A Comparative Study of Classical Relation and Fuzzy Relation

Authors

  • Abdul Alim Lecturer, Dept. of Natural Sciences (Mathematics), BGMEA University of Fashion & Technology, Dhaka-1230, Bangladesh

Keywords:

Characteristic function, Membership grade, Max-min operation, Max-product operation, Max-avg operation.

Abstract

Fuzzy relation is an extension of classical relation as fuzzy set is an extension of classical set. This work represents an overview of classical relation and fuzzy relation. Some definitions related to fuzzy relation are discussed and also explained by giving example. Max-min operation and max-product operation are discussed for both classical relations and fuzzy relations. Max-avg operation is also discussed for fuzzy relations. Finally, fuzzy equivalence relation is discussed.

References

[1] L. A. Zadeh, , Fuzzy Sets, Information and Control, 8(1965) 338-353.
[2] George J, Klir, Bo Yuan, Fuzzy Sets and Fuzzy Logic, Theory and Applications, Prentice Hall Inc. N.J. U.S.A. 1995.
[3] H. J. Zimmermann, Fuzzy Set Theory and its Applications, Third Edition, Kluwer Academic Publishers, Boston, U.S.A. 1995
[4] Majid Hussain, Fuzzy Relations, Thesis for the degree Master of Science (two years) in Mathematical Modeling and Simulation, May 2010.
[5] D. Dubis, H. Prade, Fuzzy Sets and Systems, Theory and Applications, New York, 1980.

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Published

2017-05-18

How to Cite

Alim, A. (2017). A Comparative Study of Classical Relation and Fuzzy Relation. American Scientific Research Journal for Engineering, Technology, and Sciences, 31(1), 240–248. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/2922

Issue

Vol. 31 No. 1 (2017)

Section

Articles

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