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WITHDRAWN: Roughness in L-algebras

Abstract The aim of this paper is to introduce rough approximation on L−algebras. We investigate the relationship between subalgebras, ideals and rough subalgebras, rough ideals of L−algebras, and study homomorphic images of rough ideals on L−algebras. Furthermore, the rough set algebra as an L−algebra is expressed by select the implication operator appropriately. Continue the study of fuzzy set theory on L−algebras, we apply rough fuzzy set theory on L−algebras, we construct a representation theorem that determines when a pair of fuzzy sets is a rough fuzzy set on L−algebras. Finally, uncertainty measures on L−algebras and the relationship between rough operations and uncertainty measures of L−algebras are studied. We verify that there is a bijection between the low approximation and inner measure on L−algebras. MSC(2010): 03B50, 06A15, 03B47, 03E72.

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Qiuyan Zhan A. Borumand Saeid

2023

Title: WITHDRAWN: Roughness in L-algebras

Description:

Abstract The aim of this paper is to introduce rough approximation on L−algebras.

We investigate the relationship between subalgebras, ideals and rough subalgebras, rough ideals of L−algebras, and study homomorphic images of rough ideals on L−algebras.

Furthermore, the rough set algebra as an L−algebra is expressed by select the implication operator appropriately.

Continue the study of fuzzy set theory on L−algebras, we apply rough fuzzy set theory on L−algebras, we construct a representation theorem that determines when a pair of fuzzy sets is a rough fuzzy set on L−algebras.

Finally, uncertainty measures on L−algebras and the relationship between rough operations and uncertainty measures of L−algebras are studied.

We verify that there is a bijection between the low approximation and inner measure on L−algebras.

MSC(2010): 03B50, 06A15, 03B47, 03E72.

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