Approximating Arbitrary Fuzzy Subsets by Extensional Ones

An interesting problem within the theory of indistinguishability operators is how to approximate an arbitrary fuzzy subset by a similar extensional one. In this paper, we aim to solve this question and provide three methods to find extensional approximations of fuzzy subsets μ. These methods are exhaustively explained for different Archimedean t-norms, and an example is provided to illustrate them.