The solution set of a fuzzy relational equation with sup-conjunctor composition in a complete lattice

Fuzzy Sets and Systems

Volumn 153, Issue 2, 2005, Pages 249-260

  Wang, Xue Ping ^a   Xiong, Qing Quan ^a  

^a SICHUAN NORMAL UNIVERSITY   (China)

Author keywords

Complete lattice; Conjunctor; Minimal solution; Relational equation; Solution set

Indexed keywords

BOUNDARY CONDITIONS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; SET THEORY; THEOREM PROVING;

COMPLETE LATTICE; CONJUNCTOR; MINIMAL SOLUTION; RELATIONAL EQUATION; SOLUTION SET;

FUZZY SETS;

EID: 18444369630     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2004.12.001     Document Type: Article

References (13)

1. G. Birkhoff, Lattice Theory. vol. XXV, third ed., American Mathematical Society Colloquium Publications, Providence, RI, 1979.
2. P. Crawley, and R.P. Dilworth Algebraic Theory of Lattices 1973 Prentice-Hall Englewood Cliffs, NJ
3. B. De Baets An order-theoretic approach to solving sup- T equations D. Ruan Fuzzy Set Theory and Advanced Mathematical Applications 1995 Kluwer Academic Publishers Dordrecht 67 87
4. B. De Baets Analytical solution methods for fuzzy relational equations D. Dubois H. Prade Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series vol. 1 2000 Kluwer Academic Publishers Dordrecht 291 340
5. A. Di Nola, S. Sessa, W. Pedrycz, and E. Sanchez Fuzzy Relation Equations and Their Applications to Knowledge Engineering 1989 Kluwer Academic Publishers Dordrecht
6. J.C. Fodor Strict preference relations based on weak t-norms Fuzzy Sets and Systems 43 1991 327 336
7. E. Sanchez Resolution of composite fuzzy relation equations Inform. and Control 30 1976 38 48
8. X.P. Wang Method of solution to fuzzy relation equations in a complete Brouwerian lattice Fuzzy Sets and Systems 120 2001 409 414
9. X.P. Wang Infinite fuzzy relational equation in a complete Brouwerian lattice Indian J. Pure Appl. Math. 33 2002 87 95
10. X.P. Wang Conditions under which a fuzzy relational equation has minimal solutions in a complete Brouwerian lattice Adv. in Math. 31 2002 220 228 (in Chinese)
11. Z.D. Wang, and Y.D. Yu Pseudo-t-norms and implication operators on a complete Brouwerian lattice Fuzzy Sets and Systems 132 2002 113 124
12. Z.D. Wang, and Y.D. Yu Direct product decomposition of pseudo t-norms and implications J. China Univ. Sci. Tech. 31 2001 657 662 (in Chinese)
13. C.K. Zhao On matrix equations in a class of complete and completely distributive lattice Fuzzy Sets and Systems 22 1987 303 320