Fuzzy normal subgroups and fuzzy cosets

Mukherjee, N.; Bhattacharya, Prabir

doi:10.1016/0020-0255(84)90050-1

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Cited by 133 publications

(34 citation statements)

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“…Rosenfeld [2] and many others [3], [4], [5] have studied about the fuzzy normal subgroup. Anthony and Sherwood [6] redefined fuzzy subgroups using t-norm.…”

Section: Introductionmentioning

confidence: 99%

Implication-Based T-Fuzzy Subgroup of a Finite Group and Its Properties

Rathi¹,

Spinneli²

2017

Int. J. of Pure and Appl. Math.

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Based on the definition of implication-based fuzzy subgroup of a finite group given by Yuan, implication-based T-fuzzy subgroup and implication-based T-normal fuzzy subgroup of a finite group is defined. Some properties of them are proved in this paper. Also T − product,Ṫ − product and T ′ − product of these implication-based T-fuzzy subgroups of a finite group are defined and its properties are discussed.

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“…Rosenfeld [2] and many others [3], [4], [5] have studied about the fuzzy normal subgroup. Anthony and Sherwood [6] redefined fuzzy subgroups using t-norm.…”

Section: Introductionmentioning

confidence: 99%

Implication-Based T-Fuzzy Subgroup of a Finite Group and Its Properties

Rathi¹,

Spinneli²

2017

Int. J. of Pure and Appl. Math.

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“…N.P. Mukherjee [5] introduced and studied the concepts of fuzzy normal subgroups and fuzzy cosets in groups. He proved that µ is a fuzzy normal subgroup of finite group G if and if the level subgroups of µ are normal subgroups of G.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Normal Congruences and Fuzzy Coset Relations on Groups

Shoar¹

2017

Int. J. of Pure and Appl. Math.

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“…Many authors [3,5,9,11] have mainly investigated various algebraic notions based on his approach. In fact, in Rosenfeld's work, only the subset are fuzzy, but the group operation is crisp.…”

Section: Introductionmentioning

confidence: 99%