Lattice operations on fuzzy implications and the preservation of the exchange principle

Vemuri, N R and Jayaram, Balasubramaniam (2016) Lattice operations on fuzzy implications and the preservation of the exchange principle. Fuzzy Sets and Systems, 301. pp. 64-78. ISSN 0165-0114

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Abstract

In this work, we solve an open problem related to the preservation of the exchange principle (EP) of fuzzy implications under lattice operations ([3], Problem 3.1.). We show that generalizations of the commutativity of antecedents (CA) to a pair of fuzzy implications (I,J)(I,J), viz., the generalized exchange principle and the mutual exchangeability are sufficient conditions for the solution of the problem. Further, we determine conditions under which these become necessary too. Finally, we investigate the pairs of fuzzy implications from different families such that (EP) is preserved by the join and meet operations.

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IITH Creators:

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

Item Type:

Article

Uncontrolled Keywords:

The commutativity of antecedents; Fuzzy implication; The exchange principle; The generalized exchange principle; The mutual exchangeability; Lattice operations

Subjects:

Mathematics

Divisions:

Department of Mathematics

Depositing User:

Team Library

Date Deposited:

21 Apr 2016 09:15

Last Modified:

20 Sep 2017 07:24

URI:

http://raiithold.iith.ac.in/id/eprint/2287