Modeling Interactive Multiattribute Decision-Making via Probabilistic Linguistic Term Set Extended by Dempster–Shafer Theory

2021 ◽  
Author(s):  
Liguo Fei ◽  
Yuqiang Feng
Keyword(s):  
Decision Making ◽  
Probabilistic Linguistic Term Set ◽  
Dempster Shafer Theory ◽  
Linguistic Term ◽  
Shafer Theory

scholarly journals Multiple Criteria Group Decision-Making Method with Dempster–Shafer Theory and Probabilistic Linguistic Term Sets

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Yuanwei Du ◽  
Susu Wang
Keyword(s):  
Decision Making ◽  
Group Decision ◽  
Individual Level ◽  
Preference Theory ◽  
Dempster Shafer Theory ◽  
Linguistic Term ◽  
Probabilistic Linguistic Term Sets ◽  
The Individual ◽  
Shafer Theory ◽  
Interval Valued

The motivation of this study is to propose a novel multiple criteria group decision-making (MCDGM) method based on Dempster–Shafer theory (DST) and probabilistic linguistic term sets (PLTSs) to handle the distinctions between compensatory information at the criterion level and noncompensatory information at the individual level in the process of information fusion. Initially, the information at the individual level is extracted by BPA functions. Then, they are fused with DST considering ignorance and DMs’ reliabilities. Next, the obtained BPA functions are transformed into interval-valued PLTSs with the assistance of intermediate belief and plausibility. Subsequently, the interval-valued PLTSs are converted into standard PLTSs. After normalization, the holistic PLTS is obtained with weighted addition operation and the round function is applied to determine the ultimate evaluation result. Finally, a case simulation study of evaluating the marine ranching ecological security is presented to verify and improve the validity and feasibility of the proposed method and algorithm in practical application. The proposed method and its relevant algorithm are both innovative combination of DST and PLTSs from the perspective of compensatory and noncompensatory features of information, which provides a new angle of view for the development of probabilistic preference theory and is beneficial to apply probabilistic preference theory in practice.

scholarly journals On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1485
Author(s):  
Pavel Sevastjanov ◽  
Ludmila Dymova ◽  
Krzysztof Kaczmarek
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Short Paper ◽  
Neutrosophic Sets ◽  
Intuitionistic Fuzzy ◽  
Dempster Shafer Theory ◽  
Methodological Problems ◽  
Shafer Theory ◽  
Sets Theory

In this short paper, a critical analysis of the Neutrosophic, Pythagorean and some other novel fuzzy sets theories foundations is provided, taking into account that they actively used for the solution of the decision-making problems. The shortcomings of these theories are exposed. It is stated that the independence hypothesis, which is a cornerstone of the Neutrosophic sets theory, is not in line with common sense and therefore leads to the paradoxical results in the asymptotic limits of this theory. It is shown that the Pythagorean sets theory possesses questionable foundations, the sense of which cannot be explained reasonably. Moreover, this theory does not completely solve the declared problem. Similarly, important methodological problems of other analyzed theories are revealed. To solve the interior problems of the Atanassov’s intuitionistic fuzzy sets and to improve upon them, this being the reason most of the criticized novel sets theories were developed, an alternative approach based on extension of the intuitionistic fuzzy sets in the framework of the Dempster–Shafer theory is proposed. No propositions concerned with the improvement of the Cubic sets theory and Single-Valued Neutrosophic Offset theory were made, as their applicability was shown to be very dubious. In order to stimulate discussion, many statements are deliberately formulated in a hardline form.

scholarly journals A Group Decision Framework for Renewable Energy Source Selection under Interval-Valued Probabilistic linguistic Term Set

Energies ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 986 ◽  
Author(s):  
Raghunathan Krishankumar ◽  
Arunodaya Raj Mishra ◽  
Kattur Soundarapandian Ravichandran ◽  
Xindong Peng ◽  
Edmundas Kazimieras Zavadskas ◽  
...  
Keyword(s):  
Decision Making ◽  
Renewable Energy ◽  
Group Decision ◽  
Decision Framework ◽  
Probabilistic Linguistic Term Set ◽  
Source Selection ◽  
Energy Assessment ◽  
Linguistic Term ◽  
Criteria Weights ◽  
Interval Valued

In recent years, the assessment of desirable renewable energy alternative has been an extremely important concern that could change the environment and economic growth. To tackle the circumstances, some authors have paid attention to selecting the desirable renewable energy option by employing the decision-making assessment and linguistic term sets. With a fast-growing interest in multi-criteria group decision-making (MCGDM) problems, researchers are tirelessly working towards new techniques for better decision-making. Decision makers (DMs) generally rate alternatives linguistically with different probabilities occurring for each term. Previous studies on linguistic decision-making have either ignored this idea or have used an only a single value for representing the weight of the linguistic term. Since expression of the complete probability distribution is hard and implicit hesitation exists, representation of weights of the linguistic terms using a single value becomes imprecise and unreasonable. To avoid this challenge, an interval-valued probabilistic linguistic term set (IVPLTS) is used, which is a generalization of (probabilistic linguistic term set) PLTS. Inspired by the usefulness of IVPLTS concept, we develop a decision framework for rational decision making. Initially, some operational laws and axioms are presented. Further, a novel aggregation operator known as interval-valued probabilistic linguistic simple weighted geometry (IVPLSWG) is developed for aggregating DMs’ preferences. Also, criteria weights are determined using the newly developed interval-valued probabilistic linguistic standard variance (IVPLSV) approach and alternatives are ranked using the extended VIKOR (VlseKriterijumskaOptimizacijaKompromisnoResenje) method under IVPLTS environment. Finally, a numerical example of renewable energy assessment is demonstrated to show the practicality of the developed decision framework. Also, the strengths and weaknesses of the developed decision framework are illustrated by comparison with existing ones.

scholarly journals Trapezoidal Intuitionistic Fuzzy Multiattribute Decision Making Method Based on Cumulative Prospect Theory and Dempster-Shafer Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xihua Li ◽  
Fuqiang Wang ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Prospect Theory ◽  
Value Function ◽  
Cumulative Prospect Theory ◽  
Intuitionistic Fuzzy Numbers ◽  
Attribute Weight ◽  
Intuitionistic Fuzzy ◽  
Dempster Shafer Theory ◽  
Fuzzy Environment ◽  
Shafer Theory

With respect to decision making problems under uncertainty, a trapezoidal intuitionistic fuzzy multiattribute decision making method based on cumulative prospect theory and Dempster-Shafer theory is developed. The proposed method reflects behavioral characteristics of decision makers, information fuzziness under uncertainty, and uncertain attribute weight information. Firstly, distance measurement and comparison rule of trapezoidal intuitionistic fuzzy numbers are used to derive value function under trapezoidal intuitionistic fuzzy environment. Secondly, the value function and decision weight function are used to calculate prospect values of attributes for each alternative. Then considering uncertain attribute weight information, Dempster-Shafer theory is used to aggregate prospect values for each alternative, and overall prospect values are obtained and thus the alternatives are sorted consequently. Finally, an illustrative example shows the feasibility of the proposed method.

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