Fuzzy weighted averages and implementation of the extension principle |
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| Institution: | 1. SISSA, International School for Advanced Studies, Mathematics, via Bonomea 265, 34136 Trieste, Italy;2. MOX – Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy;1. Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-516 Zielona Góra, Poland;2. Department of Mathematics, Texas A&M University - Kingsville, Kingsville, TX 78363-8202, USA;3. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;1. Ministry of Health, Riyadh, Saudi Arabia;2. College of Medicine, Alfaisal University, Riyadh, Saudi Arabia;3. Atlanta, GA, USA;4. MES Academy of Medical Sciences, Kerala, India;5. Center for Vaccine Research, Bamako, Mali;6. Department of Emergency Medicine, College of Medicine, King Saud bin Abdulaziz University for Health Sciences, King Abdulaziz Medical City, Ministry of National Guard Health Affairs, Riyadh, Saudi Arabia;1. Ocean College of Minjiang University, Fuzhou 350108, China;2. Institute of Satellite Navigation and Spatial Information Engineering, Minjiang University, Fuzhou 350108, China;3. Research Center of Global Navigation Satellite System, Minjiang University & Fujian Xinghai Communication Technology Co., Ltd., Fuzhou 350008, China;1. Chevron, Area 52 Technology – ETC, 5 Bisbee Ct., Santa Fe, NM 87508, United States;2. LMA, CNRS, UPR 7051, Aix-Marseille University, Centrale Marseille, F-13402 Marseille Cedex 20, France;3. Physical Acoustics Group, Instituto de Física, Universidade Federal de Alagoas, Maceió, AL 57072-900, Brazil |
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| Abstract: | This paper addresses the computational aspect of the extension principle when the principle is applied to algebraic mappings and, in particular, to weighted average operations in risk and decision analysis. A computational algorithm based on the α-cut representation of fuzzy sets and interval analysis is described. The method provides a discrete but exact solution to extended algebraic operations in a very efficient and simple manner. Examples are given to illustrate the method and its relation to other discrete methods and the exact approach by non-linear programming. The algorithm has been implemented in a computer program which can handle very general extended algebraic operations on fuzzy numbers. |
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