scholarly journals A Modified TODIM Based on Compromise Distance for MAGDM with q-Rung Orthopair Trapezoidal Fuzzy Numbers

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Benting Wan ◽  
Juelin Huang ◽  
Xiaolu Zhang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Distance Measure ◽  
Group Decision ◽  
Hamming Distance ◽  
Real Life ◽  
Decision Makers ◽  
Decision Matrix ◽  
Trapezoidal Fuzzy Numbers

The q-rung orthopair fuzzy number (q-ROFN) has been recently developed by Yager and has been widely applied in handling real-life decision-making problems. To enhance its usefulness in dealing with complex practical issues, this paper first proposes the new concept of q-rung orthopair trapezoidal fuzzy numbers (q-ROTrFNs) which is a new and useful extension of q-ROFNs. Then, we investigate the operation of q-ROTrFNs and develop a new ranking method for q-ROTrFNs. We also propose a new q-rung orthopair trapezoidal fuzzy Hamming distance measure. More important, we develop a useful q-rung orthopair trapezoidal fuzzy modified TODIM group decision-making method. In this method, a new q-rung orthopair trapezoidal fuzzy weighted aggregating (q-ROTrFWA) operator is developed to integrate individual decision matrices into the collective decision matrix, and a q-rung orthopair trapezoidal fuzzy distance measure-based compromise approach is proposed to determine the relative dominance degree of alternatives. It is worth to mention that the modified TODIM method not only expands the freedom of decision makers but also allows decision makers to choose the appropriate risk preference parameter. Finally, a case study on health management of hypertensive patients is conducted to demonstrate the feasibility of the modified TODIM group decision-making method, and the developed method is further verified by comparison analysis with the existing methods and sensitive analysis of different parameters.

scholarly journals Multiattribute Group Decision Making with Unknown Decision Expert Weights Information in the Framework of Interval Intuitionistic Trapezoidal Fuzzy Numbers

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zongcai Jiang ◽  
Yan Wang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Distance Measure ◽  
Group Decision ◽  
Fuzzy Decision ◽  
Decision Matrix ◽  
Trapezoidal Fuzzy Numbers ◽  
Overall Evaluation ◽  
The Given

The aim of this paper is to investigate an approach to multiattribute group decision making with interval intuitionistic trapezoidal fuzzy numbers, in which the decision expert weights are unknown. First, we introduce a distance measure between two interval intuitionistic trapezoidal fuzzy matrixes, and based on the distance between individual matrix and extreme matrix, as well as the average matrix, we obtain the decision expert weights. Second, we utilize the interval intuitionistic trapezoidal fuzzy weighted geometric (IITFWG) operator and the interval intuitionistic trapezoidal fuzzy ordered weighted geometric (IITFOWG) operator to aggregate all individual interval intuitionistic trapezoidal fuzzy decision matrices into a collective interval intuitionistic trapezoidal fuzzy decision matrix and then derive the group overall evaluation values of the given alternatives. Finally, an illustrative example of emergency alternatives selection is given to demonstrate the effectiveness and superiority of the proposed method.

scholarly journals Dynamic Multi-Attribute Group Decision Making Model Based on Generalized Interval-Valued Trapezoidal Fuzzy Numbers

2015 ◽  
Vol 14 (4) ◽  
pp. 11-28 ◽  
Author(s):  
Wei Lin ◽  
Guangle Yan ◽  
Yuwen Shi
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Decision Makers ◽  
Final Decision ◽  
Trapezoidal Fuzzy Numbers ◽  
Time Period ◽  
Decision Making Model ◽  
Interval Valued

Abstract In this paper we investigate the dynamic multi-attribute group decision making problems, in which all the attribute values are provided by multiple decision makers at different periods. In order to increase the level of overall satisfaction for the final decision and deal with uncertainty, the attribute values are enhanced with generalized interval-valued trapezoidal fuzzy numbers to cope with the vagueness and indeterminacy. We first define the Dynamic Generalized Interval-valued Trapezoidal Fuzzy Numbers Weighted Geometric Aggregation (DGITFNWGA) operator and give an approach to determine the weights of periods, using the probability density function of Gamma distribution, and then a dynamic multi-attribute group decision making method is developed. The method proposed employs the Generalized Interval-valued Trapezoidal Fuzzy Numbers Hybrid Geometric Aggregation (GITFNHGA) operator to aggregate all individual decision information into the collective attribute values corresponding to each alternative at the same time period, and then utilizes the DGITFNWGA operator to aggregate the collective attribute values at different periods into the overall attribute values corresponding to each alternative and obtains the alternatives ranking, by which the optimal alternative can be determined. Finally, an illustrative example is given to verify the approach developed.

Doubly Extended Fuzzy TOPSIS Method for Group Decision Making

2019 ◽  
Vol 66 (1) ◽  
pp. 27-50
Author(s):  
Dariusz Kacprzak
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Group Decision Making ◽  
Group Decision ◽  
Real Life ◽  
Fuzzy Topsis ◽  
Decision Makers ◽  
Final Decision ◽  
Topsis Method ◽  
Decision Matrix

Multiple Criteria Decision Making methods, such as TOPSIS, have become very popular in recent years and are frequently applied to solve many real-life situations. However, the increasing complexity of the decision problems analysed makes it less feasible to consider all the relevant aspects of the problems by a single decision maker. As a result, many real-life problems are discussed by a group of decision makers. In such a group each decision maker can specialize in a different field and has his/her own unique characteristics, such as knowledge, skills, experience, personality, etc. This implies that each decision maker should have a different degree of influence on the final decision, i.e., the weights of decision makers should be different. The aim of this paper is to extend the fuzzy TOPSIS method to group decision making. The proposed approach uses TOPSIS twice. The first time it is used to determine the weights of decision makers which are then used to calculate the aggregated decision matrix for all the group decision matrices provided by the decision makers. Based on this aggregated matrix, the extended TOPSIS is used again, to rank the alternatives and to select the best one. A numerical example illustrates the proposed approach.

A HYBRID FUZZY APPROACH TO FUZZY MULTI-ATTRIBUTE GROUP DECISION-MAKING

2011 ◽  
Vol 10 (04) ◽  
pp. 695-711 ◽  
Author(s):  
ZHI-XIN SU
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Distance Measure ◽  
Group Decision ◽  
Similarity Measures ◽  
Decision Makers ◽  
Gray Relational Analysis ◽  
Fuzzy Approach ◽  
Relative Closeness

The paper investigates fuzzy multi-attribute group decision-making (FMAGDM) problems. The important weights of the attributes and the ratings of the alternatives with respect to each attribute provided by multiple decision-makers are described by the linguistic variables expressed in triangular fuzzy numbers or trapezoidal fuzzy numbers. A hybrid fuzzy approach is proposed, which assesses each alternative in terms of distance measure calculated by a modified VIKOR method as well as similarity measure calculated by a modified gray relational analysis (GRA) method, to the positive ideal alternative and the negative ideal alternative. A new relative closeness coefficient is established to rank alternatives by aggregating the distance and the similarity measures. Two numerical examples for reverse logistics applications are presented to illustrate the proposed method.

scholarly journals Group Decision-Making Based on the VIKOR Method with Trapezoidal Bipolar Fuzzy Information

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1313 ◽  
Author(s):  
Shumaiza ◽  
Muhammad Akram ◽  
Ahmad N. Al-Kenani ◽  
José Carlos R. Alcantud
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Thermal Power ◽  
Decision Makers ◽  
Sources Of Information ◽  
Vikor Method ◽  
Decision Matrix ◽  
Multiple Attribute

The VIKOR methodology stands out as an important multi-criteria decision-making technique. VIKOR stands for “VIekriterijumsko KOmpromisno Rangiranje”, a Serbian term for “multi-criteria optimization and compromise solution”. It has been adapted to sources of information with sundry formats. We contribute to that strand on literature with a design of a new multiple-attribute group decision-making method called the trapezoidal bipolar fuzzy VIKOR method. It consists of a suitable redesign of the VIKOR approach so that it can use information with bipolar configurations. Bipolar fuzzy sets (and numbers) establish a symmetrical trade-off between two judgmental constituents of human thinking. The agents acquire uncertain and vague information in the form of linguistic variables parameterized by trapezoidal bipolar fuzzy numbers. Trapezoidal bipolar fuzzy numbers are considered by decision-makers for assigning the preference information of alternatives with respect to different attributes. Our non-trivial adaptation necessitates several steps. The ranking function of bipolar fuzzy numbers is employed to make a simple decision matrix with real numbers as its entries. Shannon’s entropy concept is applied to evaluate the normalized weights for attributes that may be either partially or completely unknown to the decision-makers. The ordering of the alternatives is obtained by assorting the maximum group utility and the individual regret of the opponent in an ascending manner. For illustration, the proposed technique is applied to two group decision-making problems, namely, the selection of waste treatment methods and the site to plant a thermal power station. A comparison of this method with the trapezoidal bipolar fuzzy TOPSIS method is also presented.

scholarly journals Hybrid Multiattribute Group Decision Making Based on Intuitionistic Fuzzy Information and GRA Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jian Guo
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Makers ◽  
Ideal Solution ◽  
Decision Matrix ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Intuitionistic Fuzzy Entropy ◽  
Fuzzy Group Decision Making

Hybrid multiple attribute group decision making involves ranking and selecting competing courses of action available using attributes to evaluate the alternatives. The decision makers assessment information can be expressed in the form of real number, interval-valued number, linguistic variable, and the intuitionistic fuzzy number. All these evaluation information can be transformed to the form of intuitionistic fuzzy numbers. A combined GRA with intuitionistic fuzzy group decision-making approach is proposed. Firstly, the hybrid decision matrix is standardized and then transformed into an intuitionistic fuzzy decision matrix. Then, intuitionistic fuzzy averaging operator is utilized to aggregate opinions of decision makers. Intuitionistic fuzzy entropy is utilized to obtain the entropy weights of the criteria, respectively. After intuitionistic fuzzy positive ideal solution and intuitionistic fuzzy negative ideal solution are calculated, the grey relative relational degree of alternatives is obtained and alternatives are ranked. In the end, a numerical example illustrates the validity and applicability of the proposed method.

scholarly journals A New Approach for Assessing Credit Risks under Uncertainty

2020 ◽  
Author(s):  
Teimuraz Tsabadze
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Metric Space ◽  
Theoretical Basis ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Initial Part ◽  
New Approach ◽  
Trapezoidal Fuzzy Numbers ◽  
Credit Risks

The purpose of this chapter is to introduce a new approach for an assessment of the credit risks. The initial part of the chapter is to briefly discuss the existing models of assessment of the credit risks and justify the need for a new approach. Since a new approach is created for conditions of uncertainty, we cannot do without fuzzy mathematics. The proposed approach is based on group decision-making, where experts’ opinions are expressed by trapezoidal fuzzy numbers. The theoretical basis of the offered approach is laid out in the metric space of trapezoidal fuzzy numbers. The new approach is introduced and discussed, and two realization algorithms are given. The toy example of application of the introduced approach is offered as well.

scholarly journals AHP-Group Decision Making Based on Consistency

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 242 ◽  
Author(s):  
Juan Aguarón ◽  
María Teresa Escobar ◽  
José Moreno-Jiménez ◽  
Alberto Turón
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Real Life ◽  
Decision Makers ◽  
Local Context ◽  
Consensus Matrix ◽  
Stability Intervals ◽  
The Individual ◽  
Individual Consistency

The Precise consistency consensus matrix (PCCM) is a consensus matrix for AHP-group decision making in which the value of each entry belongs, simultaneously, to all the individual consistency stability intervals. This new consensus matrix has shown significantly better behaviour with regards to consistency than other group consensus matrices, but it is slightly worse in terms of compatibility, understood as the discrepancy between the individual positions and the collective position that synthesises them. This paper includes an iterative algorithm for improving the compatibility of the PCCM. The sequence followed to modify the judgments of the PCCM is given by the entries that most contribute to the overall compatibility of the group. The procedure is illustrated by means of its application to a real-life situation (a local context) with three decision makers and four alternatives. The paper also offers, for the first time in the scientific literature, a detailed explanation of the process followed to solve the optimisation problem proposed for the consideration of different weights for the decision makers in the calculation of the PCCM.

scholarly journals A Novel Linguistic Z-Number QUALIFLEX Method and Its Application to Large Group Emergency Decision Making

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Xue-Feng Ding ◽  
Li-Xia Zhu ◽  
Mei-Shun Lu ◽  
Qi Wang ◽  
Yi-Qi Feng
Keyword(s):  
Decision Making ◽  
Group Decision ◽  
Real Life ◽  
Decision Makers ◽  
Decision Matrix ◽  
Large Group ◽  
Emergency Event ◽  
Emergency Decision Making ◽  
Emergency Decision ◽  
Alternative Solutions

After an unconventional emergency event occurs, a reasonable and effective emergency decision should be made within a short time period. In the emergency decision making process, decision makers’ opinions are often uncertain and imprecise, and determining the optimal solution to respond to an emergency event is a complex group decision making problem. In this study, a novel large group emergency decision making method, called the linguistic Z-QUALIFLEX method, is developed by extending the QUALIFLEX method using linguistic Z-numbers. The evaluations of decision makers on the alternative solutions are first expressed as linguistic Z-numbers, and the group decision matrix is then constructed by aggregating the evaluations of all subgroups. The QUALIFLEX method is used to rank the alternative solutions for the unconventional emergency event. Besides, a real-life example of emergency decision making is presented, and a comparison with existing methods is performed to validate the effectiveness and practicability of the proposed method. The results show that the proposed linguistic Z-QUALIFLEX can accurately express the evaluations of the decision makers and obtain a more reasonable ranking result of solutions for emergency decision making.

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