Intuitionistic fuzzy-valued Choquet integral and its application in multicriteria decision making

Wu, Jian‐Zhang; Chen, Fang; Nie, Cuiping; Zhang, Qiang

doi:10.1016/j.ins.2012.07.056

Cited by 77 publications

(54 citation statements)

References 57 publications

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“…The crux of applying the fuzzy measures and integrals to solve the MCDM problems is essentially about how to determine the value of the important measures. Currently, the fuzzy measures of criteria are usually given directly by experts (Buyukozkan et al, 2009;Wu et al, 2013Wu et al, , 2014Liou et al, 2014). However, it is not always easy to find suitable experts to determine the fuzzy measures used in the evaluation of airline service quality, since a considerable portion of human opinion (as opposed to scientific facts) could be involved.…”

Section: Methodsmentioning

confidence: 99%

A non-additive multiple criteria analysis method for evaluation of airline service quality

Zhang

Zhou

et al. 2015

Journal of Air Transport Management

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Section: Methodsmentioning

confidence: 99%

A non-additive multiple criteria analysis method for evaluation of airline service quality

Zhang

Zhou

et al. 2015

Journal of Air Transport Management

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“…If the set of criteria is denoted as

X = {x_{1}, x_{2}, …, x_{n}}

, then the fuzzy measure

μ (x_{i})

will present the importance degree of the criterion

x_{i}

(

i = 1, 2, …, n

) μ(C) can define the weight of the combination of criteria

\forall C \in scriptP (X)

.…”

Section: Preliminariesmentioning

confidence: 99%

“…The Choquet integral is a suitable aggregation function when using the fuzzy measure to characterize the importance of the subsets of criteria . The Chquet integral is defined as follows.…”

Section: Preliminariesmentioning

confidence: 99%

q ‐Rung orthopair fuzzy Choquet integral aggregation and its application in heterogeneous multicriteria two‐sided matching decision making

2019

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In the real decision making, q‐rung orthopair fuzzy sets ( q‐ROFSs) as a novel effective tool can depict and handle uncertain information in a broader perspective. Considering the interrelationships among the criteria, this paper extends Choquet integral to the q‐rung orthopair fuzzy environment and further investigates its application in multicriteria two‐sided matching decision making. To determine the fuzzy measures used in Choquet integral, we first define a pair of q‐rung orthopair fuzzy entropy and cross‐entropy. Then, by utilizing λ‐fuzzy measure theory, we propose an entropy‐based method to calculate the fuzzy measures upon criteria. Furthermore, we discuss q‐rung orthopair fuzzy Choquet integral operator and its properties. Thus, with the aid of q‐rung orthopair fuzzy Choquet integral, we consider the preference heterogeneity of the matching subjects and further explore the corresponding generalized model and approach for the two‐sided matching. Finally, a simulated example of loan market matching is given to illustrate the validity and applicability of our proposed approach.

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“…Meng et al 45 defined some new hybrid Choquet integral aggregation operators, and proposed a method to solve multiple criteria group decision making (MCGDM) based on intuitionistic fuzzy Choquet integral with respect to the generalized λ -Shapely index. Wu et al 47 presented a detailed discussion on the integration properties of the interval intuitionistic fuzzy conjugate Choquet integral, and applied these theoretical analysis results to software development risks decision making. In addition, some authors have also applied Choquet integral to other fields, such as hesitant fuzzy set 49 , game theory 50 , neural networks 51,52 , statistical learning 53 , and combinatorial optimization 54,55,56 .…”

Section: Introductionmentioning

confidence: 99%

Multi-attribute group decision making based on Choquet integral under interval-valued intuitionistic fuzzy environment

Qin¹,

Liu²,

Pedrycz³

2016

IJCIS

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In this paper, we propose new methods to represent interdependence among alternative attributes and experts' opinions by constructing Choquet integral using interval-valued intuitionistic fuzzy numbers. In the sequel, we apply these methods to solve the multiple attribute group decision-making (MAGDM) problems under interval-valued intuitionistic fuzzy environment. First, the concept of interval-valued intuitionistic fuzzy Choquet integral is defined, and some elementary properties are studied in detail. Next, an axiomatic system of interval-valued intuitionistic fuzzy measure is established by delivering a series of mathematical proofs. Then, with fuzzy entropy and Shapely-values in game theory, we propose the interval-valued intuitionistic fuzzy measure development methods in order to form the importance measure of attributes and correlation measure of the experts, respectively. Based on the results of theoretical analysis, a new method is proposed to handle the interval-valued intuitionistic fuzzy group decision making problems. A numerical example illustrates the procedure of the proposed methods and verifies the validity and effectiveness of our new proposed methods.Keywords: Interval-valued intuitionistic fuzzy Choquet integral, interval-valued intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy measure , multiple attribute group decision making.

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Intuitionistic fuzzy-valued Choquet integral and its application in multicriteria decision making

Cited by 77 publications

References 57 publications

A non-additive multiple criteria analysis method for evaluation of airline service quality

A non-additive multiple criteria analysis method for evaluation of airline service quality

q ‐Rung orthopair fuzzy Choquet integral aggregation and its application in heterogeneous multicriteria two‐sided matching decision making

Multi-attribute group decision making based on Choquet integral under interval-valued intuitionistic fuzzy environment

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