Research on arithmetic operations over generalized orthopair fuzzy sets

Wen, Du

doi:10.1002/int.22073

Cited by 16 publications

(13 citation statements)

References 43 publications

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“…Yager 41 proposed the concept of q ‐rung orthopair fuzzy set ( q ‐ROFS) for the decision information with the sum of MBSD and NOMBSD greater than 1. As a stronger tool than IFS in dealing with probability information and uncertainty information, it could process that the decision information with the sum of n ( n ≥ 1) power of positive MBSD and negative MBSD is greater than 1 but the sum of q ( q > n) power of them is bound to 1. q ‐ROFS has attracted a lot of attentions, and many authors have successively carried out researches from the following aspects, including basic properties, 42,43 basic operational rules, 44,45 and information aggregation operators 46‐48 . Whereas, the internal interactivities between MBSDs of decision‐making units as well as the interrelationship between attributes are not involved in the above researches.…”

Section: Literature Reviewmentioning

confidence: 99%

A decision‐making algorithm for online shopping using deep‐learning–based opinion pairs mining and q ‐rung orthopair fuzzy interaction Heronian mean operators

Yang

Ouyang

et al. 2020

Int J Intell Syst

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In the process of online shopping, consumers usually compare the review information of the same product in different e‐commerce platforms. The sentiment orientation of online reviews from different platforms interactively influences on consumers’ purchase decision. However, due to the limitation of the ability to process information manually, it is difficult for a consumer to accurately identify the sentiment orientation of all reviews one by one and describe the process of their interactive influence. To this end, we proposed an online shopping support model using deep‐learning–based opinion mining and q‐rung orthopair fuzzy interaction weighted Heronian mean (q‐ROFIWHM) operators. First, in the proposed method, the deep‐learning model is used to automatically extract different product attribute words and opinion words from online reviews, and match the corresponding attribute‐opinion pairs; meanwhile, the sentiment dictionary is used to calculate sentiment orientation, including positive, negative, and neutral sentiments. Second, the proportions of the three kinds of sentiments about each attribute of the same product are calculated. According to the proportion value of attribute sentiment from different platforms, the sentiment information is converted into multiple cross‐decision matrices, which are represented by the q‐rung orthopair fuzzy set. Third, considering the interactive characteristics of decision matrix, the q‐ROFIWHM operators are proposed to aggregate this cross‐decision information, and then the ranking result was determined by score function to support consumers' purchase decisions. Finally, an actual example of mobile phone purchase is given to verify the rationality of the proposed method, and the sensitivity and the comparison analysis are used to show its effectiveness and superiority.

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Section: Literature Reviewmentioning

confidence: 99%

A decision‐making algorithm for online shopping using deep‐learning–based opinion pairs mining and q ‐rung orthopair fuzzy interaction Heronian mean operators

Yang

Ouyang

et al. 2020

Int J Intell Syst

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“…Generalized orthopair fuzzy sets have extended intuitionistic fuzzy sets [74] and Pythagorean fuzzy sets [75,76]. The orthopair fuzzy sets have advantages in representing uncertainties [77] and have been used in a wide scope of applications [78,79]. It is more flexible, practical and efficient than intuitionistic fuzzy sets and Pythagorean fuzzy sets in dealing with ambiguity and uncertainty [80,81].…”

Section: Generalized Orthopair Fuzzy Setsmentioning

confidence: 99%

Refined Expected Value Decision Rules under Orthopair Fuzzy Environment

Xue

Deng

2020

Mathematics

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Refined expected value decision rules can refine the calculation of the expected value and make decisions by estimating the expected values of different alternatives, which use many theories, such as Choquet integral, PM function, measure and so on. However, the refined expected value decision rules have not been applied to the orthopair fuzzy environment yet. To address this issue, in this paper we propose the refined expected value decision rules under the orthopair fuzzy environment, which can apply the refined expected value decision rules on the issues of decision making that is described in the orthopair fuzzy environment. Numerical examples were applied to verify the availability and flexibility of the new refined expected value decision rules model. The experimental results demonstrate that the proposed model can apply refined expected value decision rules in the orthopair fuzzy environment and solve the decision making issues with the orthopair fuzzy environment successfully.

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“…Moreover, the addition and multiplication operations of

q

‐ROFVs are defined as follows:

x \oplus y = 〈 {(a_{1}^{q} + a_{2}^{q} - a_{1}^{q} a_{2}^{q})}^{1 ∕ q}, b_{1} b_{2} 〉,

x \otimes y = 〈 a_{1} a_{2}, {false(b_{1}^{q} + b_{2}^{q} - b_{1}^{q} b_{2}^{q} false)}^{1 / q} 〉 .

Note that operations

\oplus

and

\otimes

are commutative and associative, then for

x_{i} \in S_{q}

x_{1} \oplus x_{2} \oplus ⋯ \oplus x_{n}

and

x_{1} \otimes x_{2} \otimes ⋯ \otimes x_{n}

can be shortly represented by

\oplus_{i = 1}^{n} x_{i}

and

\otimes_{i = 1}^{n} x_{i}

, respectively. In fact, by induction, we have

\oplus_{i = 1}^{n} x_{i} = true〈 {(1 - {falsefalse}_{\prod}^{i = 1} false(1 - a_{i}^{q} false))}^{1 ∕ q}, \prod_{i = 1}^{n} b_{i} true〉,

\otimes_{i = 1}^{n}

…”

Section: Bold-italicq‐rung Orthopair Fuzzy Valuesmentioning

confidence: 99%

“…Yager et al investigated the possibility and certainty as well as plausibility and belief in the

q

‐rung orthopair fuzzy environment and studied arithmetic operations on

q

‐ROFSs via extension principle. Liu et al proposed the addition and multiplication operations for

q

‐ROFVs via the algebraic

t

‐(co)norm, while the subtraction and division operations were defined by Du in two different ways and their primary properties were examined. Gao et al discussed continuities, derivatives and differentials of

q

‐rung orthopair fuzzy functions based on arithmetic operations over

q

‐ROFVs and further studied the

q

‐rung orthopair fuzzy indefinite and definite integrals under additive operations .…”

Section: Introductionmentioning

confidence: 99%

Weighted power means of q‐rung orthopair fuzzy information and their applications in multiattribute decision making

Wen

2019

Int J Intell Syst

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Weighted power means with weights and exponents serving as their parameters are generalizations of arithmetic means. Taking into account decision makers' flexibility in decision making, each attribute value is usually expressed by a q-rung orthopair fuzzy value (q-ROFV, ≥ q 1), where the former indicates the support for membership, the latter support against membership, and the sum of their qth powers is bounded by one. In this paper, we propose the weighted power means of qrung orthopair fuzzy values to enrich and flourish aggregations on q-ROFVs. First, the q-rung orthopair fuzzy weighted power mean operator is presented, and its boundedness is precisely characterized in terms of the power exponent. Then, the q-rung orthopair fuzzy ordered weighted power mean operator is introduced, and some of its fundamental properties are investigated in detail. Finally, a novel multiattribute decision making method is explored based on developed operators under the q-rung orthopair fuzzy environment. A numerical example is given to illustrate the feasibility and validity of the proposed approach, and it is shown that the power exponent is an index suggesting the degree of the optimism of decision makers. K E Y W O R D S aggregation operator, multiattribute decision making, q-rung orthopair fuzzy value, weighted power mean 2836 | DU operations. 22 Ye et al 23 studied the single variable differential calculus under q-rung orthopair fuzzy environment. Shu et al 24 developed q-rung orthopair fuzzy definite integrals to aggregate q-rung orthopair fuzzy continuous information. Peng et al 25 presented the exponential operation of q-ROFVs, in which the bases are positive real numbers and the exponents are q-ROFVs. Joshi et al 26 introduced the notion of interval-valued q-rung orthopair fuzzy sets by combining interval-valued and q-rung orthopair fuzzy sets. In the seminal paper of Yager, 12 a general framework of constructing aggregation operators of q-ROFSs is provided. Specially, Yager et al 12,17 developed the Sugeno and Choquet aggregation operators on q-ROFSs based on a pair of dual aggregation operators. Along this line of research, Liu et al introduced a large number of operators on q-ROFSs, including the weighted averaging/geometric operator, 18 (weighted, geometric) Bonferroni mean operator, 19 (weighted) Archimedean Bonferroni mean operator, 27 power (weighted) average operator, 28 power (weighted) Maclaurin symmetric mean operator, 28 and (weighted) Heronian mean operator. 29 Wei et al further put forward the generalized (weighted) Heronian mean operator, 30 (weighted) geometric Heronian mean operator 30 and (dual, weighted) Maclaurin symmetric mean operator 31 for q-ROFSs. Wang et al 32 presented the q-rung orthopair fuzzy (weighted, dual) Muirhead mean operators for fusing q-ROFSs. Peng et al 25 proposed the q-rung orthopair fuzzy weighted exponential aggregation operator over q-ROFSs based on the exponential operation of q-ROFVs.Weighted power mean (WPM, also called the generalized weighted averaging operator) is an i...

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Research on arithmetic operations over generalized orthopair fuzzy sets

Cited by 16 publications

References 43 publications

A decision‐making algorithm for online shopping using deep‐learning–based opinion pairs mining and q ‐rung orthopair fuzzy interaction Heronian mean operators

A decision‐making algorithm for online shopping using deep‐learning–based opinion pairs mining and q ‐rung orthopair fuzzy interaction Heronian mean operators

Refined Expected Value Decision Rules under Orthopair Fuzzy Environment

Weighted power means of q‐rung orthopair fuzzy information and their applications in multiattribute decision making

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