Implicative filters of equality algebras treated as fuzzy points

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Jun Y.B.

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Journal Paper

Paper Information

Journal: JOURNAL OF ALGEBRAIC HYPERSTRUCTURES AND LOGICAL ALGEBRAS Year:2025 | Volume:6 | Issue:1 Page(s): 13-26

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Information Journal Paper

Title

Implicative filters of equality algebras treated as fuzzy points

Author(s)

Jun Y.B. | Issue Writer Certificate

Keywords

(implicative

positive implicative) (∈

∈)-fuzzy filter

∈t-set

qt-set

Abstract

The notion of fuzzy points is used to study implicative filters in equality algebras. The concept of implicative (∈, ∈)-fuzzy filters is introduced, and its properties are investigated. The relationship between (∈, ∈)-fuzzy filters, implicative (∈, ∈)- fuzzy filters and positive implicative (∈, ∈)-fuzzy filters are established. Characterizations of implicative (∈, ∈)-fuzzy filters are discussed, and the conditions for the (positive implicative) (∈, ∈)-fuzzy filter to be an implicative (∈, ∈)-fuzzy filter are explored. The extension property for the implicative (∈, ∈)- fuzzy filter is established. The properties associated with ∈tset and qt-set of a fuzzy set Ψ in E and also look for conditions under which they can become implicative filters are examined.

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