I. (Eds). Discovering World with Fuzzy Logic (2000), Physica-Verlag, Heidelberg 431-453
24. Klawonn F., Gebhardt J., and Kruse R. Fuzzy control on the basis of equality relations-with an example from idle speed control. IEEE Trans. Fuzzy Systems 3 (1995) 336-350
25. Klawonn F., and Kruse R. Equality relations as a basis for fuzzy control. Fuzzy Sets and Systems 54 (1993) 147-156
26. Klawonn F., and Kruse R. From fuzzy sets to indistinguishability and back. In: Steele N. (Ed). Proc. 1st ICSC Internat. Symp. on Fuzzy Logic. Zürich, Switzerland (1995), ICSC Academic Press, Millet A57-A59
27. Klawonn F., and Kruse R. The inherent indistinguishability in fuzzy systems. In: Lenski W. (Ed). Logic Versus Approximation, Lecture Notes in Computer Science Vol. 3075 (2004), Springer, Berlin 6-17
28. Mamdani A., and Assilian S. An experiment in linguistic synthesis with a fuzzy logic controller. Internat. J. Man-Machine Studies 7 (1975) 1-13
29. Nemitz W.C. Fuzzy relations and fuzzy functions. Fuzzy Sets and Systems 19 (1986) 177-191
30. Novák V. Fuzzy Sets and Their Applications (1989), Adam Hilger, Bristol
31. Perfilieva I. Fuzzy function as an approximate solution to a system of fuzzy relation equations. Fuzzy Sets and Systems 147 (2004) 363-383
32. Perfilieva I., and Novák V. System of fuzzy relation equations as a continuous model of IF-THEN rules. Inform. Sci. 177 (2007) 3218-3227
33. Sanchez E. Resolution of composite fuzzy relation equations. Inform. Control 30 (1976) 38-48
34. Thiele H. On the mutual definability of fuzzy tolerance relations and fuzzy tolerance coverings. Proc. 25th Internat. Symp. Multiple-Valued Logic (1995), IEEE Computer Society, Los Alamitos, CA 140-145
35. Thiele H., and Schmechel N. The mutual definability of fuzzy equivalence relations and fuzzy partitions. Proc. 4th IEEE Internat. Conf. Fuzzy Systems and 2nd Internat. Fuzzy Engineering Symp. Yokohama (1995) 1383-1390