Overlap Indices: Construction of and Application to Interpolative Fuzzy Systems

Author

Garcia-Jimenez, Santiago ; Bustince, Humberto ; Hullermeier, Eyke ; Mesiar, Radko ; Pal, Nikhil R. ; Pradera, Ana

Author_Institution

Dept. de Autom. y Comput., Univ. Publica de Navarra, Pamplona, Spain

Volume

23

Issue

4

fYear

2015

fDate

Aug. 2015

Firstpage

1259

Lastpage

1273

Abstract

In this paper, we analyze the minimal set of axioms that overlap indices between fuzzy sets must fulfill. We also present a method to build overlap indices using overlap functions, and we carry on a theoretical study about the continuity, the invariance, and some general properties of such indices. We present a generalization of the inference algorithm for interpolative fuzzy systems using overlap indices. We also propose an algorithm for choosing, among a set of overlap indices, the best one for a considered problem.

Keywords

fuzzy reasoning; fuzzy set theory; interpolation; continuity function; fuzzy sets; general properties; inference algorithm generalization; interpolative fuzzy systems; invariance function; minimal axiom set; overlap functions; overlap indices; Educational institutions; Electronic mail; Fuzzy sets; Fuzzy systems; Indexes; Inference algorithms; Interpolation; Aggregation function; fuzzy rules; interpolative fuzzy systems; overlap function; overlap index;

fLanguage

English

Journal_Title

Fuzzy Systems, IEEE Transactions on

Publisher

ieee

ISSN

1063-6706

Type

jour

DOI

10.1109/TFUZZ.2014.2349535

Filename

6880387