Ideals of roughness in L-algebras

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Shirvani Bourojeni M.

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Journal Paper

Paper Information

Journal: JOURNAL OF ALGEBRAIC HYPERSTRUCTURES AND LOGICAL ALGEBRAS Year:2023 | Volume:4 | Issue:2 Page(s): 91-106

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Information Journal Paper

Title

Ideals of roughness in L-algebras

Author(s)

Shirvani Bourojeni M. | Issue Writer Certificate

Keywords

L‎-algebra‎

‎approximation space‎

‎(lower) upper approximation‎

ideal‎

A-lower (resp.‎ ‎A-upper) rough ideal

Abstract

Rough is an exceptional mathematical tool for effectively analyzing and addressing the complexities of vague action descriptions in decision problems. This paper explores the concept of an L-algebra, which leads to the introduction of lower and upper approximations. The properties of these approximations are also discussed and elucidated. Furthermore, it is proven that the lower and upper approximations serve as interior and closure operators, respectively. Additionally, by employing A-lower and A-upper approximations, this paper presents and examines conditions for a nonempty subset to be definable. Furthermore, we investigated the circumstances under which the A-lower and A-upper approximations can be rough ideals. Finally, we define an operation ‎" -->"‎ on the set of all upper approximations of L ‎and ‎prove ‎that ‎it ‎is ‎made ‎an ‎‎L-algebra.

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