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On Fuzzy Quotient Mappings

Ramakrishnan, P.V., and Regina Mary A., (2005) On Fuzzy Quotient Mappings. Bulletin of the Malaysian Mathematical Sciences Society, 28 (2). pp. 215-221. ISSN 0126-6705

Full text not available from this repository.

Official URL: http://math.usm.my/bulletin/pdf/v28n2/v28n2p12.pdf

Affiliations

Madurai Kamaraj University, School of Mathematics
Fatima College (Autonomous), Dept. of Mathematics

Abstract

Azad [1] introduced the concepts of fuzzy semi-open sets and fuzzy semi-continuous mappings. Fuzzy $\alpha$-open sets and fuzzy $\alpha$-continuous functions were introduced by Mashhour et. al. [4] and Singal et. al. [6] respectively. The concepts of fuzzy pre-open sets and fuzzy pre-continuous mappings were introduced by Bin Sahana [2]. 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 $\alpha^\ast$-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.

Item Type:Journal
Keywords:Fuzzy semi-open sets, fuzzy α-open sets, fuzzy pre-open sets, fuzzy semi-continuous maps, fuzzy α-continuous maps, fuzzy pre-continuous maps, fuzzy α-quotient maps, fuzzy strongly α-quotient maps and fuzzy α*-quotient maps.
Subjects:Q Science, Computer Science
ID Code:1425

[1] K.K. Azad, On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl. 82(1) (1981), 14—32.

[2] A.S. Bin Shahna, On fuzzy strong semicontinuity and fuzzy precontinuity, Fuzzy Sets and Systems 44(2) (1991), 303—308.

[3] Chang, C.L. Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182—190.

[4] A.S. Mashhour, M. H. Ghanim and M. A. Fath Alla, On fuzzy noncontinuous mappings, Bull. Calcutta Math. Soc. 78(1) (1986), 57—69.

[5] M.N. Mukherjee and S.P. Sinha, Irresolute and almost open functions between fuzzy topological spaces, Fuzzy Sets and Systems 29(3) (1989), 381—388.

[6] M.K. Singal and N. Rajvanshi, Fuzzy alpha-sets and alpha-continuous maps, Fuzzy Sets and Systems 48(3) (1992), 383—390.

[7] Wong, C.K. Fuzzy topology: product and quotient theorems, J. Math. Anal. Appl. 45 (1974), 512—521.

[8] L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338—353.

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