An Axiomatic Characterization of Fuzzy Formal Contexts Based on T-implication Operators

In this paper, the fuzzy concept based on T-implication operators is studied by the axiomatic approach. An operators-oriented characterization of the fuzzy concept is proposed, that is, the fuzzy intent-extent operator and the fuzzy extent-intent operator based on T-implication operators are defined by axioms. The axiom sets of the fuzzy concept operators guarantee the existence of fuzzy relations which produce the same operators.

[1]  Samir Elloumi,et al.  A multi-level conceptual data reduction approach based on the Lukasiewicz implication , 2004, Inf. Sci..

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

[3]  Bernhard Ganter,et al.  Formal Concept Analysis: Mathematical Foundations , 1998 .

[4]  Rudolf Wille,et al.  Restructuring Lattice Theory: An Approach Based on Hierarchies of Concepts , 2009, ICFCA.

[5]  Yiyu Yao,et al.  Concept lattices in rough set theory , 2004, IEEE Annual Meeting of the Fuzzy Information, 2004. Processing NAFIPS '04..

[6]  Horst Herrlich,et al.  Galois Connections , 1985, Mathematical Foundations of Programming Semantics.

[7]  Wei-Zhi Wu,et al.  Constructive and axiomatic approaches of fuzzy approximation operators , 2004, Inf. Sci..

[8]  Radim Belohlávek,et al.  Crisply Generated Fuzzy Concepts , 2005, ICFCA.

[9]  Wei Xu,et al.  Fuzzy inference based on fuzzy concept lattice , 2006, Fuzzy Sets Syst..

[10]  Wen-Xiu Zhang,et al.  An axiomatic characterization of a fuzzy generalization of rough sets , 2004, Inf. Sci..

[11]  Ming-Wen Shao,et al.  Set approximations in fuzzy formal concept analysis , 2007, Fuzzy Sets Syst..

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

[13]  Radim Bělohlávek,et al.  Fuzzy Relational Systems: Foundations and Principles , 2002 .

[14]  Stan J. Surma.  A Galois Connection , 2007, Logica Universalis.

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

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

[17]  Nehad N. Morsi,et al.  On the Relationship of Extended Necessity Measures To Implication Operators on the Unit Interval , 1995, Inf. Sci..

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