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International Journal of Approximate Reasoning
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Fuzzy Sets and Systems
Fractional programming approach to fuzzy weighted average
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International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
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On the compatibility between defuzzification and fuzzy arithmetic operations
Fuzzy Sets and Systems
Fuzzy weighted averages revisited
Fuzzy Sets and Systems - Information processing
Information Sciences: an International Journal
Simple computation for the defuzzifications of center of sum and center of gravity
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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A simple approach to ranking a group of aggregated fuzzy utilities
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Competitiveness of manufacturing firms: an application of fuzzy weighted average
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Advances in Fuzzy Systems
A revised method for ranking fuzzy numbers using maximizing set and minimizing set
Computers and Industrial Engineering
Computers & Mathematics with Applications
International Journal of Fuzzy System Applications
A probabilistic model for prioritizing engineering design requirements in uncertain QFD
IUKM'13 Proceedings of the 2013 international conference on Integrated Uncertainty in Knowledge Modelling and Decision Making
Applying OWA operator to model group behaviors in uncertain QFD
IUKM'13 Proceedings of the 2013 international conference on Integrated Uncertainty in Knowledge Modelling and Decision Making
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Centroid defuzzification and the maximizing set and minimizing set methods are two commonly used approaches to ranking fuzzy numbers and often require membership functions to be known. In this paper, the two methods are reinvestigated when explicit membership functions are not known but alpha level sets are available. Two analytical formulas are derived under the assumption that the exact membership functions can be approximated by using piecewise linear functions based on alpha level sets. The derived analytical formulas are of significant importance and provide very useful decision supports for a wide variety of applications of the two methods in industrial engineering and other areas. Numerical examples are offered to test the derived formulas and illustrate their computational processes and applications in risk assessment of a software development.