Union of fuzzy subgroups

Dixit, Vijaya; Bhambri, S. K.; Kumar, Prem

doi:10.1016/0165-0114(95)00091-7

Cited by 7 publications

(2 citation statements)

References 4 publications

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“…The concepts of fuzzy coset and fuzzy normal subgroup were introduced by Ajmal and Prajapati [2]. Dixit et al [10] addressed fuzzy level subgroups and the union of fuzzy subgroups in 1990. Biswas [8] was the first to suggest the concept of an anti-fuzzy subgroup.…”

Section: Introductionmentioning

confidence: 99%

An Approach to Lagrange’s Theorem in Pythagorean Fuzzy Subgroups

BHUNIA,

GHORAI

2024

KgJMat

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The Pythagorean fuzzy environment is a modern way of depicting uncertainty. The concept of Pythagorean fuzzy semi-level subgroups of any group is described in this paper. The Pythagorean fuzzy order of an element in a Pythagorean fuzzy subgroup is introduced and established various algebraic attributes. The relation between the Pythagorean fuzzy order of an element of a group and the order of that group is established. The Pythagorean fuzzy normalizer and Pythagorean fuzzy centralizer of Pythagorean fuzzy subgroups are discussed. Further, the concept of Pythagorean fuzzy quotient group and the index of a Pythagorean fuzzy subgroup are deﬁned. Finally, a framework is developed for proving Lagrange’s theorem in Pythagorean fuzzy subgroups.

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Section: Introductionmentioning

confidence: 99%

An Approach to Lagrange’s Theorem in Pythagorean Fuzzy Subgroups

BHUNIA,

GHORAI

2024

KgJMat

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“…Since then many results in group theory has been generalized to fuzzy setting. Some properties of products, set products, unions, intersections, the homomorphic images and preimages of fuzzy subgroups are introduced (see [1,2,3,6,8,9,10,13,15]). Some authors discussed the relations between the fuzzy subgroups and their level subgroups.…”

Section: Introductionmentioning

confidence: 99%