Solving fuzzy linear programming problems with linear membership functions

Gasimov R. N., YENİLMEZ K.

Turkish Journal of Mathematics, cilt.26, sa.4, ss.375-396, 2002 (Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 26 Sayı: 4
  • Basım Tarihi: 2002
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.375-396
  • Anahtar Kelimeler: Fuzzy decisive set method, Fuzzy linear programming, Fuzzy number, Modified subgradient method
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

In this paper, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy technological coefficients and linear programming problems in which both the right-hand side and the technological coefficients are fuzzy numbers. We consider here only the case of fuzzy numbers with linear membership functions. The symmetric method of Bellman and Zadeh [2] is used for a defuzzification of these problems. The crisp problems obtained after the defuzzification are non-linear and even non-convex in general. We propose here the "modified subgradient method" and use it for solving these problems. We also compare the new proposed method with well known "fuzzy decisive set method". Finally, we give illustrative examples and their numerical solutions. © TÜBİTAK.