Products of elements in vague semigroups and their implementations in vague arithmetic

Demirci, Mustafa

doi:10.1016/j.fss.2005.04.001

Cited by 3 publications

(8 citation statements)

References 30 publications

(67 reference statements)

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“…The notion of the vague product of a finite number of elements in vague semigroups and its fundamental aspects are introduced in [16]. One of the aims of this section is to recall this notion and some of its elementary properties, which will be needed in this paper and the companion paper [15].…”

Section: Products Of Elements In Vague Groups and Their Fundamental Pmentioning

confidence: 99%

“…This subject will be handled towards the end of this section. The formulation of the considered notion and its properties basically depend on two subsidiary mathematical tools, ''exact product of a finite number of elements'' and ''successive product of a finite number of elements'', in vague semigroups [16]. For this reason, we first need to review these subsidiary tools.…”

Section: Products Of Elements In Vague Groups and Their Fundamental Pmentioning

confidence: 99%

“…; n À 1g ORDðÞ, ½ Q n i¼1 a i R fD i ji¼1;...;nÀ1g , ½ Q n i¼1 a i L f i ji¼1;...;nÀ1g , ½ Q n i¼1 a i R f i ji¼1;...;nÀ1g and ½ Q n i¼1 a i L fD i ji¼1;...;nÀ1g belong to the same equivalence class according to % E . Definition 3.3 [16]. Let us define the maps W R ; W L : X n Â X n !…”

Section: Products Of Elements In Vague Groups and Their Fundamental Pmentioning

confidence: 99%

“…Section 3 provides an overview to the notion of product of a finite number of elements in vague semigroups, and improves the representation properties of vague products of elements presented in [16]. As a natural implementation of the present results, it is shown in Section 3 how the product and the sum of a finite number of real numbers can be explicitly calculated in vague arithmetic.…”

Section: Introductionmentioning

confidence: 96%

“…In an analogy with classical algebra, notions of product and integral power of elements in vague groups possess the same impact on progress in vague algebra. As pronounced in [16], the formulation of properties of these notions, especially properties of the latter notion, requires a vague counterpart to the generalized associative law (called the generalized vague associative law) in vague semigroups. Due to this fact, the present paper and the follow-up paper [15] are devoted to the generalized vague associative law and its applications to integral powers of elements in vague groups.…”

Section: Introductionmentioning

confidence: 99%

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The generalized associative law in vague groups and its applications—I

DEMIRCI¹

2006

Information Sciences

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Products of elements and integral powers of elements in vague groups have a significant concern for the development and the applications of vague algebra. Formulation of properties of these notions basically depends on a many-valued counterpart to the generalized associative law (called the generalized vague associative law in vague groups). For this reason, the present paper and the forthcoming paper [M. Demirci, The generalized associative law in vague groups and its applications-II, Information Sciences, Submitted for publication] are devoted to the formulation of the generalized vague associative law and its applications in vague groups. The generalized vague associative law in vague semigroups, which is the main contribution of this exposition, and some elementary properties of the notion of a product of a finite number of elements in vague semigroups, which cover necessary preparatory results for Part II, are the subjects of this paper. Since the present paper forms an abstract foundation of the product and sum of a finite number of real numbers in vague arithmetic, some practical applications of the notions of product and sum of a finite number of real numbers in vague arithmetic are also given. Information Sciences 176 (2006) 900-936 www.elsevier.com/locate/ins

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Section: Products Of Elements In Vague Groups and Their Fundamental Pmentioning

confidence: 99%

Section: Products Of Elements In Vague Groups and Their Fundamental Pmentioning

confidence: 99%

Section: Products Of Elements In Vague Groups and Their Fundamental Pmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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The generalized associative law in vague groups and its applications—I

DEMIRCI¹

2006

Information Sciences

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The generalized associative law in vague groups and its applications—II

Demirci

2006

Information Sciences

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Multivalued representation and new algebraic structures for fuzzy numbers

Fechete¹,

Fechete²

2014

CJM

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In this paper we introduce a new representation of fuzzy numbers (called the multivalued representation) and a new multiplication on the set F of fuzzy numbers. Introducing a Dorroh type product between fuzzy numbers, we construct some semiring structures on the set F. Two important particular cases of the general Dorroh type product are the cross product, introduced in [Ban, A. I. and Bede, B., Properties of the cross product of fuzzy numbers, Journal of Fuzzy Mathematics, 14 (2006), 513–531] and the Dorroh product, introduced in this paper. An equivalence relation, compatible with the addition and the Dorroh product, is also given.

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Products of elements in vague semigroups and their implementations in vague arithmetic

Cited by 3 publications

References 30 publications

The generalized associative law in vague groups and its applications—I

The generalized associative law in vague groups and its applications—I

The generalized associative law in vague groups and its applications—II

Multivalued representation and new algebraic structures for fuzzy numbers

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