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On fuzzy quotient mappings. (English) Zbl 1185.54006
Summary: K. K. Azad [J. Math. Anal. Appl. 82, 14–32 (1981; Zbl 0511.54006)] introduced the concepts of fuzzy semi-open sets and fuzzy semi-continuous mappings. Fuzzy α-open sets and fuzzy \(\alpha\)-continuous functions were introduced by A. S. Mashhour et. al. [Bull. Calcutta Math. Soc. 78, 57–69 (1986; Zbl 0604.54008)] and M. K. Singal and N. Rajvanshi [Fuzzy Sets Syst. 48, No. 3, 383–390 (1992; Zbl 0768.54008)] respectively. The concepts of fuzzy pre-open sets and fuzzy pre-continuous mappings were introduced by A. S. Bin Shahna [Fuzzy Sets Syst. 44, No. 2, 303–308 (1991; Zbl 0753.54001)]. In this paper the concepts of fuzzy \(\alpha\)-quotient maps, fuzzy semi quotient maps, fuzzy pre quotient maps, fuzzy strongly \(\alpha\)-quotient maps, fuzzy strongly semi quotient maps, fuzzy strongly pre quotient maps, fuzzy \(\alpha^*\)-quotient maps, fuzzy semi\(^*\)-quotient maps and fuzzy pre\(^*\)-quotient maps are introduced and some of their properties are studied. Also the interconnections between the new mappings and the fuzzy quotient mappings are investigated. Some examples are given to illustrate the results.
MSC:
54A40 Fuzzy topology
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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