Topology of interval-valued intuitionistic fuzzy sets

Mondal, Tapas Kumar; Samanta, Sourav

doi:10.1016/s0165-0114(98)00436-9

Cited by 91 publications

(12 citation statements)

References 4 publications

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“…Other properties of these sets were studied and the concept of intuitionistic fuzzy sets was introduced by Atanassov [1][2][3][4][5]. The topological properties of interval valued intuitionistic fuzzy sets were studied by Mondal and Samantha [12]. αinterval valued fuzzy sets were introduced by Çuvalcıoğlu, Bal and Çitil in 2022 [6].…”

Section: Introductionmentioning

confidence: 99%

(Α,β)-Interval VALUED INTUITIONISTIC FUZZY SETS DEFINED ON (Α,β)-Interval VALUED SET

Bal

Çuvalcıoğlu

ALTINCI

2023

Journal of Universal Mathematics

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In this paper, (α,β)-interval valued set is studied. The order relation on (α,β)-interval valued set is defined. It is shown that (α,β)-interval valued set is complete lattice by giving the definitions of infumum and supremum on these sets. Then, negation function on these sets is introduced. With the help of (α,β)-interval valued set ,(α,β)-interval valued intuitionistic fuzzy sets are defined. The fundamental algebraic properties of these sets are examined. The level subsets of (α,β)-interval valued intuitionistic fuzzy sets are given. Some propositions and examples are studied.

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Section: Introductionmentioning

confidence: 99%

(Α,β)-Interval VALUED INTUITIONISTIC FUZZY SETS DEFINED ON (Α,β)-Interval VALUED SET

Bal

Çuvalcıoğlu

ALTINCI

2023

Journal of Universal Mathematics

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“…Dual hesitant fuzzy set (DHFS) [1] is a recent generalization of fuzzy set (FS) [2] which consists of membership hesitant function and non-membership hesitant function' DHFS confronts several different potential values that indicate whether certainty or ambiguity is the epistemic degree. This includes FS, intuitionistic fuzzy set (IFS) [3], [4] and hesitant fuzzy set (HFS) [5], [6] so that ambiguous knowledge can be treated more flexibly in the decision-making process. Numerous researchers applied DHFS to solve problems in multi-criteria decision making (MCDM) [7]- [14].…”

Section: Introductionmentioning

confidence: 99%

Z-Score Functions of Dual Hesitant Fuzzy Set and Its Applications in Multi-Criteria Decision Making

Rodzi¹,

Ahmad²,

Ismail³

et al. 2021

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Dual hesitant fuzzy set (DHFS) consists of two parts: membership hesitant function and non-membership hesitant function. This set supports more exemplary and flexible access to set degrees for each element in the domain and can address two types of hesitant in this situation. It can be considered a powerful tool for expressing uncertain information in the decision-making process. The function of z-score, namely z-arithmetic mean, z-geometric mean, and z-harmonic mean, has been proposed with five important bases, these bases are hesitant degree for dual hesitant fuzzy element (DHFE), DHFE deviation degree, parameter , (the importance of the hesitant degree), parameter  , (the importance of the deviation degree) and parameter , (the importance of membership (positive view) or non-membership (negative view). A comparison of the z-score with the existing score function was made to show some of their drawbacks. Next, the z-score function is then applied to solve multi-criteria decision making (MCDM) problems. To illustrate the proposed method's effectiveness, an example of MCDM specifically in pattern recognition has been shown.

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“…Researchers recognized that FS theory has many disadvantages, but several enhancements have been done to improve the method's usage in real life applications. Some of the most known extensions of FSs include intuitionistic fuzzy sets (IFS) [2], interval-valued intuition fuzzy set (IVIFS) [3], fuzzy multiset [4] and fuzzy soft sets [5]. The hesitant fuzzy set (HFS) was initially implemented by Torra [6], [7].…”

Section: Introductionmentioning

confidence: 99%

Z-Score Functions of Hesitant Fuzzy Sets

Rodzi¹,

Ahmad²,

Ismail³

et al. 2021

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The hesitant fuzzy set (HFS) concept as an extension of fuzzy set (FS) in which the membership degree of a given element, called the hesitant fuzzy element (HFE), is defined as a set of possible values. A large number of studies are concentrating on HFE and HFS measurements. It is not just because of their crucial importance in theoretical studies, but also because they are required for almost any application field. The score function of HFE is a useful method for converting data into a single value. Moreover, the scoring function provides a much easier way to determine each alternative's ranking order for multi-criteria decision-making (MCDM). This study introduces a new hesitant degree of HFE and the z-score function of HFE, which consists of z-arithmetic mean, z-geometric mean, and z-harmonic mean. The z-score function is developed with four main bases: a hesitant degree of HFE, deviation value of HFE, the importance of the hesitant degree of HFE, , and importance of the deviation value of HFE, . These three proposed scores are compared with the existing scores functions to identify the proposed z-score function's flexibility. An algorithm based on the z-score function was developed to create an algorithm solution to MCDM. Example of secondary data on supplier selection for automated companies is used to prove the algorithms' capability in ranking order for MCDM.

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Topology of interval-valued intuitionistic fuzzy sets

Cited by 91 publications

References 4 publications

(Α,β)-Interval VALUED INTUITIONISTIC FUZZY SETS DEFINED ON (Α,β)-Interval VALUED SET

(Α,β)-Interval VALUED INTUITIONISTIC FUZZY SETS DEFINED ON (Α,β)-Interval VALUED SET

Z-Score Functions of Dual Hesitant Fuzzy Set and Its Applications in Multi-Criteria Decision Making

Z-Score Functions of Hesitant Fuzzy Sets

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