SISO fuzzy relational inference systems based on fuzzy implications are universal approximators

Mandal, S and Jayaram, Balasubramaniam (2015) SISO fuzzy relational inference systems based on fuzzy implications are universal approximators. Fuzzy Sets and Systems, 277. pp. 1-21. ISSN 0165-0114

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Abstract

In this work, we show that single input single output (SISO) fuzzy inference systems based on Fuzzy Relational Inference (FRI) with implicative interpretation of the rule base are universal approximators under suitable choice of operations for the other components of the fuzzy system. The presented proofs make no assumption on the form or representations of the considered fuzzy implications and hence show that a much larger class of fuzzy implications other than what is typically considered in the literature can be employed meaningfully in FRIs based on implicative models. A concept of Weak Coherence is proposed, which plays an important role in enlarging the class of fuzzy implications that can be considered.

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IITH Creators:

IITH Creators	ORCiD
Jayaram, Balasubramaniam	http://orcid.org/0000-0001-7370-3821

Item Type:

Article

Additional Information:

We sincerely thank both the anonymous reviewers for their deep and insightful remarks which have enhanced the readability and presentation of this paper. We would also like to thank Mr. Avijit Ashe, who helped us with the implementation of the FRIs proposed in Theorem 7.1 and Theorem 8.1.

Uncontrolled Keywords:

Fuzzy relational inference; Fuzzy implications; Universal approximation

Subjects:

Mathematics

Divisions:

Department of Mathematics

Depositing User:

Team Library

Date Deposited:

26 Nov 2014 09:41

Last Modified:

20 Sep 2017 07:26