Operations Research

Download An Introduction to Fuzzy Linear Programming Problems: by Jagdeep Kaur, Amit Kumar PDF

By Jagdeep Kaur, Amit Kumar

The publication offers a image of the state-of-the-art within the box of absolutely fuzzy linear programming. the main target is on displaying present equipment for locating the bushy optimum resolution of totally fuzzy linear programming difficulties within which all of the parameters and determination variables are represented by way of non-negative fuzzy numbers. It provides new equipment built by means of the authors, in addition to present tools built by way of others, and their software to real-world difficulties, together with fuzzy transportation difficulties. furthermore, it compares the results of the several tools and discusses their advantages/disadvantages. because the first paintings to assemble at one position an important equipment for fixing fuzzy linear programming difficulties, the e-book represents an invaluable reference consultant for college kids and researchers, supplying them with the required theoretical and functional wisdom to accommodate linear programming difficulties less than uncertainty.

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Additional info for An Introduction to Fuzzy Linear Programming Problems: Theory, Methods and Applications

Sample text

1, which can be solved by using the method, presented in Chap. 2, is also solved by using the method, presented in Sect. 3. 2, are solved by using the method, presented in Sect. 3. 1, can be written as: Maximize ((1, 2, 3, 4) ⊗ (x1 , y1 , z 1 , w1 ) ⊕ (2, 4, 6, 8) ⊗ (x2 , y2 , z 2 , w2 )) subject to (0, 1, 2, 3) ⊗ (x1 , y1 , z 1 , w1 ) ⊕ (1, 3, 5, 7) ⊗ (x2 , y2 , z 2 , w2 ) = (−8, 2, 27, 57) (2, 4, 7, 9) ⊗ (x1 , y1 , z 1 , w1 ) ⊕ (2, 3, 5, 6) ⊗ (x2 , y2 , z 2 , w2 ) = (−25, −8, 34, 81) where (x1 , y1 , z 1 , w1 ) and (x2 , y2 , z 2 , w2 ) are unrestricted fuzzy numbers.

M |) = h i ∀ i = 1, 2, . . , m |) = ki ∀ i = 1, 2, . . , m y j − x j ≥ 0, z j − y j ≥ 0, w j − z j ≥ 0 ∀ j = 1, 2, . . 10): Maximize/Minimize 1 ( 4 n ( j=1 pj − pj qj + qj qj − qj pj + pj −| |+ −| |+ 2 2 2 2 rj −rj sj + sj sj − sj rj +rj +| |+ +| |)) 2 2 2 2 subject to n ( ai j − ai j ai j + ai j −| |) = bi ∀ i = 1, 2, . . , m 2 2 j=1 n b +b ij ij ( 2 j=1 n c +c ij ij ( 2 j=1 n d +d ij ij ( j=1 2 −| bi j − bi j |) = gi ∀ i = 1, 2, . . , m 2 +| ci j − ci j |) = h i ∀ i = 1, 2, . . , m 2 +| di j − di j |) = ki ∀ i = 1, 2, .

M j=1 where c˜ j , x˜ j , a˜ ij and b˜ i are non-negative triangular fuzzy numbers. 2) n (aij , bij , cij ) ⊗ (xj , yj , zj ) = (bi , gi , hi ) ∀ i = 1, 2, . . , m j=1 where (xj , yj , zj ) is a non-negative triangular fuzzy number. 3): n [pj + (qj − pj )λ, rj − (rj − qj )λ][xj + (yj − xj )λ, zj − (zj − yj )λ] Maximize j=1 subject to n [aij + (bij − aij )λ, cij − (cij − bij )λ][xj + (yj − xj )λ, zj − (zj − yj )λ] j=1 = [bi + (gi − bi )λ, hi − (hi − gi )λ] ∀ i = 1, 2, . . , m xj ≥ 0, yj − xj ≥ 0, zj − yj ≥ 0 ∀ j = 1, 2, .

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