Open AccessOn Fuzzy Rough Sets and Their Topological Structures
Author(s) -
Weidong Tang,
Jinzhao Wu,
Dingwei Zheng
Publication year - 2014
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.262
H-Index - 62
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/2014/546372
Subject(s) - mathematics , fuzzy set operations , topological space , fuzzy subalgebra , rough set , fuzzy number , fuzzy set , fuzzy logic , type 2 fuzzy sets and systems , topology (electrical circuits) , defuzzification , fuzzy classification , fuzzy mathematics , fuzzy measure theory , discrete mathematics , computer science , artificial intelligence , combinatorics
The core concepts of rough set theory are information systems and approximation operators of approximation spaces. Approximation operators draw close links between rough set theory and topology. This paper is devoted to the discussion of fuzzy rough sets and their topological structures. Fuzzy rough approximations are further investigated. Fuzzy relations are researched by means of topology or lower and upper sets. Topological structures of fuzzy approximation spaces are given by means of pseudoconstant fuzzy relations. Fuzzy topology satisfying (CC) axiom is investigated. The fact that there exists a one-to-one correspondence between the set of all preorder fuzzy relations and the set of all fuzzy topologies satisfying (CC) axiom is proved, the concept of fuzzy approximating spaces is introduced, and decision conditions that a fuzzy topological space is a fuzzy approximating space are obtained, which illustrates that we can research fuzzy relations or fuzzy approximation spaces by means of topology and vice versa. Moreover, fuzzy pseudoclosure operators are examined. ? 2014 Weidong Tang et al.
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