By Jagdeep Kaur, Amit Kumar

ISBN-10: 3319312731

ISBN-13: 9783319312736

ISBN-10: 331931274X

ISBN-13: 9783319312743

The e-book provides a image of the cutting-edge within the box of absolutely fuzzy linear programming. the main target is on exhibiting present equipment for locating the bushy optimum answer of absolutely fuzzy linear programming difficulties within which all of the parameters and determination variables are represented through non-negative fuzzy numbers. It provides new equipment built through the authors, in addition to latest equipment built by means of others, and their program to real-world difficulties, together with fuzzy transportation difficulties. furthermore, it compares the results of the several equipment and discusses their advantages/disadvantages. because the first paintings to assemble at one position an important tools for fixing fuzzy linear programming difficulties, the ebook represents an invaluable reference consultant for college students and researchers, offering them with the mandatory theoretical and sensible wisdom to house linear programming difficulties below uncertainty.

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2, the fully fuzzy linear programming problem, obtained in Step 1, can be written as: Maximize ((min{−2w1 , 6x1 }, min{−z 1 , 3y1 }, max{−y1 , 3z 1 }, max{−2x1 , 6w1 }) ⊕ (min{ 2x2 , 8x2 }, min{4y2 , 6y2 }, max{4z 2 , 6z 2 }, max{2w2 , 8w2 })) subject to (min{−3w1 , 7x1 }, min{2y1 , 5y1 }, max{2z 1 , 5z 1 }, max{7w1 , −3x1 }) ⊕ (min{−2w2 , 7x2 }, min{−z 2 , 5y2 }, max{−y2 , 5z 2 }, max{−2x2 , 7w2 }) = (−42, −17, 45, 91) (min{x1 , 4x1 }, min{2y1 , 3y1 }, max{2z 1 , 3z 1 }, max{w1 , 4w1 }) ⊕ (min{−4w2 , −w2 }, min{ − 3z 2 , −2z 2 }, max{−3y2 , −2y2 }, max{−4x2 , −x2 }) = (−48, −27, −4, 28) y1 − x1 ≥ 0, z 1 − y1 ≥ 0, w1 − z 1 ≥ 0 y2 − x2 ≥ 0, z 2 − y2 ≥ 0, w2 − z 2 ≥ 0 Step 3 Using the arithmetic operations, defined in Sect.

4 Product of a Non-negative Trapezoidal Fuzzy Number with Unrestricted Trapezoidal Fuzzy Number For solving the fully fuzzy linear programming problems, there is a need to find the product of fuzzy coefficients and fuzzy variables. Since, in the fully fuzzy linear programming problems, the fuzzy coefficients are known and the product of fuzzy numbers depends upon the nature of fuzzy numbers. So, in this section, on the basis of nature of fuzzy coefficients product, proposed by Kumar et al. [2], with the help of existing product of two fuzzy numbers [3], is presented.

12): n (pj , qj , rj , sj ) ⊗ (xj , yj , zj , wj ) Maximize/Minimize j=1 subject to n aij = bi ∀ i = 1, 2, . . , m j=1 n bij = gi ∀ i = 1, 2, . . 12) j=1 n cij = hi ∀ i = 1, 2, . . , m j=1 n dij = ki ∀ i = 1, 2, . . , m j=1 xj ≥ 0, yj − xj ≥ 0, zj − yj ≥ 0, wj − zj ≥ 0 ∀ j = 1, 2, . . , our aim is to find max (or min){ 1≤t≤l n j=1 (pj , qj , rj , sj ) ⊗ (xjt , yjt , zjt , wjt )}. ’s Method to Find the Non-negative Fuzzy Optimal … 25 n Maximize/Minimize ( (pj , qj , rj , sj ) ⊗ (xj , yj , zj , wj )) j=1 subject to n aij = bi ∀ i = 1, 2, .

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An Introduction to Fuzzy Linear Programming Problems: Theory, Methods and Applications by Jagdeep Kaur, Amit Kumar


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