The ⊛-composition of fuzzy implications: Closures with respect to properties, powers and families

Vemuri, N R and Jayaram, Balasubramaniam (2015) The ⊛-composition of fuzzy implications: Closures with respect to properties, powers and families. Fuzzy Sets and Systems, 275. pp. 58-87. ISSN 0165-0114

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Recently, Vemuri and Jayaram proposed a novel method of generating fuzzy implications from a given pair of fuzzy implications. Viewing this as a binary operation ⊛ on the set II of fuzzy implications they obtained, for the first time, a monoid structure (I,⊛)(I,⊛) on the set II. Some algebraic aspects of (I,⊛)(I,⊛) had already been explored and hitherto unknown representation results for the Yager's families of fuzzy implications were obtained in [53] (N.R. Vemuri and B. Jayaram, Representations through a monoid on the set of fuzzy implications, fuzzy sets and systems, 247 (2014) 51–67). However, the properties of fuzzy implications generated or obtained using the ⊛-composition have not been explored. In this work, the preservation of the basic properties like neutrality, ordering and exchange principles , the functional equations that the obtained fuzzy implications satisfy, the powers w.r.t. ⊛ and their convergence, and the closures of some families of fuzzy implications w.r.t. the operation ⊛, specifically the families of (S,N)(S,N)-, R-, f- and g-implications, are studied. This study shows that the ⊛-composition carries over many of the desirable properties of the original fuzzy implications to the generated fuzzy implications and further, due to the associativity of the ⊛-composition one can obtain, often, infinitely many new fuzzy implications from a single fuzzy implication through self-composition w.r.t. the ⊛-composition.

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IITH Creators:
IITH CreatorsORCiD
Jayaram, Balasubramaniam
Item Type: Article
Uncontrolled Keywords: Fuzzy implication; Basic properties; Functional equations; Self-composition; Closure; (SN)-implications; R-implications; f-implications; g-implications
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: Team Library
Date Deposited: 26 Nov 2014 09:00
Last Modified: 20 Sep 2017 07:26
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