Multi-criteria optimization in terms of fuzzy criteria definitions

The problems of multi-criteria optimization are considered. Known methods for solving these problems are generalized to the case when weights that take into account the relative importance of particular criteria are not clearly defined. The procedure for constructing membership functions of fuzzy numbers, given by sets of intervals of possible values, using a linearized computation of least squares methods is substantiated. In this case, for the description of fuzzy numbers, the membership functions of (L-R)-type were chosen.

multi-criteria optimization
fuzzy source data
optimization of a fractional non-linear functional
Pareto-set.
  1. Saaty T. L. Mathematical Methods of Operations Research. McGraw-Hill (1959).
  2. Seraja O. V. Mnogomernye modeli logistiki v uslovijah neopredelennosti. Harkiv, FOP Stecenko (2010), (in Russian).
  3. Zadeh L. A. Fuzzy Sets. Information and Control. 8 (3), 338–353 (1965).
  4. Kaufmann A. Introduction a la théorie des sous-ensembles flous. Paris, New York, Barcelone, Milan, MASSON (1977), (in French).
  5. Raskin L. G., Seraja O. V. Nechetkaja matematika. Osnovy teorii. Prilozhenija. Harkiv, Parus (2008), (in Russian).
  6. Ventcel E. S. Teorija verojatnostej : uchebnik. Moskva, KNORUS (2010), (in Russian).
  7. Dubois D., Prade H. Théorie des possibilités. Applications à la représentation des connaissances en informatique. Paris, Milan, Barcelona, Mexico, MASSON (1988), (in French).
  8. Leonenkov A.V. Nechetkoe modelirovanie v srede MATLAB i fuzzyTECH. SPb., BHV-Peterburg (2005), (in Russian).
  9. Dantzig G.B. Linear programming and extensions. Princeton, New Jersey, PRINCETON UNIVERSITY PRESS (1963).
  10. Yudin D. B., Golshtejn E. G. Linejnoe programmirovanie: teorija, metody i prilozhenija. Moskva, Nauka (1969), (in Rusiian).
  11. Liu B. Theory and Practice of Uncertain Programming. Heidelberg, Physica-Verlag (2002).
  12. Pawlak Z. Rough Sets and Fuzzy Sets. Fuzzy Sets and Systems. 17 (1), 99–102 (1985).
  13. Raskin L., Sira O. Fuzzy models of rough mathematics. Eastern-European Journal of Enterprise Technologies. 6 (4), 53–60 (2016), (in Russian).
  14. Sira O. V., Al-Shqeerat K. H. A New Approach for Resolving Equations with Fuzzy Parameters. European Journal of Scientific Research. 38 (4), 619–625 (2009).
  15. Raskin L., Sira O. Method of solving fuzzy problems of mathematical programming. Eastern-European Journal of Enterprise Technologies. 5 (4), 23–28 (2016), (in Russian).