An interval-valued intuitionistic fuzzy principal component analysis model-based method for complex multi-attribute large-group decision-making

Liu, Bingsheng; Shen, Yinghua; Zhang, Wei; Chen, Xiaohong; Wang, Xueqing

doi:10.1016/j.ejor.2015.02.025

Cited by 144 publications

(39 citation statements)

References 40 publications

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“…This task must be achieved while trying to reduce as much as possible the number of necessary dimensions for approximating the observed data. Liu et al (2014Liu et al ( , 2015b) suggested a group decision-making method based on the interval-valued intuitionistic fuzzy PCA. Calcagnì et al (2016) proposed a dimension reduction technique for two-mode non-convex fuzzy data.…”

Section: Principal Component Analysis For Imprecise Datamentioning

confidence: 99%

Exploratory multivariate analysis for empirical information affected by uncertainty and modeled in a fuzzy manner: a review

D’Urso

2017

Granul. Comput.

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Section: Principal Component Analysis For Imprecise Datamentioning

confidence: 99%

Exploratory multivariate analysis for empirical information affected by uncertainty and modeled in a fuzzy manner: a review

D’Urso

2017

Granul. Comput.

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“…Since the introduction of intuitionistic fuzzy sets proposed by Atanassov [28], the intuitionistic fuzzy decision-making has become a promising topic [29,30]. Intuitionistic linguistic variables [31] are discussed in the decision-making process, and the distance and similarity measures of intuitionistic fuzzy sets [32] are presented.…”

Section: Introductionmentioning

confidence: 99%

A Scalar Expected Value of Intuitionistic Fuzzy Random Individuals and Its Application to Risk Evaluation in Insurance Companies

Jin

2018

Mathematical Problems in Engineering

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Randomness and uncertainty always coexist in complex systems such as decision-making and risk evaluation systems in the real world. Intuitionistic fuzzy random variables, as a natural extension of fuzzy and random variables, may be a useful tool to characterize some high-uncertainty phenomena. This paper presents a scalar expected value operator of intuitionistic fuzzy random variables and then discusses some properties concerning the measurability of intuitionistic fuzzy random variables. In addition, a risk model based on intuitionistic fuzzy random individual claim amount in insurance companies is established, in which the claim number process is regarded as a Poisson process. The mean chance of the ultimate ruin is investigated in detail. In particular, the expressions of the mean chance of the ultimate ruin are presented in the cases of zero initial surplus and arbitrary initial surplus, respectively, if individual claim amount is an exponentially distributed intuitionistic fuzzy random variable. Finally, two illustrated examples are provided.

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“…To overcome these limitations, Atanassov and Gargov 18 proposed the concept of the interval-valued intuitionistic fuzzy set (IVIFS), in which the attributes are taken the form with interval-valued intuitionistic fuzzy number (IVIFN). Many studies were completed in recent years and various approaches to solve MADM problems under interval-valued intuitionistic fuzzy environment have been developed 24,25,26,27,28,29,30,31,32,33,34 . For example, Farhadinia 31 generalized recent results for the entropy of interval-valued fuzzy set (IVFS) based on the intuitionistic distance measure and its relationship with the similarity measure, and then applied them to interval-valued intuitionistic fuzzy decision making problem.…”

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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An interval-valued intuitionistic fuzzy principal component analysis model-based method for complex multi-attribute large-group decision-making

Cited by 144 publications

References 40 publications

Exploratory multivariate analysis for empirical information affected by uncertainty and modeled in a fuzzy manner: a review

Exploratory multivariate analysis for empirical information affected by uncertainty and modeled in a fuzzy manner: a review

A Scalar Expected Value of Intuitionistic Fuzzy Random Individuals and Its Application to Risk Evaluation in Insurance Companies

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

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