Title :
Approximating Arbitrary Fuzzy Subsets by Extensional Ones
Author :
Mattioli, G. ; Recasens, J.
Author_Institution :
Dept. of Mat. i Inf. ETS Arquitectura del Valles, Univ. Politec. de Catalunya, Sant Cugat del Valles, Spain
Abstract :
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.
Keywords :
approximation theory; fuzzy set theory; mathematical operators; Archimedean t-norms; arbitrary fuzzy subset approximation; extensional approximations; indistinguishability operators; Additives; Approximation algorithms; Approximation methods; Generators; Image color analysis; Indexes; Quadratic programming; Extensional fuzzy subset; indistinguishability operator; lower approximation; power with respect to a t-norm; quasi-arithmetic mean; upper approximation;
Journal_Title :
Fuzzy Systems, IEEE Transactions on
DOI :
10.1109/TFUZZ.2014.2321593
