scholarly journals Hesitant Fuzzy 2-Dimension Linguistic Programming Technique for Multidimensional Analysis of Preference for Multicriteria Group Decision Making

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3196
Author(s):  
Xiaoyue Liu ◽  
Dawei Ju
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Programming Model ◽  
Multidimensional Analysis ◽  
Programming Technique ◽  
Relative Closeness ◽  
Criteria Weights ◽  
Multicriteria Group Decision Making ◽  
The Individual

The hesitant fuzzy 2-dimension linguistic element (HF2DLE) allows decision makers to express the importance or reliability of each term included in a hesitant fuzzy linguistic element as a linguistic term. This paper investigates a programming technique for multidimensional analysis of preference for hesitant fuzzy 2-dimension linguistic multicriteria group decision making. Considering the flexibility of HF2DLEs in expressing hesitant qualitative preference information, we first adopt HF2DLEs to depict both the evaluation values of alternatives and the truth degrees of alternative comparisons. To calculate the relative closeness degrees (RCDs) of alternatives, the Euclidean distances between HF2DLEs are defined. Based on RCDs and preference relations on alternatives, the group consistency and inconsistency indices are constructed, and a bi-objective hesitant fuzzy 2-dimension linguistic programming model is established to derive the criteria weights and positive and negative ideal solutions. Since the objective functions and partial constraint coefficients of the established model are HF2DLEs, an effective solution is developed, through which the RCDs can be calculated to obtain the individual rankings of alternatives. Furthermore, a single-objective assignment model is constructed to determine the best alternative. Finally, a case study is conducted to illustrate the feasibility of the proposed method, and its effectiveness is demonstrated by comparison analyses.

scholarly journals Rough-Number-Based Multiple-Criteria Group Decision-Making Method by Combining the BWM and Prospect Theory

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Fan Jia ◽  
Xingyuan Wang
Keyword(s):  
Decision Making ◽  
Prospect Theory ◽  
Group Decision Making ◽  
Group Decision ◽  
Programming Model ◽  
Weighting Function ◽  
Information Aggregation ◽  
Criteria Weights ◽  
Multicriteria Group Decision Making ◽  
Novel Method

Multicriteria group decision-making (MCGDM) problems have been a research hotspot in recent years, and prospect theory is introduced to cope with the risk and imprecision in the process of decision-making. To guarantee the effectiveness of information aggregation and extend the feasibility of prospect theory, this paper proposes a novel decision-making approach based on rough numbers and prospect theory to solve risky and uncertain MCGDM problems. Firstly by combining rough numbers and the best-worst method (BWM), we construct a linear programming model to calculate rough criteria weights, which are defined by lower limitations and upper limitations. Then for the imprecision of value function and weighting function in prospect theory, we propose a novel method with the aid of combining rough numbers and prospect theory to handle the risk in decision-making problems. Finally, a numerical example involving investment is introduced to illustrate the application and validity of the proposed method.

FUZZY LINMAP METHOD FOR MULTIATTRIBUTE GROUP DECISION MAKING WITH LINGUISTIC VARIABLES AND INCOMPLETE INFORMATION

2007 ◽  
Vol 15 (02) ◽  
pp. 153-173 ◽  
Author(s):  
DENG-FENG LI ◽  
TAO SUN
Keyword(s):  
Decision Making ◽  
Linear Programming ◽  
Group Decision Making ◽  
Group Decision ◽  
Programming Model ◽  
Implementation Process ◽  
Fuzzy Linear Programming ◽  
Multidimensional Analysis ◽  
Linguistic Variables ◽  
Programming Technique

The aim of this paper is to develop a fuzzy linear programming technique for multidimensional analysis of preference (FLINMAP) in multiattribute group decision making problems with linguistic variables and incomplete preference information. In this paper, linguistic variables are used to assess an alternative on qualitative attributes using fuzzy ratings corresponding to some triangular fuzzy numbers. Each alternative is assessed on the basis of its distance to a fuzzy positive ideal solution (FPIS) which is unknown a priori. The FPIS and the weights of attributes are calculated by constructing a new linear programming model based on the group consistency and inconsistency indices defined on the basis of preferences between alternatives given by the decision makers. The distance of each alternative to the FPIS can be calculated to determine the ranking order of all alternatives. The implementation process of this methodology is demonstrated with an example.

scholarly journals 2-Tuple Unbalanced Linguistic Multiple Criteria Group Decision Making using Prospect Theory Data Envelopment Analysis

2021 ◽  
Author(s):  
Imran Khan ◽  
Anjana Gupta ◽  
Aparna Mehra
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Prospect Theory ◽  
Group Decision Making ◽  
Group Decision ◽  
Programming Model ◽  
Multiple Criteria ◽  
Data Envelopment ◽  
Linguistic Term ◽  
Criteria Weights

Abstract The linguistic terms in a balanced linguistic term set describing qualitative data are symmetrical around the central linguistic word. With the growing complexity of the problems, the symmetric linguistic term set appears to be confined. This work examines the multiple criteria group decision-making problems where decision-makers employ a 2-tuple unbalanced linguistic term set to provide entries of alternative-criteria matrices.We adopt a data envelopment analysis (DEA) method and create a linear programming model to evaluate alternative-criteria weights for each decision-maker. The value function from prospect theory models the non-rational aspect of risk in criteria. The values of prospect gain and prospect loss on cost and benefit criteria are computed and used to create a DEA model that evaluates the weights of each criterion on each alternative. Finally, the entropy values of the cross-efficiency scores deliver a ranking of the alternatives. A numerical example illustrates the proposed methodology

scholarly journals Generalizing and Integrating TOPSIS and Cook-Seiford Method for Multicriteria Group Decision-Making with Both Cardinal and Ordinal Data

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Wu Li ◽  
Guanqi Guo ◽  
Xiaoqiang Zhou
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Ordinal Data ◽  
Choice Function ◽  
Group Decision ◽  
Social Choice Function ◽  
Weighted Distance ◽  
Ordinal Preferences ◽  
Criteria Weights ◽  
Multicriteria Group Decision Making

The TOPSIS and Cook-Seiford social choice function are generalized and integrated for multicriteria group decision-making (MCGDM) with both cardinal evaluations and ordinal preferences of the alternatives. Unlike traditional TOPSIS, at first, the group’s positive ideal solution and negative ideal solution under cardinal and ordinal preferences are defined, respectively. Thus the group rankings of the alternatives with respect to each criterion are derived from the individual preferences by the modified group TOPSIS considering the weights of decision makers under each criterion. Then the weighted distance function representing the total inconsistency between the comprehensive rankings of all alternatives and the ones under all criteria is presented after the criteria weights are taken into account. Form the perspective of minimizing the criteria-weighted distance of the rankings, a nonlinear integer programming is developed and transformed into an assignment problem to obtain the final rankings of all alternatives. An illustrative case is presented and some comparisons on the results show that the developed approach is practical and effective. This study extends TOPSIS to group decision-making with ordinal preferences and generalizes Cook-Seiford social choice function to multicriteria decision-making considering the criteria weights and can be a novel benchmark for MCGDM with both cardinal and ordinal data.

scholarly journals A New Grey Approach for Using SWARA and PIPRECIA Methods in a Group Decision-Making Environment

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1554
Author(s):  
Dragiša Stanujkić ◽  
Darjan Karabašević ◽  
Gabrijela Popović ◽  
Predrag S. Stanimirović ◽  
Muzafer Saračević ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Multiple Criteria Decision Making ◽  
Grey System Theory ◽  
Multiple Criteria ◽  
Decision Making Process ◽  
Grey System ◽  
Criteria Weights

The environment in which the decision-making process takes place is often characterized by uncertainty and vagueness and, because of that, sometimes it is very hard to express the criteria weights with crisp numbers. Therefore, the application of the Grey System Theory, i.e., grey numbers, in this case, is very convenient when it comes to determination of the criteria weights with partially known information. Besides, the criteria weights have a significant role in the multiple criteria decision-making process. Many ordinary multiple criteria decision-making methods are adapted for using grey numbers, and this is the case in this article as well. A new grey extension of the certain multiple criteria decision-making methods for the determination of the criteria weights is proposed. Therefore, the article aims to propose a new extension of the Step-wise Weight Assessment Ratio Analysis (SWARA) and PIvot Pairwise Relative Criteria Importance Assessment (PIPRECIA) methods adapted for group decision-making. In the proposed approach, attitudes of decision-makers are transformed into grey group attitudes, which allows taking advantage of the benefit that grey numbers provide over crisp numbers. The main advantage of the proposed approach in relation to the use of crisp numbers is the ability to conduct different analyses, i.e., considering different scenarios, such as pessimistic, optimistic, and so on. By varying the value of the whitening coefficient, different weights of the criteria can be obtained, and it should be emphasized that this approach gives the same weights as in the case of crisp numbers when the whitening coefficient has a value of 0.5. In addition, in this approach, the grey number was formed based on the median value of collected responses because it better maintains the deviation from the normal distribution of the collected responses. The application of the proposed approach was considered through two numerical illustrations, based on which appropriate conclusions were drawn.

scholarly journals A Novel Multi-Criteria Group Decision-Making Approach Based on Bonferroni and Heronian Mean Operators under Hesitant 2-Tuple Linguistic Environment

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1489
Author(s):  
Shahzad Faizi ◽  
Wojciech Sałabun ◽  
Nisbha Shaheen ◽  
Atiq ur Rehman ◽  
Jarosław Wątróbski
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Geometric Bonferroni Mean ◽  
The Individual ◽  
Heronian Mean

Ambiguous and uncertain facts can be handled using a hesitant 2-tuple linguistic set (H2TLS), an important expansion of the 2-tuple linguistic set. The vagueness and uncertainty of data can be grabbed by using aggregation operators. Therefore, aggregation operators play an important role in computational processes to merge the information provided by decision makers (DMs). Furthermore, the aggregation operator is a potential mechanism for merging multisource data which is synonymous with cooperative preference. The aggregation operators need to be studied and analyzed from various perspectives to represent complex choice situations more readily and capture the diverse experiences of DMs. In this manuscript, we propose some valuable operational laws for H2TLS. These new operational laws work through the individual aggregation of linguistic words and the collection of translation parameters. We introduced a hesitant 2-tuple linguistic weighted average (H2TLWA) operator to solve multi-criteria group decision-making (MCGDM) problems. We also define hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator, hesitant 2-tuple linguistic geometric Bonferroni mean (H2TLGBM) operator, hesitant 2-tuple linguistic Heronian mean (H2TLHM) operator, and a hesitant 2-tuple linguistic geometric Heronian mean (H2TLGHM) operator based on the novel operational laws proposed in this paper. We define the aggregation operators for addition, subtraction, multiplication, division, scalar multiplication, power and complement with their respective properties. An application example and comparison analysis were examined to show the usefulness and practicality of the work.

A multicriteria group decision-making method based on AIVIFSs, Z-numbers, and trapezium clouds

2021 ◽  
Vol 566 ◽  
pp. 38-56
Author(s):  
Qianlei Jia ◽  
Jiayue Hu ◽  
Qizhi He ◽  
Weiguo Zhang ◽  
Ehab Safwat
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Multicriteria Group Decision Making

scholarly journals Interval-Valued Probabilistic Hesitant Fuzzy Set Based Muirhead Mean for Multi-Attribute Group Decision-Making

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 342 ◽  
Author(s):  
Krishankumar ◽  
Ravichandran ◽  
Ahmed ◽  
Kar ◽  
Peng
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Partial Information ◽  
Programming Model ◽  
Hesitant Fuzzy Set ◽  
Occurrence Probability ◽  
Source Selection ◽  
Interval Valued

As a powerful generalization to fuzzy set, hesitant fuzzy set (HFS) was introduced, which provided multiple possible membership values to be associated with a specific instance. But HFS did not consider occurrence probability values, and to circumvent the issue, probabilistic HFS (PHFS) was introduced, which associates an occurrence probability value with each hesitant fuzzy element (HFE). Providing such a precise probability value is an open challenge and as a generalization to PHFS, interval-valued PHFS (IVPHFS) was proposed. IVPHFS provided flexibility to decision makers (DMs) by associating a range of values as an occurrence probability for each HFE. To enrich the usefulness of IVPHFS in multi-attribute group decision-making (MAGDM), in this paper, we extend the Muirhead mean (MM) operator to IVPHFS for aggregating preferences. The MM operator is a generalized operator that can effectively capture the interrelationship between multiple attributes. Some properties of the proposed operator are also discussed. Then, a new programming model is proposed for calculating the weights of attributes using DMs’ partial information. Later, a systematic procedure is presented for MAGDM with the proposed operator and the practical use of the operator is demonstrated by using a renewable energy source selection problem. Finally, the strengths and weaknesses of the proposal are discussed in comparison with other methods.

Sign in / Sign up

Export Citation Format

Share Document