Approximating arbitrary fuzzy subsets by extensional ones

© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.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 mu. These methods are exhaustively explained for different Archimedean t-norms, and an example is provided to illustrate them.Peer Reviewe