FMEA Using Combination Weighting and Fuzzy VIKOR Method
Due to its characteristics and capabilities, the VIKOR method has been employed by Liu et al. (2012) to resolve the risk evaluation problem under fuzzy environment. To overcome the shortcomings and enhance the assessment capability of FMEA, Liu et al. (20
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FMEA Using Combination Weighting and Fuzzy VIKOR Method
Due to its characteristics and capabilities, the VIKOR method has been employed by Liu et al. (2012) to resolve the risk evaluation problem under fuzzy environment. To overcome the shortcomings and enhance the assessment capability of FMEA, Liu et al. (2015) further presented a hybrid MCDM approach for risk analysis based on combination weighting and fuzzy VIKOR method. Combination of fuzzy analytic hierarchy process (AHP) and entropy method is applied for risk factor weighting in the proposed approach. The risk priorities of the identified failure modes are obtained through next steps based on fuzzy VIKOR method. The combination weighting method considering both subjective and objective weights of risk factors is helpful to reflect the essential characteristics of the risk evaluation problem. In addition, the fuzzy VIKOR method helps decision makers in FMEA achieve an acceptable compromise of the maximum group utility for the “majority” and the minimum of the individual regret for the “opponent.”
12.1
Preliminaries
12.1.1 Fuzzy Set Theory The basic definitions related to fuzzy sets and triangular fuzzy numbers can be found in Sects. 7.1.1 and 11.1.1. In this section, we only introduce the distance between triangular fuzzy numbers and the center of area (COA) method which will be utilized in the proposed FMEA model. Definition 12.1 According to Chen (2000), the distance between the triangular fuzzy numbers ~ a ¼ ða1 ; a2 ; a3 Þ and ~b ¼ ðb1 ; b2 ; b3 Þ is calculated by using the vertex method as
© Springer Science+Business Media Singapore 2016 H.-C. Liu, FMEA Using Uncertainty Theories and MCDM Methods, DOI 10.1007/978-981-10-1466-6_12
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FMEA Using Combination Weighting and Fuzzy VIKOR Method
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i 1h d ~ a; b~ ¼ ða1 b1 Þ2 þ ða2 b2 Þ2 þ ða3 b3 Þ2 : 3
ð12:1Þ
Definition 12.2 Using the COA method, the crisp value of the triangular fuzzy number ~ a ¼ ða1 ; a2 ; a3 Þ is expressed by the following relation (Liu et al. 2015): 1 x0 ð~aÞ ¼ ½ða3 a1 Þ þ ða2 a1 Þ þ a1 ; 3
ð12:2Þ
where x0 ð~ aÞ is the defuzzified value of the fuzzy number ~a.
12.1.2 Fuzzy AHP Method The analytic hierarchy process (AHP) (Saaty 1980) is a useful approach to tackle the complexity of decision problems by means of a hierarchy of decision layers. However, the classical AHP uses exact numerical values in the pairwise comparison matrix and is not fully capable of reflecting the human judgments. As a result, fuzzy extension of the AHP (Buckley et al. 2001) was presented to ease its adaptation to real-life problems, which is employed in this chapter to calculate subjective risk factor weights. Assuming l decision makers DMk ðk ¼ 1; 2; . . .; lÞ, we proceed to make decision on m alternatives with n criteria. Each decision maker DMk is given a weight P kk [ 0 ðk ¼ 1; . . .; lÞ satisfying l1 kk ¼ 1 to reflect his/her relative importance in the decision-making process. The procedure for det
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