scholarly journals Discussion on fuzzy decision making based on fuzzy number and compositional rule of inference

2015 ◽  
Vol 25 (2) ◽  
pp. 271-282 ◽  
Author(s):  
Ping-Teng Chang ◽  
Lung-Ting Hung
Keyword(s):  
Decision Making ◽  
Medical Diagnosis ◽  
Fuzzy Numbers ◽  
Fuzzy Theory ◽  
Matrix Multiplication ◽  
Original Method ◽  
Fuzzy Decision Making ◽  
Stochastic Matrices ◽  
Fuzzy Decision ◽  
Multiplication Operation

This paper provides an improved decision making approach based on fuzzy numbers and the compositional rule of inference by Yao and Yao (2001). They claimed to have created a new method that combines statistical methods and fuzzy theory for medical diagnosis. Currently, numerous papers have cited that work. In this study, we show that if we follow their matrix multiplication operation approach, we will obtain the same result as the original method proposed by Klir and Yuan (1995). Owing to a wellknown property of (row) stochastic matrices, if the multiplication is closed, the fuzzy and defuzzy procedure of Yao and Yao (2001) is redundant. Therefore, we advise researchers to think twice before applying this approach to medical diagnosis.

scholarly journals Fuzzy Insurance

1990 ◽  
Vol 20 (1) ◽  
pp. 33-55 ◽  
Author(s):  
Jean Lemaire
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Life Insurance ◽  
Fuzzy Set Theory ◽  
Fuzzy Numbers ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Basic Concepts ◽  
Definition Of

AbstractFuzzy set theory is a recently developed field of mathematics, that introduces sets of objects whose boundaries are not sharply defined. Whereas in ordinary Boolean algebra an element is either contained or not contained in a given set, in fuzzy set theory the transition between membership and non-membership is gradual. The theory aims at modelizing situations described in vague or imprecise terms, or situations that are too complex or ill-defined to be analysed by conventional methods. This paper aims at presenting the basic concepts of the theory in an insurance framework. First the basic definitions of fuzzy logic are presented, and applied to provide a flexible definition of a “preferred policyholder” in life insurance. Next, fuzzy decision-making procedures are illustrated by a reinsurance application, and the theory of fuzzy numbers is extended to define fuzzy insurance premiums.

A QUANTITY PROPERTY-BASED FUZZY NUMBER RANKING METHOD FOR DECISION MAKING WITH UNCERTAINTY

2012 ◽  
Vol 20 (supp01) ◽  
pp. 133-145 ◽  
Author(s):  
FACHAO LI ◽  
FEI GUAN ◽  
CHENXIA JIN
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Ranking Method ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Interval Numbers ◽  
Interval Representation ◽  
Ranking Model ◽  
Key Issues

One of the key issues for support fuzzy decision-making is fuzzy number ranking. The existing ranking methods either do not provide a total ordering or cannot be effectively applied to decision-making processes. In this paper, we first give five basic principles that interval number ranking must satisfy, and construct a quantitative ranking model of interval numbers based on the synthesis effects of each index. We then propose a new constructions method of synthesis effect function systematically. Third, we also develop a new fuzzy numbers ranking model based on numerical characteristics, combining with the interval representation theorem of fuzzy numbers, and analyze the performance and characteristics of this ranking method by a case-based example. The results indicate that this proposed ranking method has good operability and interpretability, which can integrate the decision consciousness into decision process effectively and serve as a guideline for constructing different fuzzy decision methods.

Analyzing the Ranking Method for Fuzzy Numbers in Fuzzy Decision Making Based on the Magnitude Concepts

2016 ◽  
Vol 19 (5) ◽  
pp. 1279-1289 ◽  
Author(s):  
Vincent F. Yu ◽  
Luu Huu Van ◽  
Luu Quoc Dat ◽  
Ha Thi Xuan Chi ◽  
Shuo-Yan Chou ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Ranking Method ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision

scholarly journals A New Ranking Principle For Ordering Trapezoidal Intuitionistic Fuzzy Numbers

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-24 ◽  
Author(s):  
Lakshmana Gomathi Nayagam Velu ◽  
Jeevaraj Selvaraj ◽  
Dhanasekaran Ponnialagan
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Partial Ordering ◽  
Fuzzy Decision Making ◽  
Accuracy Score ◽  
Fuzzy Decision ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Area Score ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

Modelling real life (industrial) problems using intuitionistic fuzzy numbers is inevitable in the present scenario due to their efficiency in solving problems and their accuracy in the results. Particularly, trapezoidal intuitionistic fuzzy numbers (TrIFNs) are widely used in describing impreciseness and incompleteness of a data. Any intuitionistic fuzzy decision-making problem requires the ranking procedure for intuitionistic fuzzy numbers. Ranking trapezoidal intuitionistic fuzzy numbers play an important role in problems involving incomplete and uncertain information. The available intuitionistic fuzzy decision-making methods cannot perform well in all types of problems, due to the partial ordering on the set of intuitionistic fuzzy numbers. In this paper, a new total ordering on the class of TrIFNs using eight different score functions, namely, imprecise score, nonvague score, incomplete score, accuracy score, spread score, nonaccuracy score, left area score, and right area score, is achieved and our proposed method is validated using illustrative examples. Significance of our proposed method with familiar existing methods is discussed.

Ranking generalized fuzzy numbers in fuzzy decision making based on the left and right transfer coefficients and areas

2013 ◽  
Vol 37 (16-17) ◽  
pp. 8106-8117 ◽  
Author(s):  
Vincent F. Yu ◽  
Ha Thi Xuan Chi ◽  
Luu Quoc Dat ◽  
Phan Nguyen Ky Phuc ◽  
Chien-wen Shen
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Transfer Coefficients ◽  
Left And Right ◽  
Generalized Fuzzy Numbers

The reference ideal TOPSIS method for linguistic q-rung orthopair fuzzy decision making based on linguistic scale function

2020 ◽  
Vol 39 (3) ◽  
pp. 4111-4131
Author(s):  
Donghai Liu ◽  
Yuanyuan Liu ◽  
Lizhen Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Ideal Theory ◽  
Distance Measures ◽  
Weighted Averaging ◽  
Fuzzy Decision Making ◽  
Scale Function ◽  
Fuzzy Decision ◽  
Topsis Method ◽  
Linguistic Scale Function

The linguistic q-rung orthopair fuzzy set is a powerful tool in representing linguistic assessments. Considering that the traditional decision making methods cannot deal with the situation that the best choice may not be the minimum or the maximum but between them, we propose an innovative TOPSIS method with linguistic q-rung orthopair fuzzy numbers based on the reference ideal theory. Firstly, the new operations of linguistic q-rung orthopair fuzzy sets are introduced based on the linguistic scale function. In addition, we propose the Minkowski distance measure of linguistic q-rung orthopair fuzzy numbers to make up for the defects of the existing distance measures based on the linguistic scale function. By using the new operations of linguistic q-rung orthopair fuzzy numbers, we propose the linguistic q-rung orthopair fuzzy weighted averaging operator and the linguistic q-rung orthopair fuzzy weighted geometric operator to aggregate linguistic decision information. Furthermore, we develop a reference ideal TOPSIS method to the linguistic q-rung orthopair fuzzy decision making problems. Finally, an example concerning the postgraduate entrance qualification assessment is given to illustrate the feasibility of the proposed method. Some comparative analysis is also given to show the efficiency of the method, in addition, the sensitivity analysis and stability analysis of the proposed method are also given.

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