Interval valued q-rung orthopair fuzzy sets and their properties

Joshi, Bhagawati Prasad; Singh, Akhilesh Kumar; Bhatt, Pradeep Kumar; Vaisla, Kunwar Singh

doi:10.3233/jifs-169806

Cited by 157 publications

(117 citation statements)

References 15 publications

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“…,¯=¯= ,̄=¯. In addition, it is easy to check the validity of Conditions (24) and (25). Therefore, from Theorem 4.1 we conclude the desired (33).…”

Section: Derivatives Of Ivq-roffssupporting

confidence: 56%

“…In such situation, it is more convenient for DMs to provide their judgements through a subset of closed interval [0,1]. Therefore, Joshi et al presented the notion of interval‐valued q ‐rung orthopair fuzzy set (IV q ‐ROFS) whose membership degree and nonmembership degree are all intervals instead of two real numbers. Some of its set operations, such as negation, union, and intersection, were also studied.…”

Section: Introductionmentioning

confidence: 99%

“…Joshi et al25 ). An IVq-ROFS  over the set X is defined as follows: ˜( ) [0, 1]˜are intervals, and moreover,…”

mentioning

confidence: 99%

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Differential calculus of interval‐valued q ‐rung orthopair fuzzy functions and their applications

Gao

Zhang

2019

Int J Intell Syst

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The interval‐valued q‐rung orthopair fuzzy set (IVq‐ROFS) provides an extension of Yager's q‐rung orthopair fuzzy set (q‐ROFS), where membership and nonmembership degrees are subsets of the closed interval [ 0 , 1 ]. In such a situation, it is more superior for decision makers to provide their judgments by intervals instead of crisp numbers due to the uncertainty and vagueness in real life. In this paper, we study the calculus theories of IVq‐ROFS from the microscopic. In particular, we first introduce the elementary arithmetic of interval‐valued q‐rung orthopair fuzzy values (IVq‐ROFVs), including addition, multiplication, and their inverse. They are the basis for analysis and calculation throughout the work. In addition, we discuss and prove in detail the operation properties and aggregation operators of IVq‐ROFVs. Then, we introduce the concept of interval‐valued q‐rung orthopair fuzzy functions (IVq‐ROFFs), which is the main research object of this paper. After that, we further discuss the continuity, derivatives and differentials of IVq‐ROFFs. We also find that the derivatives of IVq‐ROFFs are closely related to elasticity, which is an important concept in economics. Finally, we provide some application examples to verify the feasibility and effectiveness of the derived results.

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“…,¯=¯= ,̄=¯. In addition, it is easy to check the validity of Conditions (24) and (25). Therefore, from Theorem 4.1 we conclude the desired (33).…”

Section: Derivatives Of Ivq-roffssupporting

confidence: 56%

Section: Introductionmentioning

confidence: 99%

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Differential calculus of interval‐valued q ‐rung orthopair fuzzy functions and their applications

Gao

Zhang

2019

Int J Intell Syst

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“…Du presented some q‐ rung orthopair fuzzy Minkowski‐type distance measures for solving some MADM issues. Extensions. Joshi et al and Wang et al extended the q‐ ROFS into interval form with its membership and nonmembership, named q‐ rung interval‐valued orthopair fuzzy set ( q‐ RIVOFS) or interval‐valued q‐ ROFS (IV q‐ ROFS). As real issues are getting more and more complicated and the linguistic preference information may be easily accepted.…”

Section: Introductionmentioning

confidence: 99%

Generalized orthopair fuzzy weighted distance‐based approximation (WDBA) algorithm in emergency decision‐making

2019

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With the intensification of global warming trends, the frequent occurrence of natural disasters has brought severe challenges to the sustainable development of society. Emergency decision‐making (EDM) in natural disasters is playing an increasingly important role in improving disaster response capacity. In the case of EDM evaluation, the essential problem arises serious incompleteness, impreciseness, subjectivity, and incertitude. The q‐rung orthopair fuzzy set (q‐ROFS), disposing the indeterminacy portrayed by membership and nonmembership with the sum of qth power of them, is a more viable and effective means to seize indeterminacy. The aim of paper is to present a new score function of q‐rung orthopair fuzzy number (q‐ROFN) for solving the failure problems when comparing two q‐ROFNs. Firstly, we introduce some basic set operations for q‐ROFS. The properties of these operations are also discussed in detail. Later, we propose a q‐rung orthopair fuzzy decision‐making method based on weighted distance‐based approximation (WDBA), in which the weights of decision‐makers are obtained from a nonliner optimization model according to the deviation‐based method. Finally, some examples are investigated to illustrate the feasibility and validity of the proposed approach. The salient features of the proposed method, compared to the existing q‐rung orthopair fuzzy decision‐making methods, are as follows: (a) it can obtain the optimal alternative without counterintuitive phenomena and (b) it has a great power in distinguishing the optimal alternative.

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“…Obviously, q-ROFS can be regarded as the extension of the IFS and PFS, when q = 1, the q-ROFS reduces to IFS, when q = 2, the q-ROFS reduces to PFS (see Figure 1). Afterwards, more and more works about q-ROFS have been studied by numerous scholars [19][20][21][22][23][24][25].…”

mentioning

confidence: 99%

Dual Hesitant q-Rung Orthopair Fuzzy Hamacher Aggregation Operators and their Applications in Scheme Selection of Construction Project

et al. 2019

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The q-rung orthopair fuzzy set (q-ROFS), which is the extension of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS), satisfies the sum of q-th power of membership degree and nonmembership degree is limited 1. Evidently, the q-ROFS can depict more fuzzy assessment information and consider decision-maker's (DM's) hesitance. Thus, the concept of a dual hesitant q-rung orthopair fuzzy set (DHq-ROFS) is developed in this paper. Then, based on Hamacher operation laws, weighting average (WA) operator and weighting geometric (WG) operator, some dual hesitant q-rung orthopair fuzzy Hamacher aggregation operators are developed, such as the dual hesitant q-rung orthopair fuzzy Hamacher weighting average (DHq-ROFHWA) operator, the dual hesitant q-rung orthopair fuzzy Hamacher weighting geometric (DHq-ROFHWG) operator, the dual hesitant q-rung orthopair fuzzy Hamacher ordered weighted average (DHq-ROFHOWA) operator, the dual hesitant q-rung orthopair fuzzy Hamacher ordered weighting geometric (DHq-ROFHOWG) operator, the dual hesitant q-rung orthopair fuzzy Hamacher hybrid average (DHq-ROFHHA) operator, and the dual hesitant q-rung orthopair fuzzy Hamacher hybrid geometric (DHq-ROFHHG) operator. The precious merits and some particular cases of above mentioned aggregation operators are briefly introduced. In the end, an actual application for scheme selection of construction project is provided to testify the proposed operators and deliver a comparative analysis.Keywords: multiple attribute decision-making (MADM) problems; Hamacher operation laws; dual hesitant q-rung orthopair fuzzy set (DHq-ROFS); the DHq-ROFHWA operator; the DHq-ROFHWG operator Symmetry 2019, 11, 771 2 of 26 of the membership degree µ and nonmembership degree v, which satisfies µ 2 + v 2 ≤ 1, so, it is obvious that the PFS can express more assessment information than the IFS. However, the scope of assessment information is still limited under Pythagorean fuzzy environment. For instance, given the evaluation value (0.7,0.9), we can easily find that 0.7 2 + 0.9 2 ≤ 1, which indicates that PFS cannot deal with such MADM problems. Then, to describe more evaluation information, Yager [18] further defined the q-rung orthopair fuzzy set (q-ROFS), q-ROFS is also consisted of the membership degree µ and nonmembership degree v which satisfies µ q + v q ≤ 1. Obviously, q-ROFS can be regarded as the extension of the IFS and PFS, when q = 1, the q-ROFS reduces to IFS, when q = 2, the q-ROFS reduces to PFS (see Figure 1). Afterwards, more and more works about q-ROFS have been studied by numerous scholars [19][20][21][22][23][24][25].

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Interval valued q-rung orthopair fuzzy sets and their properties

Cited by 157 publications

References 15 publications

Differential calculus of interval‐valued q ‐rung orthopair fuzzy functions and their applications

Differential calculus of interval‐valued q ‐rung orthopair fuzzy functions and their applications

Generalized orthopair fuzzy weighted distance‐based approximation (WDBA) algorithm in emergency decision‐making

Dual Hesitant q-Rung Orthopair Fuzzy Hamacher Aggregation Operators and their Applications in Scheme Selection of Construction Project

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