Fuzzy Set Theory and Mathematical Programming

Mathematical programming is one of the areas to which fuzzy set theory has been applied extensively. Primarily based on Bellman and Zadeh’s model of decision in fuzzy environments, models have been suggested which allow flexibility in constraints and fuzziness in the objective function in linear and nonlinear programming. This paper surveys major models and theories in this area and offers some indication on future developments.

[1]  M. K. Luhandjula.  Linear programming under randomness and fuzziness , 1983 .

[2]  H. Zimmermann,et al.  Sensitivity analysis in fuzzy linear programming , 1978 .

[3]  F. Behringer.  A simplex based algorithm for the lexicographically extended linear maxmin problem , 1981 .

[4]  Hideo Tanaka,et al.  On Fuzzy-Mathematical Programming , 1973 .

[5]  Michael Wagenknecht,et al.  On fuzzy rank-ordering in polyoptimization , 1983 .

[6]  Fred Alois Behringer,et al.  Lexicographic quasiconcave multiobjective programming , 1977, Math. Methods Oper. Res..

[7]  H. Zimmermann,et al.  Duality in Fuzzy Linear Programming , 1980 .

[8]  Brigitte Werners.  Interaktive Entscheidungsunterstützung durch ein flexibles mathematisches Programmierungssystem , 1984 .

[9]  H. Leberling.  On finding compromise solutions in multicriteria problems using the fuzzy min-operator , 1981 .

[10]  S. A. Orlovsky,et al.  ON PROGRAMMING WITH FUZZY CONSTRAINT SETS , 1977 .

[11]  E. Hannan.  Linear programming with multiple fuzzy goals , 1981 .

[12]  H. Zimmermann,et al.  Latent connectives in human decision making , 1980 .

[13]  W. Ostasiewicz.  A new approach to fuzzy programming , 1982 .

[14]  S. Chanas.  The use of parametric programming in fuzzy linear programming , 1983 .

[15]  H. Zimmermann,et al.  On the suitability of minimum and product operators for the intersection of fuzzy sets , 1979 .

[16]  H. Zimmermann,et al.  Decisions and evaluations by hierarchical aggregation of information , 1983 .

[17]  M. K. Luhandjula.  Fuzzy approaches for multiple objective linear fractional optimization , 1984 .

[18]  H. Zimmermann.  Fuzzy programming and linear programming with several objective functions , 1978 .

[19]  Hans-Jürgen Zimmermann,et al.  Analyse, Beschreibung und Optimierung von unscharf formulierten Problemen , 1977, Math. Methods Oper. Res..

[20]  H. Zimmermann.  DESCRIPTION AND OPTIMIZATION OF FUZZY SYSTEMS , 1975 .

[21]  K. Tanaka,et al.  FUZZY PROGRAMS AND THEIR EXECUTION , 1975 .

[22]  T. Pavlidis,et al.  Fuzzy sets and their applications to cognitive and decision processes , 1977 .

[23]  K. Asai,et al.  Fuzzy linear programming problems with fuzzy numbers , 1984 .

[24]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[25]  R. Narasimhan,et al.  Fuzzy goal programming with nested priorities , 1984 .

[26]  C. L. Chang,et al.  INTERPRETATION AND EXECUTION OF FUZZY PROGRAMS , 1975 .

[27]  J. Verdegay.  A dual approach to solve the fuzzy linear programming problem , 1984 .