On fuzzy strongly C - pre open sets and fuzzy strongly C - pre closed sets in fuzzy topological spaces

Abstract

The concept of complement function is used to define a fuzzy closed subset of a fuzzy topological space. That is a fuzzy subset l is fuzzy closed if the standard complement 1-l = l¢ is fuzzy open. Here the standard complement is obtained by using the function C: [0, 1]® [0, 1] defined by C (x) = 1-x, for all x I[0, 1]. Several fuzzy topologists used this type of complement while extending the concepts in general topological spaces to fuzzy topological spaces. But there are other complements in the fuzzy literature. This motivated the second and third authors to introduce the concepts of fuzzy C -closed sets, and fuzzy C - pre closed sets, in fuzzy topological spaces. In this paper, we generalize the concept of fuzzy strongly pre open and fuzzy strongly pre closed sets by using the arbitrary complement function C, instead of the usual fuzzy complement function, and by using fuzzy C – pre closure instead of fuzzy pre closure. The concepts of fuzzy strongly C – pre open and strongly C – pre closed sets in fuzzy topological spaces and studied their properties in the third and fourth section, respectively. Key words: Fuzzy strongly C – pre open, fuzzy strongly C – pre closed sets and fuzzy topology.