Download e-book for iPad: Fuzzy and Multi-Level Decision Making: An Interactive by E. Stanley Lee

By E. Stanley Lee

ISBN-10: 1447106830

ISBN-13: 9781447106838

ISBN-10: 144711177X

ISBN-13: 9781447111771

Managerial judgements in hierarchy corporations, resembling some of the production and repair businesses, are tricky to formalize or even more challenging to optimize. through exploring the common fuzziness, vagueness, or the "not-well-defined" nature of such corporations, this booklet provides the 1st finished therapy of this hard and virtually very important challenge. the benefits of the proposed fuzzy interactive method are that it considerably reduces computational requisites. both, the illustration of the process is made extra reasonable in the course of the reputation of the inherent fuzziness of such huge companies. either the multi-ploy and the game-like determination making approaches, sometimes called multi-level programming and the bushy interactive method, are mentioned intimately. The emphasis is on numerical algorithms and various examples are solved and in comparison. The suggestions of fuzzy set and fuzzy linguistic illustration, which shape an essential component of any managerial determination, also are discussed.

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Additional resources for Fuzzy and Multi-Level Decision Making: An Interactive Computational Approach

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7. In the following discussions, we follow the solution obtained by Anandalingam and White [1990]. where X 2 solves: subject to: -xl-2x2~-10 xl-2x2~6 2x1-X2~21 Xl + 2x2 ~ 38 ° -xl+2x2~18 Xl,X2~ For simplicity, X will be used to denote the above constraint set. The dual constraints of the lower-level problem are: W=(WI> w 2, w3 , w4 , w s? 2W2 0, i = 1, ... ,5 = - 2Wl Wi ~ W3 + 2W4 + 2ws ~ - 3 The solution procedure proceeds as follows [Anandalingam and White 1990]: Iteration 1. Step o. 1. Step 1.

5. 2). We also solved the problem with M = 100,000, 1,000,000, 10,000,000, and 100,000,000, the solution remains the same. The solution is quite stable and is different from that obtained by the fCI'-best approach, whose solution optimum was at point C. It appears that the upper-level DM dominates the solution for this particular case. Because of the introduction of the zero-one integer variables, 11, this mixedinteger programming problem is not easy to solve. This is especially true for practical problems, which are usually large and complex.

The basic idea is to add every objective of lower-level agent to the objective of upper level so that the problem becomes: subject to: b, k= 1,2 and i = 1,2, ... , sir /= 1,2, ... ,p w/;;::0,1=1,2, ... ,p xj ;;:: 0, j = 1, 2, ... iA/dX/d $; w/ A/;;::c211, 54 Fuzzy and Multi-level Decision Making where K is a large positive constant, j = 1, 2, ... , n represents the jth decision variable, andxj for j = 2,3, ... , n are decisions of the p divisions in the lower level. Notice again that n-l = p. Let the vectors X and W; represent the primal feasible region and the dual feasible region, respectively.

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Fuzzy and Multi-Level Decision Making: An Interactive Computational Approach by E. Stanley Lee

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