Cut Sets on Interval-Valued Intuitionistic Fuzzy Sets

Yuan, Xiao; Li, Hongxing

doi:10.1109/fskd.2009.606

Cited by 4 publications

(2 citation statements)

References 14 publications

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“…Then we recover an IVFS knowing only its level sets, which is the topic of the Decomposition Theorem. In the literature there is a lot of papers related to these topics (see, e.g., Huidobro et al 2020;Yuan and Li 2009). Finally we prove the properties of this proposal for convexity.…”

Section: Introductionmentioning

confidence: 58%

Convexity and level sets for interval-valued fuzzy sets

Huidobro

Alonso

Janiš

et al. 2022

Fuzzy Optim Decis Making

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Convexity is a deeply studied concept since it is very useful in many fields of mathematics, like optimization. When we deal with imprecision, the convexity is required as well and some important applications can be found fuzzy optimization, in particular convexity of fuzzy sets. In this paper we have extended the notion of convexity for interval-valued fuzzy sets in order to be able to cover some wider area of imprecision. We show some of its interesting properties, and study the preservation under the intersection and the cutworthy property. Finally, we applied convexity to decision-making problems.

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Section: Introductionmentioning

confidence: 58%

Convexity and level sets for interval-valued fuzzy sets

Huidobro

Alonso

Janiš

et al. 2022

Fuzzy Optim Decis Making

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“…In the succession of fuzzification of subgroups, the idea of level subgroup was initiated by Das [8]. Yuan and Li [9] studied the impact of these level sets in the field of intuitionistic fuzzy sets. To see more on the level sets and level subgroups, we refer to [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

On Structural Properties of $ξ$ -Complex Fuzzy Sets and Their Applications

et al. 2020

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Complex fuzzy sets are the novel extension of Zadeh’s fuzzy sets. In this paper, we comprise the introduction to the concept of ξ -complex fuzzy sets and proofs of their various set theoretical properties. We define the notion of α , δ -cut sets of ξ -complex fuzzy sets and justify the representation of an ξ -complex fuzzy set as a union of nested intervals of these cut sets. We also apply this newly defined concept to a physical situation in which one may judge the performance of the participants in a given task. In addition, we innovate the phenomena of ξ -complex fuzzy subgroups and investigate some of their fundamental algebraic attributes. Moreover, we utilize this notion to define level subgroups of these groups and prove the necessary and sufficient condition under which an ξ -complex fuzzy set is ξ -complex fuzzy subgroup. Furthermore, we extend the idea of ξ -complex fuzzy normal subgroup to define the quotient group of a group G by this particular ξ -complex fuzzy normal subgroup and establish an isomorphism between this quotient group and a quotient group of G by a specific normal subgroup G A ξ .

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Interval Valued Intuitionistic Fuzzy Gaussian Membership Function: A Novel Extension

Bharatraj

2020

Advances in Intelligent Systems and Computing

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The Interval-valued intuitionistic fuzzy sets (IVIFSs) have long been used to model vagueness and have been used in decision making, pattern recognition, image processing, and other applications. In this study, IVIFSs are defined using Gaussian membership functions (GMFs), and new measures of the distance, the overlap, and the angle between two sets are developed. The proposed methodology is used to determine the similarities between test subjects in genetic brain profiling.

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Cut Sets on Interval-Valued Intuitionistic Fuzzy Sets

Cited by 4 publications

References 14 publications

Convexity and level sets for interval-valued fuzzy sets

Convexity and level sets for interval-valued fuzzy sets

On Structural Properties of $ξ$ -Complex Fuzzy Sets and Their Applications

Interval Valued Intuitionistic Fuzzy Gaussian Membership Function: A Novel Extension

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Cut Sets on Interval-Valued Intuitionistic Fuzzy Sets

Cited by 4 publications

References 14 publications

Convexity and level sets for interval-valued fuzzy sets

Convexity and level sets for interval-valued fuzzy sets

On Structural Properties of ξ -Complex Fuzzy Sets and Their Applications

Interval Valued Intuitionistic Fuzzy Gaussian Membership Function: A Novel Extension

Contact Info

Product

Resources

About

On Structural Properties of $ξ$ -Complex Fuzzy Sets and Their Applications