scholarly journals An Extended VIKOR Method Based on q-Rung Orthopair Shadowed Set and Its Application to Multi-Attribute Decision Making

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1508
Author(s):  
Huidong Wang ◽  
Yao Zhang ◽  
Jinli Yao
Keyword(s):  
Decision Making ◽  
Normal Distribution ◽  
Distance Measures ◽  
Basic Operation ◽  
Interval Numbers ◽  
Location Selection ◽  
Operation Rules ◽  
Shadowed Set ◽  
Multi Attribute Decision Making ◽  
Shadowed Sets

In the multi-attribute decision making (MADM) process, the attribute values are sometimes provided by experts or the public in the form of words. To model the linguistic evaluation more accurately, this paper proposes the q-rung orthopair shadowed set (q-ROSS) to represent attribute values and extends the VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje) method to solve MADM problems in the q-ROSS context. First, we propose the q-ROSS to express evaluation information. Some basic operation rules and distance measures are investigated accordingly. When the amount of data is large, the left and right endpoints of the collected interval numbers will obey symmetric normal distribution. Secondly, based on the normal distribution assumption, the collected data intervals are mapped to shadowed sets through a data processing approach. Furthermore, we extend the VIKOR model to tackle the MADM problem where the evaluation values are expressed by q-rung orthopair shadowed numbers. A location selection problem verifies the practicability of our method, and the effectiveness and superiority of the presented approach are reflected through comparative analysis.

scholarly journals Shadowed Sets-Based Linguistic Term Modeling and Its Application in Multi-Attribute Decision-Making

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 688 ◽  
Author(s):  
Huidong Wang ◽  
Shifan He ◽  
Xiaohong Pan ◽  
Chengdong Li
Keyword(s):  
Decision Making ◽  
Score Function ◽  
Linguistic Variables ◽  
Linguistic Terms ◽  
Linguistic Term ◽  
Shadowed Set ◽  
Multi Attribute Decision Making ◽  
Shadowed Sets ◽  
Supplier Selection Problem

For many multi-attribute decision-making (MADM) problems, linguistic variables are more convenient for people to express the attribute values. In this paper, a novel shadowed set-based method is proposed to deal with linguistic terms, where the linguistic term sets are symmetrical both in meaning and form. Firstly, to effectively express the linguistic variables, we develop a data-driven method to construct the shadowed set model for the linguistic terms. Secondly, the Pythagorean shadowed set is defined, and some theorems are subsequently explored. Thirdly, we propose the score function of the Pythagorean shadowed number and develop a new MADM method on the basis of the Pythagorean shadowed set. Finally, a case study of the supplier selection problem is provided to illustrate the effectiveness of the proposed method, and the superiority of our method is demonstrated by comparison analysis.

scholarly journals Risky Multi-Attribute Decision-Making Method Based on the Interval Number of Normal Distribution

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 264
Author(s):  
Sha Fu ◽  
Xi-Long Qu ◽  
Ye-Zhi Xiao ◽  
Hang-Jun Zhou ◽  
Guo-Bing Fan
Keyword(s):  
Decision Making ◽  
Normal Distribution ◽  
Interval Number ◽  
Information Environment ◽  
Decision Makers ◽  
Standard Normal Distribution ◽  
Risky Decision ◽  
Possibility Degree ◽  
Standard Normal ◽  
Multi Attribute Decision Making

Focusing on risky decision-making problems taking the interval number of normal distribution as the information environment, this paper proposes a decision-making method based on the interval number of normal distribution. Firstly, the normalized matrix based on the decision maker’s attitude is obtained through analysis and calculation. Secondly, according to the existing properties of standard normal distribution, the risk preference factors of the decision makers are considered to confirm the possibility degree of each scheme. The possibility degree is then used for establishing a possibility degree matrix and, consequently, sequencing of all schemes is conducted according to existing theories of possibility degree meaning and the value size of possibility degree. Finally, the feasibility and validity of this method is verified through calculation example analysis.

Location selection of seawater pumped hydro storage station in China based on multi-attribute decision making

2019 ◽  
Vol 139 ◽  
pp. 410-425 ◽  
Author(s):  
Yunna Wu ◽  
Ting Zhang ◽  
Chuanbo Xu ◽  
Xiaoyu Zhang ◽  
Yiming Ke ◽  
...  
Keyword(s):  
Decision Making ◽  
Location Selection ◽  
Storage Station ◽  
Multi Attribute Decision Making ◽  
Selection Of

Probabilistic Interval Reference Ordering Sets in Multi-Criteria Group Decision Making

2017 ◽  
Vol 25 (02) ◽  
pp. 189-212 ◽  
Author(s):  
Yue He ◽  
Zeshui Xu ◽  
Weiling Jiang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Investment Decision ◽  
Silk Road ◽  
Decision Makers ◽  
Distance Measures ◽  
Basic Operation ◽  
Preference Ordering ◽  
Inaccurate Information

Uncertain preference orderings have been widely applied in real world decision making problems as a useful and convenient tool to express preference information. When the number of decision makers is great, the importance degrees of preference interval orderings provided by the decision makers are usually difficult to be determined and may be ignored, which probably lead to the erroneous decision results when the weight information is missing. In order to make full use of information, we define the concepts of probabilistic interval preference ordering set (PIPOS) and probabilistic interval preference ordering element (PIPOE). Then, we give the score and the basic operation laws of PIPOEs, based on which we develop some aggregation operators and the distance measures for PIPOEs. After that, due to the limited cognitions and knowledge of the decision makers, we propose an algorithm to remove the inaccurate information and adjust the probabilities. Furthermore, we put forward the aggregation-based approach and the TOPSIS approach with probabilistic interval preference orderings for multi-criteria group decision making. Finally, in order to illustrate our approaches, we make a detailed case study concerning the infrastructure investment decision making problem on “the Silk Road Economic Belt and the 21st-Century Maritime Silk Road” (B&R) strategy.

Projection Method for Material Selection Problem with Interval Numbers

2014 ◽  
Vol 1022 ◽  
pp. 14-17 ◽  
Author(s):  
Lian Wu Yang
Keyword(s):  
Decision Making ◽  
Projection Method ◽  
Coefficient Of Variation ◽  
Material Selection ◽  
Influence Factors ◽  
Selection Problem ◽  
Variation Method ◽  
Interval Numbers ◽  
Decision Method ◽  
Multi Attribute Decision Making

Material selection problem is important for the product design, and contains many influence factors. Thus it is actually a multi-attribute decision making (MADM) problems. The aim of this paper is to propose a new decision method based on the projection method for the material selection problem, in which attribute values expressed with interval numbers. An objective determining weights method is proposed according to coefficient of variation method. A practical example is used to illustrate the effectiveness and practicability of the proposed method.

Multi-attribute decision-making method based on a novel distance measure of linguistic intuitionistic fuzzy sets

2021 ◽  
Vol 40 (1) ◽  
pp. 1147-1160
Author(s):  
Yali Cheng ◽  
Yonghong Li ◽  
Jie Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Linguistic Intuitionistic Fuzzy Sets ◽  
Linguistic Scale Function ◽  
Different Response

Linguistic intuitionistic fuzzy sets can qualitatively rather than quantitatively express data in the form of membership degree. But quantitative tools are required to handle qualitative information. Therefore, an improved linguistic scale function, which can more accurately manifest the subjective feelings of decision-makers, is employed to deal with linguistic intuitionistic information. Subsequently, due to some commonly used distance measures do not comprehensively evaluate the information of linguistic intuitionistic fuzzy sets, an improved distance measure of linguistic intuitionistic fuzzy sets is designed. It considers the cross-evaluation information to get more realistic reasoning results. In addition, a new similarity measure defined by nonlinear Gaussian diffusion model is proposed, which can provide different response scales for different information between various schemes. The properties of these measures are also studied in detail. On this basis, a method in linguistic intuitionistic fuzzy environment is developed to handle multi-attribute decision-making problems. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method and the influence of the parameters is analyzed.

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