A Historical Account of Types of Fuzzy Sets and Their Relationships

Bustince, Humberto; Barrenechea, Edurne; Pagola, Miguel; Fernández, Javier; Zhang, Xu; Bedregal, Benjamín R. C.; Montero, Javier; Hagras, Hani; Herrera, Francisco; Baets, Bernard De

doi:10.1109/tfuzz.2015.2451692

Cited by 406 publications

(175 citation statements)

References 153 publications

(163 reference statements)

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“…Being one of the widely adopted ways in the literature, to deal with such situations is to represent these parameters as fuzzy numbers [2] and its extensions [3]. Thamaraiselvi and Santhi [4] pointed out that neutrosophic set [5], one of the extensions of fuzzy set, is used in different research areas.…”

Section: Introductionmentioning

confidence: 99%

Modified Approach for Optimization of Real Life Transportation Problem in Neutrosophic Environment

Singh

Kumar

Appadoo

2017

Mathematical Problems in Engineering

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To the best of our knowledge, there is only one approach for solving neutrosophic cost minimization transportation problems. Since neutrosophic transportation problems are a new area of research, other researchers may be attracted to extend this approach for solving other types of neutrosophic transportation problems like neutrosophic solid transportation problems, neutrosophic time minimization transportation problems, neutrosophic transshipment problems, and so on. However, after a deep study of the existing approach, it is noticed that a mathematical incorrect assumption has been used in these existing approaches; therefore there is a need to modify these existing approaches. Keeping the same in mind, in this paper, the existing approach is modified. Furthermore, the exact results of some existing transportation problems are obtained by the modified approach.

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Section: Introductionmentioning

confidence: 99%

Modified Approach for Optimization of Real Life Transportation Problem in Neutrosophic Environment

Singh

Kumar

Appadoo

2017

Mathematical Problems in Engineering

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“…In order to understand the history behind Hesitant Fuzzy Sets, we will briefly discuss here some of the ideas given by Bustince et al in [9] which analyzed the relationships among different types of fuzzy sets (FSs). Besides, they also observed that in fact the concept of HFSs are the same as SVFSs, as defined by Grattan-Guinness in 1976 [13].…”

Section: A Brief Historical Overviewmentioning

confidence: 99%

“…A IFSs may be recovered taking into account the mathematical equivalence between them and IVFSs. [9] 2 Notice that the result of this process is not a THFE, but a finite and non-empty multiset over [0,1]. This is equivalent to consider an increasing reordering (via permutation) of the elements of X.…”

Section: Definitionmentioning

confidence: 99%

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Construction of Typical Hesitant Triangular Norms regarding Xu-Xia-partial Order

Santos¹,

Bedregal²,

Santiago³

et al. 2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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Fuzzy Sets theory has been applied in many fields to handle uncertainty, which can be reflected on the membership degree of the objects belonging to a set. Moreover, Hesitant Fuzzy Sets are useful whenever there is indecision among several possible values for the preferences over objects in the process of decision-making. In this sense, the aim of this work is to consider the notion of aggregation functions regarding Xu-Xia-partial order for typical hesitant fuzzy elements and to study Typical Hesitant Triangular Norms and some of the properties usually demanded to such operator.

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“…In some applications, such as decision making, it has been proven that the systematic use of extensions of fuzzy sets is a useful tool [1]. This is the case, for instance, of interval-valued fuzzy sets [2,3] or, equivalently, Atanassov intuitionistic fuzzy sets [4].…”

Section: Introductionmentioning

confidence: 99%

Construction of admissible linear orders for pairs of intervals

Miguel¹,

Bustince²,

Induráin³

et al. 2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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A Historical Account of Types of Fuzzy Sets and Their Relationships

Abstract: Abstract-In this work we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used.

Cited by 406 publications

References 153 publications

Modified Approach for Optimization of Real Life Transportation Problem in Neutrosophic Environment

Modified Approach for Optimization of Real Life Transportation Problem in Neutrosophic Environment

Construction of Typical Hesitant Triangular Norms regarding Xu-Xia-partial Order

Construction of admissible linear orders for pairs of intervals

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