A new type of fuzzy n-ary hyperstructures

Leoreanu-Fotea, V.

doi:10.1016/j.ins.2009.03.017

Cited by 12 publications

(5 citation statements)

References 13 publications

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“…Definition 5.6 and Theorem 5.7 are similar to the one proposed by Leoreanu-Fotea [21] on fuzzy (m, n)-ary hyperrings and (m, n)-ary hyperrings and Ameri and Nozari [28] proposed a similar Definition and Theorem on hyperalgebras.…”

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confidence: 55%

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(m,n)-Semihyperrings and an Algebra of Fuzzy (m,n)-Semihyperrings

Alam¹,

Aljahdali²,

Hundewale³

2015

Preprint

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We propose a new class of algebraic structure named as (m, n)semihyperring which is a generalization of usual semihyperring. We define the basic properties of (m, n)-semihyperring like identity elements, weak distributive (m, n)-semihyperring, zero sum free, additively idempotent, hyperideals, homomorphism, inclusion homomorphism, congruence relation, quotient (m, n)-semihyperring etc. We propose some lemmas and theorems on homomorphism, congruence relation, quotient (m, n)-semihyperring, etc and prove these theorems. We further extend it to introduce the relationship between fuzzy sets and (m, n)semihyperrings and propose fuzzy hyperideals and homomorphism theorems on fuzzy (m, n)-semihyperrings and the relationship between fuzzy (m, n)-semihyperrings and the usual (m, n)-semihyperrings.

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confidence: 55%

“…In [19] Davvaz studied the fuzzy hyperideals of the Krasner (m, n)-hyperring. Generalization of hyperstructures are also studied by [2,8,20,21].…”

Section: Introductionmentioning

confidence: 99%

(m,n)-Semihyperrings and an Algebra of Fuzzy (m,n)-Semihyperrings

Alam¹,

Aljahdali²,

Hundewale³

2015

Preprint

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“…For example, given a crisp hypergroup (X, +) and a fuzzy set l, then we say that l is a fuzzy (sub) hypergroup of (X, +) if every cut of l, say l t , is a (crisp) subhypergroup of (X, +). This was initiated by Zahedi et al [65] and continued by Davvaz [15,16] and Davvaz et al [11,17,19,20,22,24,29], 44,45], Kazancı et al [36,62], Zhan et al [67,68], also see [3].…”

Section: Introductionmentioning

confidence: 97%

Fuzzy hyperrings (Hv-rings) based on fuzzy universal sets

Davvaz

Fathi

Salleh

2010

Information Sciences

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“…In [30], Sen, Ameri and Chowdhury introduced and analyzed fuzzy semihypergroups. In [24], Leoreanu Fotea extended this study to fuzzy n-ary hyperstructures.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Γ-hypergroups

Leoreanu-Fotea

Davvaz

Feng

2014

Journal of Intelligent &Amp; Fuzzy Systems

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In this paper, we introduce and analyze fuzzy -hypergroups. We study fuzzy -hypergroups and fuzzy -hypergroup homomorphisms in connections with the associated -hypergroups and -hypergroup homomorphisms, respectively. Finally, since the fuzzy regular relations play an important role in getting quotient -structures, we introduce and analyze fuzzy regular and fuzzy strongly regular relations on fuzzy -hypergroups.

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A new type of fuzzy n-ary hyperstructures

Cited by 12 publications

References 13 publications

(m,n)-Semihyperrings and an Algebra of Fuzzy (m,n)-Semihyperrings

(m,n)-Semihyperrings and an Algebra of Fuzzy (m,n)-Semihyperrings

Fuzzy hyperrings (Hv-rings) based on fuzzy universal sets

Fuzzy Γ-hypergroups

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