Volume 8, no. 4Pages 14 - 29

Analyzing and Solving Problems of Decision Making with Parametric Fuzzy

M.G. Matveev
The method of solution of decision making problems presented as models with parameters in the form of LR fuzzy numbers is proposed. This methodic is based on using of alpha-level representation of fuzzy numbers, their subsequent modification by a convex linear transformation of the boundaries of alpha-intervals, preserving the basic characteristics of fuzziness, proposed algebra of modified fuzzy numbers and a convex linear combination of the boundaries of alpha-change interval. Bounded growth of uncertainty in fuzzy information processing, preservation of natural interpretation of intermediate and final results of calculations and the possibility of algorithm realization in software environments working with real numbers are the advantages of the proposed method. The usage of the alpha-level representation causes the problem of fuzzy solutions stability. We give the definition of stability for solutions in the form of a fuzzy point in tn-dimensional space and in the form of a fuzzy function. For several kinds of problems we give a stability criteria, which is easily verified in practical calculations. We have examples of solving the problems with parametric fuzziness using the proposed method, confirming the validity of the results.
Full text
Keywords
the models with parametric fuzziness; LR-fuzzy numbers; alpha-level representation; algebra of fuzzy numbers; stability of fuzzy solution.
References
1. Fuzzy Theory Systems: Techniques and Applicatons. Ed. by Cornelius T. Leondes. London, Academic Press, 1999. 1777 p.
2. Intelligent Systems for Information Processing: From Representation to Applications. Eds.
by Bouchon-Meunier B., Foulloy L., Yager R.R. Amsterdam, Elsevier, 2003. 488 p.
3. Hanss M. Applied Fazzy Arithmetic: An Introduction with Engineering Applications. Netherlands, Springer, 2005. 256 p.
4. Averkin A.N., Batyrshin I.Z., Blishun A.F. etc. Nechetkie mnozhestva v modelyakh upravleniya i iskusstvennogo intellekta [Fuzzy Sets in Management Models and Artificial Intelligence]. Moscow, Nauka, 1986. 312 p.
5. Borisov A.M., Krumberg O.A., Fedorov I.P Prinyatie resheniy na osnove nechetkikh modeley: primery ispol'zovaniya [Decision-Making Based on Fuzzy Models: Examples of Use]. Riga, Nauka, 1990. 184 p.
6. Piegat A. Fuzzy Modelling and Control. New York, Springer-Heidelberg, 2001. 371 p. DOI: 10.1007/978-3-7908-1824-6
7. Chen S.P., Hsueh Y.J. A Simple Approach to Fuzzy Critical Path Analysis in Project Networks. Applied Mathematical Modelling, 2008, vol. 32, pp. 1289-1297. DOI: 10.1016/j.apm.2007.04.009
8. Bekheet S.S., Mohammed A., Hefny H.A. An Enhanced Fuzzy Multi Criteria Decision Making Model with a Proposed Polygon Fuzzy Number. International Journal of Advanced Computer Science and Applications, 2014, vol. 5, no. 5, pp. 118-121. DOI: 10.14569/IJACSA.2014.050517
9. Vorontsov Y.A. Matveev M.G. Algebraic Operations with LR Fuzzy Numbers Using L Conversion. Software Engineering, 2014, no. 8, pp. 23-29. (in Russian)
10. Vorontsov Y.A. Matveev M.G. Arithmetic Operations on Two-Component Fuzzy Numbers. Proceedings of Voronezh State University. Series: System Analysis and Information Technologies, 2014, no. 2, pp. 75-82. (in Russian)
11. Ashmanov S.A. Lineynoe programmirovanie [Linear Programming]. Moscow, Nauka, 1981. 340 p.
12. Agayan G.M., Ryutin A.A., Tikhonov A.N. The Problem of Linear Programming with Approximate Data. USSR Computational Mathematics and Mathematical Physics, 1984, vol. 24, no. 5, pp. 14-19. DOI: 10.1016/0041-5553(84)90149-6