I-fuzzy topological groups

Authors:
Cong-hua Yan;Sheng-zhang Guo
Affiliations:
Institute of Mathematics, School of Mathematics, Nanjing Normal University, Nanjing, Jiangsu 210046, People's Republic of China;Institute of Mathematics, School of Mathematics, Nanjing Normal University, Nanjing, Jiangsu 210046, People's Republic of China
Venue:
Fuzzy Sets and Systems
Year:
2010

Citing 9
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Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology

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Abstract

In this paper, the concept of I-fuzzy topological groups is introduced and some of its properties are discussed. Considering Jin-ming Fang's notion of I-fuzzy quasi-coincident neighborhood system [Fuzzy Sets and Systems 147 (2004) 317-325], we obtained a characterization of I-fuzzy topological groups in terms of the corresponding I-fuzzy quasi-coincident neighborhood system at identity element. Finally, we showed that the category of I-fuzzy topological groups and fuzzy continuous homomorphisms is isomorphic to the category of antichain I-topological groups and I-continuous homomorphisms; and the category I-fuzzy topological groups is topological over the category of groups with respect to the forgetful functor.