Linear Diophantine Fuzzy Set Theory Applied to BCK/BCI-Algebras

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dc.contributor.authorAl-Tahan, Madeline
dc.contributor.authorMahboob, Ahsan
dc.contributor.authorAl-Kaseasbeh, Saba
dc.contributor.authorETAL..
dc.date.accessioned2024-06-04T07:10:22Z
dc.date.available2024-06-04T07:10:22Z
dc.date.issued2022-06-19
dc.descriptionFuzzy set theory was launched in 1965 by Zadeh [1] as a generalization of the theory of classical sets. In a classical set, an element is either a member of the set or it is not a member of it, whereas in a fuzzy set, the membership of an element is a real number of the closed unit interval. So, in a fuzzy set, the sum of degree of belongingness of an element with its degree of non-belongingness is equal to one. Soon after their launch, fuzzy sets became an object of extensions by themselves. In 1983, Atanassov [2] generalized fuzzy sets to intuitionistic fuzzy sets (IFS). An IFS has two non-negative functions: the membership function and the non-membership function in a way that the sum of the degree of membership of an element with its degree of non-membership is in the unit real interval. Both fuzzy sets and intuitionistic fuzzy sets have their own restrictions related to the functions of membership and non-membership. To eliminate these restrictions by using reference parameters, Riaz and Hashmi [3] in 2019 found a new extension of fuzzy sets and called it linear Diophantine fuzzy sets (𝐿𝐷𝐹𝑆 ). Using the corresponding reference parameters to the membership and non-membership fuzzy relations, S. Ayub et al. [4] established a robust fusion of 𝐿𝐷𝐹𝑆 s and binary relations and introduced linear Diophantine fuzzy relations.
dc.description.abstractIn this paper, we apply the concept of linear Diophantine fuzzy sets in 𝐵𝐶𝐾/𝐵𝐶𝐼-algebras. In this respect, the notions of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are introduced and some vital properties are discussed. Additionally, characterizations of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are considered. Moreover, the associated results for linear Diophantine fuzzy subalgebras, linear Diophantine fuzzy ideals and linear Diophantine fuzzy commutative ideals are obtained. Keywords: BCI-algebra; BCK-algebra; linear Diophantine fuzzy set (LDFS); LDF-subalgebra; LDF-ideal; LDF-commutative ideal
dc.identifier.citationMuhiuddin, G., Al-Tahan, M., Mahboob, A., Hoskova-Mayerova, S., & Al-Kaseasbeh, S. (2022). Linear Diophantine fuzzy set theory applied to BCK/BCI-Algebras. Mathematics, 10(12), 2138.
dc.identifier.doihttps://doi.org/10.3390/math10122138
dc.identifier.urihttps://dspace.adu.ac.ae/handle/1/5611
dc.language.isoen
dc.publisherMDPI
dc.titleLinear Diophantine Fuzzy Set Theory Applied to BCK/BCI-Algebras
dc.typeArticle

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