A Comparative Study of Classical Relation and Fuzzy Relation

Abdul Alim

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.


Keywords


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

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References


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

George J, Klir, Bo Yuan, Fuzzy Sets and Fuzzy Logic, Theory and Applications, Prentice Hall Inc. N.J. U.S.A. 1995.

H. J. Zimmermann, Fuzzy Set Theory and its Applications, Third Edition, Kluwer Academic Publishers, Boston, U.S.A. 1995

Majid Hussain, Fuzzy Relations, Thesis for the degree Master of Science (two years) in Mathematical Modeling and Simulation, May 2010.

D. Dubis, H. Prade, Fuzzy Sets and Systems, Theory and Applications, New York, 1980.


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