An Intuitionistic Fuzzy Multi-Criteria Decision-Making Method Based on an Exponential-Related Function

2017 ◽  
Vol 6 (4) ◽  
pp. 33-46 ◽  
Author(s):  
Daniel Aikhuele ◽  
Faiz Turan
Keyword(s):  
Decision Making ◽  
Real Life ◽  
Multiple Criteria Decision Making ◽  
Score Function ◽  
Pairwise Comparison ◽  
Ideal Solution ◽  
Related Function ◽  
Intuitionistic Fuzzy ◽  
Relative Closeness ◽  
Priority Weights

Intuitionistic fuzzy multiple criteria decision making (MCDM) method which is based on an exponential-related function, adopted in the Technique for order preference by similarity to ideal solution (TOPSIS) has been proposed in this study. The exponential-related function which is used for comparing intuitionistic-fuzzy-sets (IFS), and as a replacement for the traditional exponential score function which is only effective for determining priority weights that involve pairwise-comparison, has been applied, for computing the separation measure from the fuzzy positive and negative ideal solution to determine the relative closeness-coefficients of alternatives. The main advantage of this method includes (1) its ability to account for Decision-makers (DMs) attitudinal-character in the decision-making process as-well-as to represent the aggregated effect of the positive/negative evaluations in the performance ratings of the alternatives based on the IFS-data and (2) The simplicity of the method both in its concept and computational procedures. To demonstrate the feasibility of the method, it has been applied for the evaluation of some hypothetical design-related problems and for a real-life case study.

A Multicriteria Interval-Valued Intuitionistic Fuzzy Set TOPSIS Decision-Making Approach Based on the Improved Score Function

2016 ◽  
Vol 25 (2) ◽  
pp. 239-250 ◽  
Author(s):  
Wei-wei Li ◽  
Chong Wu
Keyword(s):  
Decision Making ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Criteria Decision Making ◽  
Score Function ◽  
Intuitionistic Fuzzy ◽  
Cumulative Score ◽  
Criterion Weight ◽  
Relative Closeness ◽  
Interval Valued ◽  
Evaluation Information

AbstractIn this paper, an improved technique for order preference by similarity to an ideal solution (TOPSIS) method was proposed based on completely unknown attribute weight information, as well as taking multiple criteria decision making of interval-valued intuitionistic fuzzy number as the evaluation information. First of all, a cumulative interval score function considering the influence of hesitation as well as a cumulative score function containing the risk preference of the decision maker were constructed. Then, a new information entropy function was constructed by using the newly defined score function, which presents a new method that directly utilizes evaluation information to obtain criterion weight. Next, all schemes were sequenced by virtue of relative closeness and the criterion weight of each alternative and ideal scheme. Finally, the effectiveness of the proposed method was illustrated by comparison with examples.

scholarly journals New Ranking Functions for Interval-Valued Intuitionistic Fuzzy Sets and Their Application to Multi-Criteria Decision-Making Problem

2021 ◽  
Vol 21 (1) ◽  
pp. 3-18
Author(s):  
Melda Kokoç ◽  
Süleyman Ersöz
Keyword(s):  
Decision Making ◽  
High Performance ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Score Function ◽  
Multi Criteria Decision Making ◽  
Ranking Functions ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Interval Valued

Abstract Many authors agree that the Interval-Valued Intuitionistic Fuzzy Set (IVIFS) theory generates as realistic as possible evaluation of real-life problems. One of the real-life problems where IVIFSs are often preferred is the Multi-Criteria Decision-Making (MCDM) problem. For this problem, the ranking of values obtained by fuzzing the opinions corresponding to alternatives is an important step, as a failure in ranking may lead to the selection of the wrong alternative. Therefore, the method used for ranking must have high performance. In this article, a new score function SKE and a new accuracy function HKE are developed to overcome the disadvantages of existing ranking functions for IVIFSs. Then, two illustrative examples of MCDM problems are presented to show the application of the proposed functions and to evaluate their effectiveness. Results show that the functions proposed have high performance and they are the eligibility for the MCDM problem.

scholarly journals A New Multiple Criteria Decision Making Method and its Application in Cloud Computing for Education

2015 ◽  
Vol 10 (8) ◽  
pp. 21
Author(s):  
Heng Sun
Keyword(s):  
Decision Making ◽  
Cloud Computing ◽  
Membership Function ◽  
Fuzzy Set ◽  
Choquet Integral ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Criteria Decision Making ◽  
Score Function ◽  
Multiple Criteria ◽  
Intuitionistic Fuzzy

Cloud computing can extend the traditional education framework. In education, cloud can provide students and teachers with tools to deploy computing resources on-demand for lectures and labs according to their learning needs. But how to select a perfect cloud server is a key point, which is considered as a multiple criteria decision making problem. So, in this paper, intuitionistic fuzzy set is first introduced to express the decision maker’s views. Intuitionistic fuzzy set (IFS) includes a membership function and a non-membership function. More importantly, a new operator with choquet integral is developed to deal with assessment of education using cloud computing. Meanwhile, score function and accuracy function are demonstrated to obtain the final result. Finally, we develop this method to apply in a case study to show its applicability.

Interval-Valued Intuitionistic Fuzzy Sets based Method for Multiple Criteria Decision-Making

2016 ◽  
Vol 5 (4) ◽  
pp. 192-210 ◽  
Author(s):  
Bhagawati Prasad Joshi
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Real Life ◽  
Multiple Criteria Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Multiple Criteria ◽  
Decision Makers ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Interval Valued

Due to the huge applications of fuzzy set theory, many generalizations were available in literature. Atanassov (1983) and Atanassov and Gargov (1989) introduced the notions of intuitionistic fuzzy sets (IFSs) and interval-valued intuitionistic fuzzy sets (IVIFSs) respectively. It is observed that IFSs and IVIFSs are more suitable tools for dealing with imprecise information and very powerful in modeling real life problems. However, many researchers made efforts to rank IVIFSs due to its importance in fusion of information. In this paper, a new ranking method is introduced and studied for IVIFSs. The proposed method is compared and illustrated with other existing methods by numerical examples. Then, it is utilized to identify the best alternative in multiple criteria decision-making problems in which criterion values for alternatives are IVIFSs. On the basis of the developed approach, it would provide a powerful way to the decision-makers to make his or her decision under IVIFSs. The validity and applicability of the proposed method are illustrated with practical examples.

scholarly journals AN IVIF-ELECTRE OUTRANKING METHOD FOR MULTIPLE CRITERIA DECISION-MAKING WITH INTERVAL-VALUED INTUITIONISTIC FUZZY SETS

2015 ◽  
Vol 22 (3) ◽  
pp. 416-452 ◽  
Author(s):  
Ting-Yu CHEN
Keyword(s):  
Decision Making ◽  
Multiple Criteria Decision Making ◽  
Score Function ◽  
Multiple Criteria ◽  
Outranking Method ◽  
Intuitionistic Fuzzy ◽  
Ranking Procedures ◽  
Complete Ranking ◽  
Electre Method ◽  
Interval Valued

The method of ELimination Et Choix Traduisant la REalité (ELimination and Choice Expressing Reality, ELECTRE) is a well-known and widely used outranking method for handling decision-making problems. The purpose of this paper is to develop an interval-valued intuitionistic fuzzy ELECTRE (IVIF-ELECTRE) method and apply it to multiple criteria decision analysis (MCDA) involving the multiple criteria evaluation/selection of alternatives. Using interval-valued intuitionistic fuzzy (IVIF) sets with an inclusion comparison approach, concordance and discordance sets are identified for each pair of alternatives. Next, concordance and discordance indices are determined using an aggregate importance weight score function and a generalised distance measurement between weighted evaluative ratings, respectively. Based on the concordance and discordance dominance matrices, two IVIF-ELECTRE ranking procedures are developed for the partial and complete ranking of the alternatives. The feasibility and applicability of the proposed methods are illustrated with a multiple criteria decision-making problem of watershed site selection. A comparative analysis of other MCDA methods is conducted to demonstrate the advantages of the proposed IVIF-ELECTRE methods. Finally, an empirical study of job choices is implemented to validate the effectiveness of the current methods in the real world.

scholarly journals An Interval-Valued Intuitionistic Fuzzy TOPSIS Method Based on an Improved Score Function

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Zhi-yong Bai
Keyword(s):  
Decision Making ◽  
Score Function ◽  
Fuzzy Topsis ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Topsis Method ◽  
Intuitionistic Fuzzy ◽  
Relative Closeness ◽  
Intuitionistic Fuzzy Topsis ◽  
Interval Valued

This paper proposes an improved score function for the effective ranking order of interval-valued intuitionistic fuzzy sets (IVIFSs) and an interval-valued intuitionistic fuzzy TOPSIS method based on the score function to solve multicriteria decision-making problems in which all the preference information provided by decision-makers is expressed as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by IVIFS value and the information about criterion weights is known. We apply the proposed score function to calculate the separation measures of each alternative from the positive and negative ideal solutions to determine the relative closeness coefficients. According to the values of the closeness coefficients, the alternatives can be ranked and the most desirable one(s) can be selected in the decision-making process. Finally, two illustrative examples for multicriteria fuzzy decision-making problems of alternatives are used as a demonstration of the applications and the effectiveness of the proposed decision-making method.

scholarly journals ACO with Intuitionistic Fuzzy Pheromone Updating Applied on Multiple-Constraint Knapsack Problem

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1456
Author(s):  
Stefka Fidanova ◽  
Krassimir Todorov Atanassov
Keyword(s):  
Decision Making ◽  
Knapsack Problem ◽  
Propositional Logic ◽  
Optimization Problems ◽  
Real Life ◽  
Combinatorial Optimization Problems ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Multiple Constraint

Some of industrial and real life problems are difficult to be solved by traditional methods, because they need exponential number of calculations. As an example, we can mention decision-making problems. They can be defined as optimization problems. Ant Colony Optimization (ACO) is between the best methods, that solves combinatorial optimization problems. The method mimics behavior of the ants in the nature, when they look for a food. One of the algorithm parameters is called pheromone, and it is updated every iteration according quality of the achieved solutions. The intuitionistic fuzzy (propositional) logic was introduced as an extension of Zadeh’s fuzzy logic. In it, each proposition is estimated by two values: degree of validity and degree of non-validity. In this paper, we propose two variants of intuitionistic fuzzy pheromone updating. We apply our ideas on Multiple-Constraint Knapsack Problem (MKP) and compare achieved results with traditional ACO.

scholarly journals Additively Consistent Interval-Valued Intuitionistic Fuzzy Preference Relations and Their Application to Group Decision Making

Information ◽  
2018 ◽  
Vol 9 (10) ◽  
pp. 260 ◽  
Author(s):  
Hua Zhuang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Weighted Averaging ◽  
Preference Relations ◽  
Intuitionistic Fuzzy ◽  
Priority Weights ◽  
Interval Valued ◽  
Fuzzy Preference

This paper aims to propose an innovative approach to group decision making (GDM) with interval-valued intuitionistic fuzzy (IVIF) preference relations (IVIFPRs). First, an IVIFPR is proposed based on the additive consistency of an interval-valued fuzzy preference relation (IVFPR). Then, two mathematical or adjusted programming models are established to extract two special consistent IVFPRs. In order to derive the priority weight of an IVIFPR, after taking the two special IVFPRs into consideration, a linear optimization model is constructed by minimizing the deviations between individual judgments and between the width degrees of the interval priority weights. For GDM with IVIFPRs, the decision makers’ weights are generated by combining the adjusted subjective weights with the objective weights. Subsequently, using an IVIF-weighted averaging operator, the collective IVIFPR is obtained and utilized to derive the IVIF priority weights. Finally, a practical example of a supplier selection is analyzed to demonstrate the application of the proposed method.

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.

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