Supremum and Infimum Operations on Fuzzy Sets

Afroja Akter; Abeda Sultana; Md. Abdul Alim

Afroja Akter Faculty of Mathematics, CAAS, IUBAT-International University of Business Agriculture and Technology, Bangladesh
Abeda Sultana Professor, Dept. of Mathematics, Jahanginagar University, Bangladesh
Md. Abdul Alim Lecturer in Mathematics, BGMEA University of Fashion & Technology, Bangladesh

Keywords: Fuzzy set, Membership function, Standard Union & Intersection

Abstract

In this paper we have shown comparison between classical set and fuzzy set. Also we have discussed some basic definitions and properties related to fuzzy set that is used in this paper. Then we collected three theorems by reviewing some papers, which were unproved there and we proved these theorems. We have reviewed some research papers with proper references to do our work.

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References

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

George J Klir, Yuan Bo, Fuzzy sets and fuzzy logic, Theory and Applications, Prentice-Hall Inc. N.J. U.S.A. 1995.

Lowen, Fuzzy set theorey, Department of Mathematics and Computer Science, University of Antwerp; Belgium, Basic Concepts, Techniques and Bibliography, Kluwer Academic Publishers Dordrecht/ Boston/ London.

Mitra N.K., Fuzzy set and fuzzy relational structure using T-norm and Matlab, Department of Mathematics, University of Dhaka.

Steve Carlson, Fuzzy Sets and Fuzzy Topologies, Early ideals and Obstacles, Rose-Hulman Institute of Technology, Part I (May 10).

C.L. Chang, Fuzzy topological spaces, Journal of Mathematical Analysis and Application, 24,182-190(1968).

David H. Foster, Fuzzy Topological Groups, Journal of Mathematical Analysis and Application, Academic Press, New York and London, Vol. 67, No.2, February 1979.