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

By E. Stanley Lee

Managerial judgements in hierarchy firms, comparable to a few of the production and repair businesses, are tricky to formalize or even tougher to optimize. via exploring the common fuzziness, vagueness, or the "not-well-defined" nature of such organisations, this ebook provides the 1st finished therapy of this hard and essentially vital challenge. some great benefits of the proposed fuzzy interactive technique are that it considerably reduces computational specifications. both, the illustration of the method is made extra sensible throughout the acceptance of the inherent fuzziness of such huge businesses. either the multi-ploy and the game-like selection making strategies, often referred to as 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 ideas of fuzzy set and fuzzy linguistic illustration, which shape an essential component of any managerial selection, also are discussed.

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

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Decreases. The global optimum is obtained at the fIrst feasible point. 75, -1) for the upper and the lower levels, respectively. For purpose of illustration, the computation is continued until 'A' is reduced to zero. 3. 2. 5, 8) f.. 4. ) fcd'-best (Bialas and Karwan) Grid search Problem size (n, n" m) (6,3,7) (10,10,6) (30,20,25) (6,3,7) (10,10,16) (30,2025) (6,3,7) (10,10,16) (30,20,25) (6,3,7) (10,10,16) (3020,25) (6,3,7) (10,10,16) (30,20,25) Average CPU time 77 136 215 34 80 194 . 6 parametrically and to terminate when the fIrst feasible point is reached.

Then for all k such that rk E R, compute: Linear Bi-Ievel Programming 39 IfZoPt~ ZL* - maxk 1[", go to Step 13. Otherwise, go to the next step. Step 7. Second direct feasibility test. If LR is infeasible, go to Step 13. Step 8. First conditional optimality test. Consider again LR with the penalty PiFor all i such that If Zopt ~ h * - Pi' fIx aj at 0 and update R. Step 9. Third direct optimality test. If R contains a relation r k such that a j = 0 for jEI", go to Step 13. Step 1O. Relational optimality test.

Thus, we have: 24 Fuzzy and Multi-level Decision Making where M is a very large positive constant. 5, the non-linear term disappeared and is replaced by two linear inequalities. 8 is a mixed-integer problem. 1 is again solved by this mixed-integer approach in the following. 3. 1 becomes: subject to: 3xI - 5x2 S; 15 3xI -X2 S 21 3xI +X2 s27 3xI +4x2 S45 +3x2 S 30 - 3x I + 5x2 + 15 S M11IY WI S (1- 111)M - 3x I + X2 + 21 SM112, W2 S (1- 112)M - 3xI - x2 + 27 S M113' W3 S (1- 113)M - 3x I - 4X2 + 45 S M114' W 4 S (1- 114)M - XI - 3x2 + 30 S M11s, Ws S (1- 11s)M - 5w I - W 2 + W3 t 4W4 + 3ws = 2 111,112,113,114,115 E {O, I} WI> W2, W3, W4,WS, XI' X2 ~ 0 XI Again, M is a very large positive constant.

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