scholarly journals IMPROVING CONSISTENCY EVALUATION IN FUZZY MULTI-ATTRIBUTE PAIRWISE COMPARISON-BASED DECISION-MAKING METHODS

2014 ◽  
Vol 31 (04) ◽  
pp. 1450024 ◽  
Author(s):  
FARHAD SHAMS ◽  
SHERIF MOHAMED ◽  
AMINAH ROBINSON FAYEK
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Decision Model ◽  
Pairwise Comparison ◽  
Pairwise Comparisons ◽  
Linguistic Data ◽  
Multi Attribute Decision Making ◽  
Numeric Scale ◽  
Consistency Evaluation

A typical approach to handle the complexity of multi-faceted decision-making problems is to use multi-attribute decision-making (MADM) methods based on pairwise comparisons. Fuzzy set theory has also been employed to cope with the uncertainty and vagueness involved in conducting the comparisons between components of a decision model. An important issue regarding the reliability of the output is the consistency of pairwise comparisons provided by the decision maker(s). Using the MADM method developed by Lu et al. (2007) as a foundation, this paper proposes an algorithm for evaluating the consistency level of pairwise comparison matrices, where linguistic data are used. A crisp numeric scale has been introduced to consider the priority of linguistic data and to avoid the complexity of handling fuzzy calculations in consistency evaluation of pairwise comparison matrices. As an advantage, the proposed method of consistency evaluation is capable of assessing the degree of inconsistency among the pairwise comparisons. Therefore, the acceptance or rejection of the pairwise comparisons can be determined based on the desired degree of tolerance in accepting inconsistent judgments. An application of a revised MADM method is then demonstrated in a case study involving flood mitigation project selection in Australia.

FAIR CONSISTENCY EVALUATION FOR RECIPROCAL RELATIONS AND IN GROUP DECISION MAKING

2009 ◽  
Vol 05 (02) ◽  
pp. 407-420 ◽  
Author(s):  
MICHELE FEDRIZZI ◽  
MATTEO BRUNELLI
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Group Decision Making ◽  
Evaluation Method ◽  
Group Decision ◽  
Pairwise Comparison ◽  
Pairwise Comparisons ◽  
Reciprocal Relations ◽  
Decision Making Processes ◽  
Consistency Evaluation

In decision-making processes, it often occurs that the decision maker is asked to pairwise compare alternatives. His/her judgements over a set of pairs of alternatives can be collected into a matrix and some relevant properties, for instance, consistency, can be estimated. Consistency is a desirable property which implies that all the pairwise comparisons respect a principle of transitivity. So far, many indices have been proposed to estimate consistency. Nevertheless, in this paper we argue that most of these indices do not fairly evaluate this property. Then, we introduce a new consistency evaluation method and we propose to use it in group decision making problems in order to fairly weigh the decision maker's preferences according to their consistency. In our analysis, we consider two families of pairwise comparison matrices: additively reciprocal pairwise comparison matrices and multiplicatively reciprocal pairwise comparison matrices.

A sequential three-way decision model based on hesitant fuzzy sets

2021 ◽  
pp. 1-12
Author(s):  
Mo Zhang ◽  
Qinghua Zhang ◽  
Man Gao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Decision Model ◽  
Hesitant Fuzzy Set ◽  
Extended Model ◽  
Uncertain Information ◽  
Fuzzy Distance ◽  
Shadowed Set ◽  
Multi Attribute Decision Making

As a new extended model of fuzzy sets, hesitant fuzzy set theory is a useful tool to process uncertain information in decision making problems. The traditional hesitant fuzzy multi-attribute decision making (MADM) can only choose an optimal strategy, which is not suitable for all of the complex scenarios. Typically, in practical application, decision making problems may be more complicated involving three options of acceptance, non-commitment and rejection decisions. Three-way decisions, which divide universe into three disjoint regions by a pair of thresholds, are more efficient to deal with these problems. Therefore, how to utilize three-way decision theory to process hesitant fuzzy information is an essential issue to be studied. In this paper, from the perspective of hesitant fuzzy distance, a hesitant fuzzy three-way decision model is proposed. First, because hesitant fuzzy element (HFE) is a set of several possible membership degrees, it cannot be compared with thresholds directly. Hence, this paper converts it into the comparison between the distance and the thresholds. Then, to calculate thresholds more reasonably, shadowed set theory is introduced to avoid the subjectivity of threshold acquisition. Furthermore, sequential strategy is adopted to solve the multi-attribute decision making problems. Finally, an example of medical diagnosis and simulation experiments are given to prove the accuracy and efficiency of the proposed hesitant fuzzy three-way decision model.

A Novel Hybrid Clustering Method for Multi-Attribute Decision-Making Datasets

2012 ◽  
Vol 482-484 ◽  
pp. 103-108
Author(s):  
Kai Ping Liu ◽  
Wen Chin Chen ◽  
Ting Cheng Chang
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set Theory ◽  
Uncertain Data ◽  
Clustering Method ◽  
Hybrid Scheme ◽  
Index Function ◽  
Single Attribute ◽  
Multi Attribute Decision Making

A function is proposed for descritizing and classifying the uncertain data of multi-attribute decision-making (MADM) datasets using a hybrid scheme incorporating fuzzy set theory, Rough Set (RS) theory and a modified form of the PBMF index function. The proposed MADM index function is used to extend the applicability of the single-attribute decision-making (SADM) function. The validity of the proposed MADM index function is evaluated by comparing the descritizing results obtained for a simple hypothetical function with those obtained using a SADM function and the conventional PBMF function.

scholarly journals SOLUTION OF A MULTI-CRITERIA DECISION- MAKING PROBLEM ON BASE OF PROMETHEE METHOD

2020 ◽  
Author(s):  
Salimov Vagif Hasan Oglu
Keyword(s):  
Decision Making ◽  
Pairwise Comparison ◽  
Preference Function ◽  
Pairwise Comparisons ◽  
Multi Criteria Decision Making ◽  
Job Selection ◽  
Decision Making Problem ◽  
Practice Problem ◽  
Promethee Method ◽  
Large Groups

Multi criteria decision making problem was considered. Review of existing multi criteria decision making methods was presented. Methods of solving this problem can be divided into two large groups: methods using the aggregation of all alternatives according to all criteria and the solution of the obtained one-criterion problem, the second group is associated with the procedure of pairwise comparisons. Promethee method have been considered with details. This method is based on the pairwise comparison of alternatives and specific aggregation procedures. The preference function are considered for minimization and maximization cases. As practice problem the job selection is considered. Three important criteria are used: salary, time, risk. The results of all computations are presented.

scholarly journals Multi-attribute decision-making based on soft set theory: a systematic review

2018 ◽  
Vol 23 (16) ◽  
pp. 6899-6920 ◽  
Author(s):  
Azadeh Zahedi Khameneh ◽  
Adem Kılıçman
Keyword(s):  
Systematic Review ◽  
Decision Making ◽  
Set Theory ◽  
Soft Set ◽  
Multi Attribute Decision Making

Fuzzy Analytic Hierarchy Process and Its Application to E-Marketplace Selection

2013 ◽  
pp. 26-44 ◽  
Author(s):  
Beyza Ahlatcioglu Ozkok ◽  
Elisa Pappalardo
Keyword(s):  
Decision Making ◽  
Analytic Hierarchy Process ◽  
Fuzzy Ahp ◽  
Multi Criteria Decision Making ◽  
Linguistic Variables ◽  
Analytic Hierarchy ◽  
Multi Attribute Decision Making ◽  
Electronic Parts ◽  
Hierarchy Process

Making decisions is a part of daily life. The nature of decision-making includes multiple and usually conflicting criteria. Multi Criteria Decision-Making (MCDM) problems are handled under two main headings: Multi Attribute Decision Making (MADM) and Multi Objective Decision Making (MODM). Analytic Hierarchy Process (AHP) is a widely used multi-criteria decision making approach and has successfully been applied to many practical problems. Traditional AHP requires exact or crisp judgments (numbers). However, due to the complexity and uncertainty involved in real world decision problems, decision makers might be more reluctant to provide crisp judgments than fuzzy ones. Furthermore, even when people use the same words, individual judgments of events are invariably subjective, and the interpretations that they attach to the same words may differ. This is why fuzzy numbers and fuzzy sets have been introduced to characterize linguistic variables. Here, the authors overview the most known fuzzy AHP approaches and their application, and they present a case study to select an e-marketplace for a firm, which produces and sells electronic parts of computers in Turkey.

A Decision Support System and Visualisation Tools for AHP-GDM

2021 ◽  
pp. 703-722
Author(s):  
Alberto Turón ◽  
Juan Aguarón ◽  
María Teresa Escobar ◽  
José María Moreno-Jiménez
Keyword(s):  
Decision Making ◽  
Decision Support ◽  
Decision Support System ◽  
Group Decision Making ◽  
Support System ◽  
Pairwise Comparison ◽  
Decision Makers ◽  
Consensus Matrix ◽  
Minimum Number

The Precise Consistency Consensus Matrix (PCCM) is a decisional tool for AHP-Group Decision Making (AHP-GDM). Based on the initial pairwise comparison matrices of the individuals, the PCCM constructs a consensus matrix for the group using the concept of consistency. This paper presents a decision support system (PRIOR-PCCM) that facilitates the construction of the PCCM in the context of AHP-GDM, and the calculus of four indicators that allows comparison of the behaviour of group consensus matrices. PRIOR-PCCM incorporates the possibility of considering different weights for the decision makers and includes a module that permits the extension of the initial PCCM which can achieve the minimum number of non-null entries required for deriving priorities or establishing a complete PCCM matrix. It also includes two cardinal indicators for measuring consistency and compatibility and two ordinal indicators for evaluating the number of violations of consistency and priority. The paper introduces some new visualisation tools that improve comprehension of the process followed for obtaining the PCCM matrix and allow the cognitive exploitation of the results. These original contributions are illustrated with a case study.

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