Theory of Fuzzy Sets: An Overview

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Mamoni Dhar 1,* Hemanta. K. Baruah 2

1. Department of Mathematics, Science College, Kokrajhar, Assam, India

2. Department of Statistics, Gauhati University, Assam, India

* Corresponding author.


Received: 12 May 2013 / Revised: 20 Jun. 2013 / Accepted: 25 Jul. 2013 / Published: 8 Sep. 2013

Index Terms

Reference Function, Membership Value, The Randomness-Fuzziness Consistency Principles


In this article, we would like to revisit and comment on the definition of complementation of fuzzy sets and also on some of the theories and formulas associated with this. Furthermore, the existing probability-possibility consistency principles are also revisited and related results are viewed from the standpoint of the Randomness-Fuzziness consistency principles. It is found that the existing definition of complementation as well as the probability – possibility consistency principles is not well defined. Consequently the results obtained from these would be inappropriate from our standpoints. Hence we would like to suggest some new definitions for some of the terms often used in the theory of fuzzy sets whenever possible.

Cite This Paper

Mamoni Dhar, Hemanta .K. Baruah, "Theory of Fuzzy Sets: An Overview", International Journal of Information Engineering and Electronic Business(IJIEEB), vol.5, no.3, pp.22-33, 2013. DOI:10.5815/ijieeb.2013.03.03


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