Research on Multi-Attribute Decision-Making Method Based on Fuzzy Set Theory

2008 ◽  
Author(s):  
Zhang Wei ◽  
Zhu Jinfu
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Multi Attribute Decision Making

scholarly journals Decision-Making Approach under Pythagorean Fuzzy Yager Weighted Operators

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 70 ◽  
Author(s):  
Gulfam Shahzadi ◽  
Muhammad Akram ◽  
Ahmad N. Al-Kenani
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Ordered Weighted Averaging ◽  
Multi Attribute Decision Making ◽  
Parametric Families

In fuzzy set theory, t-norms and t-conorms are fundamental binary operators. Yager proposed respective parametric families of both t-norms and t-conorms. In this paper, we apply these operators for the analysis of Pythagorean fuzzy sets. For this purpose, we introduce six families of aggregation operators named Pythagorean fuzzy Yager weighted averaging aggregation, Pythagorean fuzzy Yager ordered weighted averaging aggregation, Pythagorean fuzzy Yager hybrid weighted averaging aggregation, Pythagorean fuzzy Yager weighted geometric aggregation, Pythagorean fuzzy Yager ordered weighted geometric aggregation and Pythagorean fuzzy Yager hybrid weighted geometric aggregation. These tools inherit the operational advantages of the Yager parametric families. They enable us to study two multi-attribute decision-making problems. Ultimately we can choose the best option by comparison of the aggregate outputs through score values. We show this procedure with two practical fully developed examples.

Multi-Attribute Decision Making Using Interval Type-2 Fuzzy AHP and Its Application on Borsa Istanbul (BIST)

2021 ◽  
pp. 30-56
Author(s):  
Beyza Ahlatcioglu Ozkok ◽  
Hale Gonce Kocken
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Ahp ◽  
Short Review ◽  
Analytic Hierarchy ◽  
Multi Attribute Decision Making ◽  
Interval Type

Analytic hierarchy process (AHP) is a widely used multi-attribute decision-making (MADM) approach. Due to the complexity and uncertainty involved in real world problems, decision makers might be prefer to make fuzzy judgments instead of crisp 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 has been introduced to characterize linguistic variables. Fuzzy AHP methods have recently been extended by using type-2 fuzzy sets. Type-2 fuzzy set theory incorporates the uncertainty of membership functions into the fuzzy set theory. In this chapter, the authors firstly provide a short review on applications of interval type-2 fuzzy AHP on MADM problems. Then, they present a very efficient MADM technique, interval type-2 fuzzy AHP, to solve the portfolio selection problem that is to decide which stocks are to be chosen for investment and in what proportions they will be bought. And finally, they provided a case study on BIST.

Research on Interval-valued Intuitionistic Fuzzy Multi-attribute Decision Making Based on Projection Model

2019 ◽  
Vol 13 ◽  
Author(s):  
Sha Fu ◽  
Xi-long Qu ◽  
Ye-zhi Xiao ◽  
Hang-jun Zhou ◽  
Yun Zhou
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Ideal Point ◽  
Projection Model ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Ideal ◽  
Multi Attribute Decision Making ◽  
Interval Valued

Background: Regarding the multi-attribute decision making where the decision information is the interval-valued intuitionistic fuzzy number and the attribute weight information is not completely determined. Method: Intuitionistic fuzzy set theory introduces non-membership function, as an extension of the fuzzy set theory, it has certain advantages in solving complex decision making problems. a projection model based interval-valued intuitionistic fuzzy multi-attribute decision making scheme was proposed in this study. The objective weight of the attribute was obtained using improved interval-valued intuitionistic fuzzy entropy, and thus the comprehensive weight of the attribute was obtained according to the preference information. Results: In the aspect of the decision-making matrix processing, the concept of interval-valued intuitionistic fuzzy ideal point and its related concepts were defined, the score vector of each scheme was calculated, the projection model was constructed to measure the similarity between each scheme and the interval-valued intuitionistic fuzzy ideal point, and the scheme was sorted according to the projection value. Conclusion: The efficiency and usability of the proposed approach are considered on the case study.

scholarly journals Multi-Attribute Multi-Perception Decision-Making Based on Generalized T-Spherical Fuzzy Weighted Aggregation Operators on Neutrosophic Sets

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 780 ◽  
Author(s):  
Quek ◽  
Selvachandran ◽  
Munir ◽  
Mahmood ◽  
Ullah ◽  
...  
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Aggregation Operators ◽  
Neutrosophic Sets ◽  
Operational Laws ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making ◽  
Do So

The framework of the T-spherical fuzzy set is a recent development in fuzzy set theory that can describe imprecise events using four types of membership grades with no restrictions. The purpose of this manuscript is to point out the limitations of the existing intuitionistic fuzzy Einstein averaging and geometric operators and to develop some improved Einstein aggregation operators. To do so, first some new operational laws were developed for T-spherical fuzzy sets and their properties were investigated. Based on these new operations, two types of Einstein aggregation operators are proposed namely the Einstein interactive averaging aggregation operators and the Einstein interactive geometric aggregation operators. The properties of the newly developed aggregation operators were then investigated and verified. The T-spherical fuzzy aggregation operators were then applied to a multi-attribute decision making (MADM) problem related to the degree of pollution of five major cities in China. Actual datasets sourced from the UCI Machine Learning Repository were used for this purpose. A detailed study was done to determine the most and least polluted city for different perceptions for different situations. Several compliance tests were then outlined to test and verify the accuracy of the results obtained via our proposed decision-making algorithm. It was proved that the results obtained via our proposed decision-making algorithm was fully compliant with all the tests that were outlined, thereby confirming the accuracy of the results obtained via our proposed method.

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.

Fuzzy Decision Making in Politics: A Linguistic Fuzzy-Set Approach (LFSA)

2005 ◽  
Vol 13 (1) ◽  
pp. 23-56 ◽  
Author(s):  
Badredine Arfi
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Multiple Criteria ◽  
Decision Makers ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Trust And Power

In this article I use linguistic fuzzy-set theory to analyze the process of decision making in politics. I first introduce a number of relevant elements of (numerical and linguistic) fuzzy-set theory that are needed to understand the terminology as well as to grasp the scope and depth of the approach. I then explicate a linguistic fuzzy-set approach (LFSA) to the process of decision making under conditions in which the decision makers are required to simultaneously satisfy multiple criteria. The LFSA approach is illustrated through a running (hypothetical) example of a situation in which state leaders need to decide how to combine trust and power to make a choice on security alignment.

Evaluation of Quantified Statements Using Gradual Numbers

2011 ◽  
pp. 246-269 ◽  
Author(s):  
Ludovic Liétard ◽  
Daniel Rocacher
Keyword(s):  
Decision Making ◽  
Expert Systems ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Relational Databases ◽  
Fuzzy Numbers ◽  
Theoretical Background ◽  
Definition Of ◽  
Flexible Querying

This chapter is devoted to the evaluation of quantified statements which can be found in many applications as decision making, expert systems, or flexible querying of relational databases using fuzzy set theory. Its contribution is to introduce the main techniques to evaluate such statements and to propose a new theoretical background for the evaluation of quantified statements of type “Q X are A” and “Q B X are A.” In this context, quantified statements are interpreted using an arithmetic on gradual numbers from Nf, Zf, and Qf. It is shown that the context of fuzzy numbers provides a framework to unify previous approaches and can be the base for the definition of new approaches.

Decision Making Approach using Weighted Coefficient of Correlation along with Generalized Parametric Fuzzy Entropy Measure

2016 ◽  
Vol 5 (3) ◽  
pp. 30-41 ◽  
Author(s):  
Priti Gupta ◽  
Pratiksha Tiwari
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Entropy Measure ◽  
Managerial Decision ◽  
Coefficient Of Correlation ◽  
Different Types ◽  
Segmentation Of Images ◽  
Real World Problems

Decision making involves various attributes along with several decision takers. Recently it has become more complex. This gives raise to uncertainty and associated with the information provided. So it may be appropriate to suggest that uncertainty demonstrates itself in numerous forms and of different types. Uncertainties may arise due to human behaviour, fluctuations of information, unknown facts. Fuzzy set theory is tool to deal with uncertainty in a better way. Both Fuzzy set theory and information theory are involved in dealing with various real-world problems such as segmentation of images, medical diagnosis, managerial decision making etc. Several methods and concepts dealing with imprecision and uncertainty have been proposed by many researchers. In the present communication, the authors have proposed a parametric generalization of entropy introduced by De Luca and Termini along with its basic properties. Further, a new measure of weighted coefficient of correlation is developed and applied to solve decision making problems involving uncertainty.

Test of a Fuzzy Set Based Decision Model as an AID in Solving Human Factors Design Problems

1981 ◽  
Vol 25 (1) ◽  
pp. 306-310
Author(s):  
Richard A. Newman
Keyword(s):  
Decision Making ◽  
Human Factors ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Decision Aid ◽  
Decision Model ◽  
Decision Rules ◽  
Design Problems ◽  
Weighting Rule

Fuzzy Set Theory has proved popular for development of decision making models. However, most such models have not been tested using problems such as commonly found in Human Factors system design. This study used a decision model that combined Fuzzy Set decision rules with an eigenvector weighting rule. Five experienced Human Factors Designers solved six design problems, half manually, and half using a computer program that served as a decision making aid, using the model. On completion of the procedure, the computer model made a recommendation for a solution. The user could accept or reject the model's choice. Comparisons were made between manual and computer aided decision making, and the Fuzzy Set decision rule was compared with other possible decision rules using the same data. Results showed that use of the model-based decision aid was accepted by the users, and were reasonable. In addition, a possible measure of decision making quality was found in the measure of weighting inconsistency which is part of the eigenvector procedure.

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