### SOME PROPOSITIONS OF INTERIOR OF FUZZY SET WITH NUMERICAL EXAMPLES ON THE BASIS OF REFERENCE FUNCTION

Bhimraj Basumatary
Assistant Professor, Department of Mathematical Sciences
Bodoland University, BTC,Assam, India

Abstract
The main aim of this article is to define the interior of fuzzy sets on the basis of reference function and give the example of the interior of fuzzy sets. In this article we try to give the examples of propositions of interior of fuzzy sets on the basis of reference function.

Key words: Fuzzy membership function, fuzzy reference function, fuzzy membership value, interior of fuzzy set

1 Introduction
Fuzzy set theory was discovered by Professor Zadeh (1965) in 1965. Chang (1968) introduced fuzzy topology. After the introduction of fuzzy sets and fuzzy topology, several researches were conducted on the generalizations of the notions of fuzzy sets and fuzzy topology. The theory of fuzzy sets actually have been a generalization of the classical theory of sets in the sense that the theory of sets should have been a special case of the theory of fuzzy sets. But unfortunately it has been accepted that for fuzzy set A and its complement AC, neither A AC is empty set nor A AC is the universal set. Whereas the operations of union and intersection of crisp sets are indeed special cases of the corresponding operation of two fuzzy sets, they end up giving peculiar results while defining A AC and A AC.