Fuzzy inference based on fuzzy concept lattice

In this paper, a fuzzy inference method based on the notion of fuzzy concept lattice is studied. We first propose a new form of fuzzy concept lattice, and then based on three kinds of known fuzzy concept lattices and our new fuzzy concept lattice, two coherent fuzzy inference methods, the lower approximate fuzzy inference and the upper approximate fuzzy inference, are proposed, and the combined use of the two methods will make the fuzzy inference more precise.

[1]  Irina Perfilieva,et al.  Fuzzy function as an approximate solution to a system of fuzzy relation equations , 2004, Fuzzy Sets Syst..

[2]  Samir Elloumi,et al.  Galois connection, formal concepts and Galois lattice in real relations: application in a real classifier , 2002, J. Syst. Softw..

[3]  R. Belohlávek.  Fuzzy Relational Systems: Foundations and Principles , 2002 .

[4]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[5]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[6]  J. Goguen.  L-fuzzy sets , 1967 .

[7]  Didier Dubois,et al.  A new perspective on reasoning with fuzzy rules , 2002, Int. J. Intell. Syst..

[8]  Andrei Popescu,et al.  Non-dual fuzzy connections , 2004, Arch. Math. Log..

[9]  Andrei Popescu,et al.  A general approach to fuzzy concepts , 2004, Math. Log. Q..

[10]  Radim Belohlávek,et al.  Concept lattices and order in fuzzy logic , 2004, Ann. Pure Appl. Log..

[11]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[12]  Dexue Zhang,et al.  Galois connections between categories of L-topological spaces , 2005, Fuzzy Sets Syst..

[13]  Yee Leung,et al.  Integrated semantics and logic metric spaces , 2003, Fuzzy Sets Syst..

[14]  D. Dubois,et al.  Fuzzy sets in approximate reasoning, part 1: inference with possibility distributions , 1999 .

[15]  Ramón Fuentes-González,et al.  The study of the L-fuzzy concept lattice , 1994 .

[16]  Elie Sanchez,et al.  Resolution of Composite Fuzzy Relation Equations , 1976, Inf. Control..

[17]  Irina Perfilieva,et al.  COMPATIBILITY OF SYSTEMS OF FUZZY RELATION EQUATIONS , 2000 .

[18]  Didier Dubois,et al.  Implicative and conjunctive fuzzy rules - A tool for reasoning from knowledge and examples , 1999, AAAI/IAAI.

[19]  Martin Gavalec.  Solvability and unique solvability of max-min fuzzy equations , 2001, Fuzzy Sets Syst..

[20]  Radim Belohlávek,et al.  Fuzzy Galois Connections , 1999, Math. Log. Q..

[21]  Radim Bělohlávek,et al.  Lattices of Fixed Points of Fuzzy Galois Connections , 2001 .

[22]  F. Klawonn.  Fuzzy points, fuzzy relations and fuzzy functions , 2000 .

[23]  R. P. Dilworth,et al.  Residuated Lattices. , 1938, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Marc Roubens,et al.  Theory and Applications of Relational Structures as Knowledge Instruments II, International Workshops of COST Action 274, TARSKI, 2002-2005, Selected Revised Papers , 2006, Theory and Applications of Relational Structures as Knowledge Instruments.

[25]  Ivo Düntsch,et al.  Approximation Operators in Qualitative Data Analysis , 2003, Theory and Applications of Relational Structures as Knowledge Instruments.