Duality Theory in Fuzzy Mathematical Programming Problems with Fuzzy Coefficients
نویسنده
چکیده
Abstract In this paper, the notions of subgradmnt, subdifferentla[, and differential with respect to convex fuzzy mappings are investigated, whmh provides the basis for the fuzzy extremum problem theory We consider the problems of minimizing or maximizing a convex fuzzy mapping over a convex set and develop the necessary and/or sufficient optlmahty conditions. Furthermore, the concept of saddle-points and mimmax theorems under fuzzy environment is discussed The results obtained are used to formulate the Lagranglan dual of fuzzy programming. Under certain fuzzy convexity assumptions, KKT conditions for fuzzy programming are derived, and the "perturbed" convex fuzzy programming is considered Finally, these results are applied to fuzzy linear programming and fuzzy quadratic programming. (~) 2005 Elsevmr Ltd All rights reserved.
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