Abstract
We introduce the concept of fuzzy (r,s)-minimal β-open set on an (r,s)-fuzzy minimal space and basic some properties. We also introduce the concept of fuzzy (r,s)-M β-continuous mapping which is a generalization of fuzzy (r,s)-M semicontinuous mapping and fuzzy (r,s)-M precontinuous mapping, and investigate characterization for such mappings.
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References
Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20(1), 87–96 (1986)
Chang, C.L.: Fuzzy topological spaces. J. Math. Anal. Appl. 24, 182–190 (1968)
Chattopadhyay, K.C., Hazra, R.N., Samanta, S.K.: Gradation of openess: fuzzy topology. Fuzzy Sets and Systems 49, 237–242 (1992)
Çoker: An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets and Systems 88, 81–89 (1997)
Çoker, D., Dimirci, M.: An introduction to intuitionistic fuzzy topological spaces in Šostak sense. Buseful 67, 67–76 (1996)
Höhle, U.: Upper semicontinuous fuzzy sets and applications. J. Math. Anall. Appl. 78, 659–673 (1980)
Höhle, U., Šostak, A.P.: A general theory of fuzzy topological spaces. Fuzzy Sets and Systems 73, 131–149 (1995)
Höhle, U., Šostak, A.P.: Axiomatic Foundations of Fixed-Basis fuzzy topology, ch. 3. The Handbooks of Fuzzy sets series, vol. 3. Kluwer Academic Publishers, Dordrecht (1999)
Kubiak, T.: On fuzzy topologies. Ph. D. Thesis, A. Mickiewicz, Poznan (1985)
Kubiak, T., Šostak, A.P.: Lower set-valued fuzzy topologies. Quaestions Math. 20(3), 423–429 (1997)
Min, W.K., Abbas, S.E.: (r,s)-fuzzy minimal structures and (r,s)-fuzzy minimal spaces. Journal of Intelligent and Fuzzy Systems, doi:10.3233/IFS-120669 (accepted)
Min, W.K., Kim, Y.K.: Fuzzy (r, s)-minimal preopen sets and fuzzy (r, s)-M precontinuous mappings on (r, s)-fuzzy minimal spaces (submitted)
Min, W.K., Kim, Y.K.: Fuzzy (r, s)-minimal semiopen sets and fuzzy (r, s)-M semicontinuous mappings on (r, s)-fuzzy minimal spaces (submitted)
Samanta, S.K., Mondal, T.K.: On intuitionistic gradation of openness. Fuzzy Sets and Systems 131, 323–336 (2002)
Šostak, A.P.: On a fuzzy topological structure, Suppl. Rend. Circ. Matem. Palerms Ser. II 11, 89–103 (1985)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)
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Kim, Y.K., Min, W.K. (2014). On Fuzzy (r,s)-Minimal β-Open Sets on (r,s)-Fuzzy Minimal Spaces. In: Cho, Y., Matson, E. (eds) Soft Computing in Artificial Intelligence. Advances in Intelligent Systems and Computing, vol 270. Springer, Cham. https://doi.org/10.1007/978-3-319-05515-2_2
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DOI: https://doi.org/10.1007/978-3-319-05515-2_2
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05514-5
Online ISBN: 978-3-319-05515-2
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