scholarly journals A Novel Portfolio Based on Interval-Valued Intuitionistic Fuzzy AHP with Improved Combination Weight Method and New Score Function

2021 ◽  
Author(s):  
Xue Deng ◽  
Fengting Geng ◽  
Jianxin Yang
Keyword(s):  
Mathematical Proof ◽  
Fuzzy Ahp ◽  
Score Function ◽  
Decision Matrix ◽  
Entropy Weight ◽  
Analytic Hierarchy ◽  
Weighting Method ◽  
Score Functions ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Abstract The classical Analytic Hierarchy Process (AHP) requires an exact value to compare the relative importance of two attributes, but experts often can not obtain an accurate assessment of every attribute in the decision-making process, there are always some uncertainty and hesitation. Compared with classical AHP, our new defined interval-valued intuitionistic fuzzy AHP has accurately descripted the vagueness and uncertainty. In decision matrix, the real numbers are substituted by fuzzy numbers. In addition, each expert will make different evaluations according to different experiences for each attribute in the subjective weighting method, which neglects objective factors and then generates some deviations in some cases. This paper provides two ways to make up for this disadvantage. On the one hand, by combining the interval-valued intuitionistic fuzzy AHP with entropy weight, an improved combination weighting method is proposed, which can overcome the limitations of unilateral weighted method only considering the objective or subjective factors. On the other hand, a new score function is presented by adjusting the parameters, which can overcome the invalidity of some existing score functions. In theory, some theorems and properties for the new score functions are given with strictly mathematical proof to validate its rationality and effectiveness. In application, a novel fuzzy portfolio is proposed based on the improved combination weighted method and new score function. A numerical example shows that these results of our new score function are consistent with those of most existing score functions, which verifies that our model is feasible and effective.

scholarly journals Minkowski Weighted Score Functions of Intuitionistic Fuzzy Values

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1143
Author(s):  
Feng Feng ◽  
Yujuan Zheng ◽  
José Carlos R. Alcantud ◽  
Qian Wang
Keyword(s):  
Decision Making ◽  
Score Function ◽  
Soft Sets ◽  
Score Functions ◽  
Intuitionistic Fuzzy ◽  
Geometric Point ◽  
Weighted Score ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Value ◽  
Intuitionistic Fuzzy Soft Sets

In multiple attribute decision-making in an intuitionistic fuzzy environment, the decision information is sometimes given by intuitionistic fuzzy soft sets. In order to address intuitionistic fuzzy decision-making problems in a more efficient way, many scholars have produced increasingly better procedures for ranking intuitionistic fuzzy values. In this study, we further investigate the problem of ranking intuitionistic fuzzy values from a geometric point of view, and we produce related applications to decision-making. We present Minkowski score functions of intuitionistic fuzzy values, which are natural generalizations of the expectation score function and other useful score functions in the literature. The rationale for Minkowski score functions lies in the geometric intuition that a better score should be assigned to an intuitionistic fuzzy value farther from the negative ideal intuitionistic fuzzy value. To capture the subjective attitude of decision makers, we further propose the Minkowski weighted score function that incorporates an attitudinal parameter. The Minkowski score function is a special case corresponding to a neutral attitude. Some fundamental properties of Minkowski (weighted) score functions are examined in detail. With the aid of the Minkowski weighted score function and the maximizing deviation method, we design a new algorithm for solving decision-making problems based on intuitionistic fuzzy soft sets. Moreover, two numerical examples regarding risk investment and supplier selection are employed to conduct comparative analyses and to demonstrate the feasibility of the approach proposed in this article.

A Distance-based Method for Computing Priorities of Intuitionistic Fuzzy Preference Relation and Its Application in AHP

2019 ◽  
Vol 23 (4) ◽  
pp. 329-340
Author(s):  
Akshay Hinduja ◽  
Manju Pandey
Keyword(s):  
Fuzzy Set ◽  
Fuzzy Ahp ◽  
Preference Relation ◽  
Intuitionistic Fuzzy Set ◽  
Analytic Hierarchy ◽  
Intuitionistic Fuzzy ◽  
Course Of Action ◽  
Fuzzy Preference Relations ◽  
Priority Method ◽  
Fuzzy Preference

The notion of multi-criteria decision-making is regarded as the process of finding the best possible alternative or course of action by decision-makers. Often, it entails handling vague, incomplete and inconsistent information. The intuitionistic fuzzy set (IFS) has been proven more effective than a fuzzy set in handling vagueness and uncertainty. The aim of the article is to incorporate the effectiveness of the IFS with the powerfulness of the analytic hierarchy process (AHP) and develop intuitionistic fuzzy AHP (IF-AHP) to cope with the decision problems involving imprecise and hesitant information. In this article, we develop a distance-based novel priority method, which derives unambiguous non-fuzzy priorities of the alternatives from intuitionistic fuzzy preference relations (IFPRs). The proposed priority method is simple in computation yet effective in results. To validate the method, we applied it to the adapted supplier selection problem. This article also presents a comparison of the proposed method with classic and fuzzy AHP using Monte-Carlo simulation approach.

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