Bocharnikov, Victor and Sveshnikov, Sergey (2007): Algorithm of arithmetical operations with fuzzy numerical data.

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Abstract
In this article the theoretical generalization for representation of arithmetic operations with fuzzy numbers is considered. Fuzzy numbers are generalized by means of fuzzy measures. On the basis of this generalization the new algorithm of fuzzy arithmetic which uses a principle of entropy maximum is created. As example, the summation of two fuzzy numbers is considered. The algorithm is realized in the software "Fuzzy for Microsoft Excel".
Item Type:  MPRA Paper 

Original Title:  Algorithm of arithmetical operations with fuzzy numerical data 
English Title:  Algorithm of arithmetical operations with fuzzy numerical data 
Language:  English 
Keywords:  fuzzy measure (Sugeno), fuzzy integral (Sugeno), fuzzy numbers; arithmetical operations; principle of entropy maximum 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63  Computational Techniques; Simulation Modeling C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods 
Item ID:  17353 
Depositing User:  Sveshnikov 
Date Deposited:  16. Jun 2010 19:14 
Last Modified:  14. Feb 2013 20:42 
References:  1. D. Dubois, H. Prade, Operations on fuzzy numbers, Internat. J. Systems Sci. 9 (1978) 613–626. 2. T. Allahviranloo, M. Adabitabar Firozja, Trapezoidal approximation of fuzzy numbers, Fuzzy Sets and Systems, 158 (2007) 755756. 3. Przemysław Grzegorzewski, Edyta Mrуwka, Trapezoidal approximations of fuzzy numbers  revisited, Fuzzy Sets and Systems 158 (2007) 757768. 4. Changjiu Zhou, Fuzzyarithmeticbased Lyapunov synthesis in the design of stable fuzzy controllers: a computingwithwords approach, Appl. Math. Comput. Sci., 2002, Vol.12, No.3, 411421. 5. Witold Kosin'ski, On fuzzy number calculus, Appl. Math. Comput. Sci., 2006, Vol. 16, No. 1, 5157. 6. Michael Hanss, Kai Willner, On using fuzzy arithmetic to solve problems with uncertain model parameters, Institute of Mechanics University of Stuttgart, 2007. 7. Hartwig Jeschke, How Does Fuzzy Arithmetic Work?, Institut für Mikroelektronische Schaltungen und Systeme Universität Hannover, 2001. 8. Cedric Lesage, Discounted cashflows analysis: An interactive fuzzy arithmetic approach, European Journal of Economic and Social Systems 15 No 2 (2001) 4968. 9. F. J. RuizSánchez, J. C. CheangWong, A. CrespoSosa, A simple application of fuzzy arithmetic to automate the alignment of a crystal in channelling experiments, International Conference on Accelerator and Large Experimental Physics Control Systems, 1999, Trieste, Italy. 10. Luciano Stefanini, Laerte Sorini, An LUfuzzy Calculator for the Basic Fuzzy Calculus, Faculty of Economics, University of Urbino "Carlo Bo", 2007. 11. Pospelov D., Fuzzy sets in the models of control and artificial intelligence. Moscow, 1986.  [in Russian]. 12. D. Dubois, H. Prade, Possibility Theory. An approach to Computerized Processing of Uncertainty, Plenum Press, New York, (1988). 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/17353 