scholarly journals Distance and Similarity Measures for Octahedron Sets and Their Application to MCGDM Problems

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1690
Author(s):  
Güzide Şenel ◽  
Jeong-Gon Lee ◽  
Kul Hur
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Similarity Measures ◽  
Distance Measures ◽  
Linguistic Variables ◽  
Numerical Example

In this paper, in order to apply the concept of octahedron sets to multi-criteria group decision-making problems, we define several similarity and distance measures for octahedron sets. We present a multi-criteria group decision-making method with linguistic variables in octahedron set environment. We give a numerical example for multi-criteria group decision-making problems.

A novel q-rung orthopair fuzzy TODIM approach for multi-criteria group decision making based on Shapley value and relative entropy

2021 ◽  
Vol 40 (1) ◽  
pp. 235-250
Author(s):  
Liuxin Chen ◽  
Nanfang Luo ◽  
Xiaoling Gou
Keyword(s):  
Decision Making ◽  
Relative Entropy ◽  
Group Decision Making ◽  
Shapley Value ◽  
Group Decision ◽  
Similarity Measures ◽  
Entropy Measure ◽  
Shapley Values ◽  
Interactive Relationship ◽  
The Difference

In the real multi-criteria group decision making (MCGDM) problems, there will be an interactive relationship among different decision makers (DMs). To identify the overall influence, we define the Shapley value as the DM’s weight. Entropy is a measure which makes it better than similarity measures to recognize a group decision making problem. Since we propose a relative entropy to measure the difference between two systems, which improves the accuracy of the distance measure.In this paper, a MCGDM approach named as TODIM is presented under q-rung orthopair fuzzy information.The proposed TODIM approach is developed for correlative MCGDM problems, in which the weights of the DMs are calculated in terms of Shapley values and the dominance matrices are evaluated based on relative entropy measure with q-rung orthopair fuzzy information.Furthermore, the efficacy of the proposed Gq-ROFWA operator and the novel TODIM is demonstrated through a selection problem of modern enterprises risk investment. A comparative analysis with existing methods is presented to validate the efficiency of the approach.

scholarly journals Uncertain Linguistic Aggregation Distance Measures and Their Application to Group Decision Making

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Wei Li ◽  
Shouzhen Zeng
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Distance Measures ◽  
University Faculty ◽  
Linguistic Information ◽  
Weighted Distance ◽  
Special Cases ◽  
Decision Making Problem

We introduce a method based on distance measures for group decision making under uncertain linguistic environment. We develop some uncertain linguistic aggregation distance measures called the uncertain linguistic weighted distance (ULWD) measure, the uncertain linguistic ordered weighted distance (ULOWD) measure, and the uncertain linguistic hybrid weighted distance (ULHWD) measure. We study some of their characteristic, and we prove that the ULWD and the ULOWD are special cases of the ULHWD measure. Finally, we develop an application of the ULHWD measure in a group decision making problem concerning the evaluation of university faculty for tenure and promotion with uncertain linguistic information.

scholarly journals A statistical comparative study of different similarity measures of consensus in group decision making

2013 ◽  
Vol 221 ◽  
pp. 110-123 ◽  
Author(s):  
F. Chiclana ◽  
J.M. Tapia García ◽  
M.J. del Moral ◽  
E. Herrera-Viedma
Keyword(s):  
Decision Making ◽  
Comparative Study ◽  
Group Decision Making ◽  
Group Decision ◽  
Similarity Measures

A Novel Linguistic Group Decision-Making Model Based on Extended Hesitant Fuzzy Linguistic Term Sets

2015 ◽  
Vol 23 (03) ◽  
pp. 379-398 ◽  
Author(s):  
Cuiping Wei ◽  
Na Zhao ◽  
Xijin Tang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Distance Measures ◽  
Linguistic Terms ◽  
Linguistic Information ◽  
Linguistic Group ◽  
Linguistic Term ◽  
Decision Making Model ◽  
Fuzzy Linguistic

Hesitant fuzzy linguistic term set (HFLTS) is a set with ordered consecutive linguistic terms, and is very useful in addressing the situations where people are hesitant in providing their linguistic assessments. Wang [H. Wang, Extended hesitant fuzzy linguistic term sets and their aggregation in group decision making, International Journal of Computational Intelligence Systems 8(1) (2015) 14–33.] removed the consecutive condition to introduce the notion of extended HFLTS (EHFLTS). The generalized form has wider applications in linguistic group decision-making. By introducing distance measures for EHFLTSs, in this paper we develop a novel multi-criteria group decision making model to deal with hesitant fuzzy linguistic information. The model collects group linguistic information by using EHFLTSs and avoids the possible loss of information. Moreover, it can assess the importance weights of criteria according to their subjective and objective information and rank alternatives based on the rationale of TOPSIS. In order to illustrate the applicability of the proposed algorithm, two examples are given and comparisons are made with the other existing methods.

Research on Evaluating Theory and Application to Design of Mechanism Scheme with Uncertain Linguistic Information

2012 ◽  
Vol 201-202 ◽  
pp. 749-752
Author(s):  
Tie Jun Wang ◽  
Chang Zhong Hao
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Primary Phase ◽  
Harmonic Mean ◽  
Linguistic Variables ◽  
Product Lifecycle ◽  
Linguistic Information ◽  
Multiple Attribute ◽  
Magdm Problems

The design of mechanism scheme is the primary phase and the creative and challenging part in product lifecycle. In this paper, we research the multiple attribute group decision making (MAGDM) problems for evaluating the design of mechanism scheme with uncertain linguistic variables. We employ the uncertain linguistic weighted harmonic mean (ULWHM) operator to aggregate the uncertain linguistic information corresponding to each alternative and get the overall value of the alternatives, then rank the alternatives and select the most desirable one(s) by using the formula of the degree of possibility for the comparison between two uncertain linguistic variables. Finally, a practical example for evaluating the design of mechanism scheme is used to illustrate the developed procedures.

Some Intuitionist Fuzzy Weighted Geometric Distance Measures and Their Application to Group Decision Making

2014 ◽  
Vol 22 (05) ◽  
pp. 699-715 ◽  
Author(s):  
Bo Peng ◽  
Chunming Ye ◽  
Shouzhen Zeng
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Hamming Distance ◽  
Distance Measures ◽  
Weighted Distance ◽  
Geometric Distance ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Consensus Reaching Process

The ordered weighted distance (OWD) measure developed by Xu and Chen having been proved suitable to deal with the situation where the input arguments are represented in exact numerical values. In this paper, we develop some new geometric distance measures with intuitionistic fuzzy information, which are the generalization of some widely used distance measures, including the intuitionistic fuzzy weighted geometric distance (IFWGD) measure, the intuitionistic fuzzy ordered weighted geometric distance (IFOWGD) measure, the intuitionistic fuzzy ordered weighted geometric Hamming distance (IFOWGHD) measure, the intuitionistic fuzzy ordered weighted geometric Euclidean distance (IFOWGED) measure, the intuitionistic fuzzy hybrid weighted geometric distance (IFHWGD) measure. These developed weighted geometric distance measures are very suitable to deal with the situation where the input arguments are represented in intuitionistic fuzzy values. And then, we present a consensus reaching process based on the developed distance measures with intuitionistic fuzzy preference information for group decision making. Finally, we apply the developed approach with a numerical example to group decision making under intuitionistic fuzzy environment.

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.

scholarly journals Probabilistic Hybrid Linguistic Approaches for Multiple Attribute Group Decision Making with Decision Hesitancy and the Prioritization of Attribute Relationships

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 235
Author(s):  
Junling Zhang ◽  
Ying Hong ◽  
Xiaowen Qi ◽  
Changyong Liang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Weighted Average ◽  
Distance Measures ◽  
Distance Measurements ◽  
Information Distortion ◽  
Multiple Attribute ◽  
Wide Range ◽  
Linguistic Term

Focusing on ill-structured multiple attribute decision-making (MADM) problems, including decision hesitancy and attribute prioritization relationships, this paper investigates appropriate approaches for decision making. Firstly, we introduce the probabilistic hybrid linguistic term set (P-HLTS) for capturing probabilistic preferences about possible linguistic labels belonging to a wide range of hesitant linguistic term sets. Entropy and distance measurements for P-HLTS are developed without arbitrary complementing operations. To facilitate decision making with attribute prioritization relationships, we present a probabilistic uncertain balanced linguistic-prioritized weighted average (PUBL-PWA) operator and the probabilistic uncertain balanced linguistic-induced prioritized ordered weighted average (PUBL-IPOWA) operator. In terms of the strength of the above tools, we further construct two multiple attribute group decision-making (MAGDM) approaches under P-HLTS environments, namely, an approach for decision-making situations where attribute prioritization relationships are known in advance and the relative importance of decision makers (DMs) or decision-making units (DMUs) is not required for consideration, and second approach for decision-making situations where both attribute prioritization relationships and the weighted vectors of DMs or DMUs are explicitly unknown. In general, our proposed approaches are more flexible and practical when considering heterogeneous opinions, avoiding information distortion brought about by complementing operation-based distance measures. Furthermore, illustrative application studies are conducted to verify our developed approaches.

An Approach to Group Making Problems Based on Two-Tuple Linguistic Theory

2014 ◽  
Vol 472 ◽  
pp. 456-459
Author(s):  
Jun Wei ◽  
Xiao Jun Zhong ◽  
Jun Gong
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Linguistic Theory ◽  
Linguistic Information ◽  
Numerical Example ◽  
Judgement Matrix ◽  
The World

The group decision-making is a new way recent years in the world which is based on the analysis of linguistic information.A method for this kind of group problems based on two-tuple linguistic theory is proposed in this paper.First,the method transforms initial linguistic information into group judgement matrix,and then give the select process of optimal alternative based on an operator.Finally,a numerical example is given to illustrate the validity of the proposed method.

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