Atanassov’s intuitionistic fuzzy grade of hypergroups

Cristea, Irina; Davvaz, Bijan

doi:10.1016/j.ins.2010.01.002

Cited by 27 publications

(26 citation statements)

References 33 publications

(13 reference statements)

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“…First, we briefly present introductory concepts concerning the intuitionistic fuzzy sets connected with the complete hypergroups. In particular, we insist on the properties of the intuitionistic fuzzy set defined by Cristea-Davvaz [21], but in the framework of the complete hypergroups. The main part of the paper is covered in Section 3, where we determine necessary and sufficient conditions such that the above mentioned intuitionistic fuzzy set (that is the key element in determining the intuitionistic fuzzy grade of a hypergroup) is an intuitionistic fuzzy subhypergroup of special complete hypergroups, obtained from a group isomorphic with the additive group of integers modulo a prime number, or modulo the double of a prime number.…”

Section: Et Al / Special Intuitionistic Fuzzy Subhypergroups Of Compmentioning

confidence: 99%

Special intuitionistic fuzzy subhypergroups of complete hypergroups

Cristea

Davvaz

Sadrabadi

2015

Journal of Intelligent &Amp; Fuzzy Systems

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Any complete hypergroup H can be characterized by an ordered m-tuple of natural numbers, representing the cardinalities of the subsets of H that divide it in a specific partition. In this paper we determine necessary and sufficient conditions concerning the corresponding m-tuples such that a particular intuitionistic fuzzy set (that is the key element in determining the intuitionistic fuzzy grade of a hypergroup) is an intuitionistic fuzzy subhypergroup of special complete hypergroups, those obtained from a group isomorphic with the additive group of integers modulo a prime number, or modulo the double of a prime number. (B. Davvaz). has been determined for several remarkable classes of finite hypergroups (as complete hypergroups, 1hypergroups, i.p.s. hypergroups) by Corsini-Cristea [9-11], and then by Cristea [17], Angheluţȃ-Cristea [3], but also for a hypergraph by Corsini et al. [15], by Corsini-Leoreanu-Fotea [14], or for multivalued functions by Corsini-Mahjoob [16]. For more details regarding other connections between hyperstructures and fuzzy sets, the reader is refereed to [1, 2, 26, 32, 41, 44].On the other side, using the intuitionistic fuzzy sets, Cristea-Davvaz [21] defined the intuitionistic fuzzy grade of a hypergroup, investigated later on by the authors of this paper in the context of i.p.s. hypergroups of order less than or equal to 7 [28,29], for the hypergraphs [30], or for complete hypergroups [31,33]. The key role in the above mentioned construction is played by an intuitionistic fuzzy set A = (μ,λ), that has an interesting form for a complete hypergroup, as we will notice in the next section. Based on this reason, this specific paper focuses on the characterization of several particular complete hypergroups having A = (μ,λ) as an intuitionistic fuzzy subhypergroup. Our research can be viewed as a continuation of the work started by 1064-1246/15/$27.50

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Section: Et Al / Special Intuitionistic Fuzzy Subhypergroups Of Compmentioning

confidence: 99%

Special intuitionistic fuzzy subhypergroups of complete hypergroups

Cristea

Davvaz

Sadrabadi

2015

Journal of Intelligent &Amp; Fuzzy Systems

Self Cite

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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: 98%

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

Davvaz

Fathi

Salleh

2010

Information Sciences

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“…In [29], Leoreanu-Fotea and Davvaz studied fuzzy hyperrings. Recently, Davvaz et al [10,13,16,18,19] considered the intuitionistic fuzzification of the concept of algebraic hyperstructures and investigated some properties of such hyperstructures. Now, in this work we introduce the notion of an Atanassov's intuitionistic fuzzy − hyperideals of a − semihypergroups and investigate some basic properties about it.…”

Section: Introductionmentioning

confidence: 99%