A Visual Comparison Method and Similarity Measure for Probabilistic Linguistic Term Sets and Their Applications in Multi-criteria Decision Making

Xian, Sidong; Chai, Jiahui; Yin, Yubo

doi:10.1007/s40815-019-00632-y

Cited by 26 publications

(24 citation statements)

References 53 publications

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“…To prove the practicability and effectiveness of our method, we will compare it with other approaches 3,14,42 …”

Section: Illustrative Example and Comparative Analysismentioning

confidence: 99%

“…For Reference [14], the probabilistic linguistic multiple attribute group decision making with incomplete weight information is investigated. And Xian et al 42 proposed a visual comparison method and the similarity measure for PLTSs in multicriteria decision making. It should be noted that the expression method of evaluation information in Reference [14] is inconsistent with that in this paper.…”

Section: Illustrative Example and Comparative Analysismentioning

confidence: 99%

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Belief interval interpretation of probabilistic linguistic term sets and a visual method for solving the preference problem in multicriteria group decision making

et al. 2021

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For the application of probabilistic linguistic term sets (PLTSs) in multicriteria group decision making (MCGDM), this paper aims to develop an approach to solve the preference problem. First, a belief interval interpretation of PLTSs is presented, which makes it possible to represent the mathematical operations on PLTSs as the operations on belief intervals. This can reduce the uncertainty degree of information caused by the differentiated knowledge and cognitions of decision makers. Then, two methods of belief interval measure are proposed. One is the distance measure, which is utilized to obtain the criteria weights of each decision maker, so as to recognize the preferences for criteria. The other is the probability degree, which is used to get the partial order relation for alternatives of each decision maker, and to recognize the preferences for alternatives. Next, employing Dempster's rule of combination and graph theory, a visual algorithm is constructed to solve the MCGDM preference problem in the application of PLTSs. Finally, an illustrative example for the selection of emergency materials deployment scheme and the comparative analyses are shown to demonstrate the effectiveness of the proposed method.

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“…To prove the practicability and effectiveness of our method, we will compare it with other approaches 3,14,42 …”

Section: Illustrative Example and Comparative Analysismentioning

confidence: 99%

Section: Illustrative Example and Comparative Analysismentioning

confidence: 99%

Belief interval interpretation of probabilistic linguistic term sets and a visual method for solving the preference problem in multicriteria group decision making

et al. 2021

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“…Step 3. Utilize Equations (16) and (17) to compute the deviation degrees between each alternative and the PIS L(p) * and NIS L(p) # , respectively: (17) Step 4. Derive the closeness index CI(x i ) of each alternative x i ∈ X(i = 1, 2, • • • , 4):…”

Section: Comparative Analysismentioning

confidence: 99%

“…Many scholars also extended some classic decision-making methods to PLTS situations, and explored their usefulness in decision making areas [1,[8][9][10][11][12][13][14][15]. Several scholars have successfully explored the application of the technique for order of preference by similarity to ideal solution (TOPSIS) in the PLTS environment [1,[16][17][18].…”

Section: Introductionmentioning

confidence: 99%

A Probabilistic Linguistic Multiple Attribute Decision Making Based on a New Correlation Coefficient Method and its Application in Hospital Assessment

Luo

Zeng

2020

Mathematics

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The probabilistic linguistic term set (PLTS) is a newly emerging mathematical tool for handling uncertainties. It is considered a useful extension of linguistic term sets associated with probability information and can improve the effectiveness of multiple attribute decision making (MADM). This paper proposes a new PLTS correlation coefficient and addresses its usefulness in MADM problems. For achieving this aim, some new concepts of mean, variance, and covariance of the PLTS are first proposed. Moreover, a novel PLTS Pearson correlation coefficient is defined to overcome the shortcomings of the existing methods, whose significant feature is that it lies in the interval [−1,1], which makes it more effective in reflecting the negative and positive correlation between PLTSs. A weighted PLTS Pearson correlation coefficient is further defined to consider the importance of attribute weights and expand the scope of application. Then, a relative PLTS closeness coefficient is constructed based on the developed Pearson correlation coefficient, and based on which, a Pearson correlation-based TOPSIS (technique for order of preference by similarity to ideal solution) approach for MADM problems is developed. Finally, the effectiveness as well as the applicability of the developed method are illustrated through numerical examples and comparative analysis.

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“…Gou and Xu 21 and Liao et al 22 studied the operational rules of PLTSs, respectively. Bai et al 23 and Xian et al 24 successively used a new possibility degree formula and a visual method to rank PLTSs. Scholars also combined PLTSs with a variety of decision methods and proposed new decision methods, including the TOPSIS method, 20 the MULTIMOORA method, 25,26 the PROMETHEE II method, 27 the ELECTRE II method, 28 the TODIM method, 29 the correlation coefficient method, 30 and the deviation method 31 .…”

Section: Introductionmentioning

confidence: 99%

Z‐uncertain probabilistic linguistic variables and its application in emergency decision making for treatment of COVID‐19 patients

Chai

Xian

2020

Int J Intell Syst

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Probabilistic linguistic term sets (PLTSs) have many applications in the field of group decision making (GDM) because it includes both linguistic evaluation and probabilistic distribution when expressing preference information. However, the difference of information credibility in PLTSs is ignored, resulting in an inaccurate representation of decision information and unreasonable probability calculation. In this paper, we first consider the credibility of the information and propose the concept of Z-uncertain probabilistic linguistic variables (Z-UPLVs). Subsequently, the operational rules, normalization, distance and similarity measures, and comparison method of Z-UPLVs are introduced. Then, a probability calculation method based on credibility, an extended TOPSIS method, and some operators are proposed, which can be applied to emergency decision making in the Z-uncertain probabilistic linguistic (Z-UPL) environment. Finally, an emergency decision-making case of COVID-19 patients and comparative analysis illustrate the necessity and effectiveness of this method.

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A Visual Comparison Method and Similarity Measure for Probabilistic Linguistic Term Sets and Their Applications in Multi-criteria Decision Making

Cited by 26 publications

References 53 publications

Belief interval interpretation of probabilistic linguistic term sets and a visual method for solving the preference problem in multicriteria group decision making

Belief interval interpretation of probabilistic linguistic term sets and a visual method for solving the preference problem in multicriteria group decision making

A Probabilistic Linguistic Multiple Attribute Decision Making Based on a New Correlation Coefficient Method and its Application in Hospital Assessment

Z‐uncertain probabilistic linguistic variables and its application in emergency decision making for treatment of COVID‐19 patients

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