A New Method for Fuzzy Risk Analysis Based on Ranking Generalized Fuzzy Numbers with Different Left Heights and Right Heights Shyi-Ming Chen 1,2 , Abdul Munif 1 , Guey-Shya Chen 2 , Bor-Chen Kuo 2 , and Hsiang-Chuan Liu 3 1 Department of Computer Science and Information Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan 2 Graduate Institute of Educational Measurement and Statistics, National Taichung University of Education, Taichung, Taiwan 3 Department of Biomedical Informatics, Asia University, Taichung, Taiwan Abstract—This paper presents a new method for fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights. First, we present a method for ranking generalized fuzzy numbers with different left heights and right heights. It can overcome the drawbacks of the existing fuzzy ranking methods. Based on the proposed fuzzy ranking method of generalized fuzzy numbers with different left heights and right heights, we propose a new method for fuzzy risk analysis. The proposed fuzzy risk analysis method provides us with a useful way to deal with fuzzy risk analysis problems. Keywords—Fuzzy risk analysis, Generalized fuzzy numbers, Ranking methods, Ranking scores. I. INTRODUCTION To deal with fuzzy risk analysis problems, the evaluating values of the risk of each sub-component are usually represented by fuzzy numbers, as shown in [4], [5], [7], [8], [12], [13], [14], [16]. In [4], Chen and Chen presented a method for fuzzy risk analysis based on a similarity measure of generalized fuzzy numbers. In [5], Chen and Chen presented a method for fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers. In [7], Chen and Chen presented a method for fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. In [8], Chen and Sanguansat presented a method for fuzzy risk analysis based on ranking generalized fuzzy numbers. In [12], Kangari and Riggs presented a method for the construction risk assessment by using linguistic terms. In [13], Lee and Chen presented a method for fuzzy risk analysis based on fuzzy numbers with different shapes and different deviations. In [14], Schmucker presented a method for fuzzy risk analysis based on fuzzy number arithmetic operations. In [16], Wei and Chen presented a method for fuzzy risk analysis based on interval-valued fuzzy numbers. Some fuzzy ranking methods have been presented by researchers [5], [7], [8]. In [5], Chen and Chen presented a method for ranking generalized fuzzy numbers based on the centroid points and the standard deviations of generalized fuzzy numbers to deal with fuzzy risk analysis problems. In [7], Chen and Chen presented a method for ranking generalized fuzzy numbers by considering the defuzzified values, the heights and the spreads of the generalized fuzzy numbers to deal with fuzzy risk analysis problems. In [8], Chen and Sanguansat presented a method for ranking generalized fuzzy numbers by considering the areas on the positive side, the areas on the negative side and the heights of the generalized fuzzy numbers to deal with fuzzy risk analysis problems. In this paper, we present a new method for fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights. First, we present a new method for ranking generalized fuzzy numbers with different left heights and right heights. It can overcome the drawbacks of the existing fuzzy ranking methods. Based on the proposed fuzzy ranking method of generalized fuzzy numbers with different left heights and right heights, we propose a new method for dealing with fuzzy risk analysis problems. The proposed fuzzy risk analysis method provides us with a useful way to deal with fuzzy risk analysis problems. II. PRELIMINARIES A. Basic Concept of Generalized Fuzzy Numbers In [1], Chen proposed the concept of generalized fuzzy numbers. Fig. 1 shows the membership function A ~ μ of a generalized fuzzy number A ~ with the different left height and right height and shows the membership function F ~ μ of a fuzzy number F ~ , where ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ≤ ≤ ≤ ≤ ≤ ≤ = otherwise, , 0 , ), ( , ), ( , ), ( ) ( 4 3 3 3 2 2 2 1 1 ~ x x x x g x x x x g x x x x g x A μ ฀ (1) 978-1-4577-0653-0/11/$26.00 ©2011 IEEE 2307