Axiomatic approaches of fuzzy concept operators

In formal concept analysis, various fuzzy generalizations of formal concepts have been made. The fuzzy concept operators defined under the condition that the truth values (degrees) coming from a complete residuated lattice satisfy many interesting properties. Conversely, fuzzy concept operators can be characterized in terms of their properties. In this paper, the axiomatic approaches in the theory of fuzzy formal concept analysis based on a complete residuated lattice are presented. In the axiomatic approach, the fuzzy conceptual knowledge system is defined, and axiom sets satisfied by the fuzzy conceptual knowledge system are stated. It is proved that axioms of the fuzzy conceptual knowledge system guarantee the existence of certain types of binary fuzzy relations producing the same fuzzy formal concepts. The independence of axiom sets characterizing the fuzzy conceptual knowledge system is examined.

[1]  Lifeng Li,et al.  Attribute reduction in fuzzy concept lattices based on the T implication , 2010, Knowl. Based Syst..

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

[3]  Bijan Davvaz,et al.  Rough set theory applied to lattice theory , 2012, Inf. Sci..

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

[5]  Ramón Fuentes-González,et al.  Concept lattices defined from implication operators , 2000, Fuzzy Sets Syst..

[6]  Fei-Yue Wang,et al.  Reduction and axiomization of covering generalized rough sets , 2003, Inf. Sci..

[7]  Chen Shi-quan.  Fuzzy Concept Lattice , 2002 .

[8]  Radim Belohlávek,et al.  Grouping fuzzy sets by similarity , 2009, Inf. Sci..

[9]  Radim Belohlávek,et al.  Fast factorization by similarity in formal concept analysis of data with fuzzy attributes , 2007, J. Comput. Syst. Sci..

[10]  Helmut Thiele,et al.  On axiomatic characterisations of crisp approximation operators , 2000, Inf. Sci..

[11]  Barbara Pekala,et al.  Equivalent bipolar fuzzy relations , 2010, Fuzzy Sets Syst..

[12]  Partha Ghosh,et al.  Fuzzy graph representation of a fuzzy concept lattice , 2010, Fuzzy Sets Syst..

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

[14]  Jan Konecny,et al.  Isotone fuzzy Galois connections with hedges , 2011, Inf. Sci..

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

[16]  Vilém Vychodil,et al.  What is a fuzzy concept lattice? , 2005, CLA.

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

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

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

[20]  Xiao-Ping Yang,et al.  Minimization of axiom sets on fuzzy approximation operators , 2007, Inf. Sci..

[21]  Ramón Fuentes-González,et al.  The use of linguistic variables and fuzzy propositions in the L-Fuzzy concept theory , 2011, Comput. Math. Appl..

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

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

[24]  Jozef Pócs,et al.  Note on generating fuzzy concept lattices via Galois connections , 2012, Inf. Sci..

[25]  Jozef Pócs.  On possible generalization of fuzzy concept lattices using dually isomorphic retracts , 2012, Inf. Sci..