A generalization of fuzzy Boundary

Abstract

The concept of fuzzy C - boundary is introduced by using the arbitrary complement function C and by using fuzzy C - closure of a fuzzy topological space where C: [0, 1] [0, 1] is a function. Let A be a fuzzy subset of a fuzzy topological space X and let C be a complement function. Then the fuzzy C - boundary of A is defined as BdC A = ClC A  ClC (CA), where ClC A is the fuzzy C - closure of A and CA(x) = C (A(x)), 0  x  1. In this paper we discuss the basic properties of fuzzy C – boundary.

MSC 2010: 54A40, 3E72.

Key words: Fuzzy C - boundary, fuzzy C - closed sets and fuzzy topology.