By Jagdeep Kaur, Amit Kumar

ISBN-10: 3319312731

ISBN-13: 9783319312736

ISBN-10: 331931274X

ISBN-13: 9783319312743

The publication offers a image of the cutting-edge within the box of absolutely fuzzy linear programming. the focus is on displaying present equipment for locating the bushy optimum resolution of absolutely fuzzy linear programming difficulties during which all of the parameters and selection variables are represented by way of non-negative fuzzy numbers. It offers new equipment built by way of the authors, in addition to current tools constructed by way of others, and their software to real-world difficulties, together with fuzzy transportation difficulties. additionally, it compares the results of the various tools and discusses their advantages/disadvantages. because the first paintings to gather at one position an important tools for fixing fuzzy linear programming difficulties, the booklet represents an invaluable reference consultant for college students and researchers, offering them with the required theoretical and sensible wisdom to accommodate linear programming difficulties lower than uncertainty.

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

**Example text**

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 n min{bi j , bi j } = gi ∀ i = 1, 2, . . 5) j=1 n max{ci j , ci j } = h i ∀ i = 1, 2, . . , m j=1 n max{di j , di j } = ki ∀ i = 1, 2, . . , m j=1 y j − x j ≥ 0, z j − y j ≥ 0, w j − z j ≥ 0 ∀ j = 1, 2, . . , n Step 4 As discussed in Step 4 of Sect. 6): n ( p j , q j , r j , s j ) ⊗ (x j , y j , z j , w j )) Maximize/Minimize ( j=1 subject to n min{ai j , ai j } = bi ∀ i = 1, 2, . . , m j=1 n min{bi j , bi j } = gi ∀ i = 1, 2, . . , m j=1 n max{ci j , ci j } = h i ∀ i = 1, 2, .

1, cannot be solved by any of the existing methods. Although, the uncapacitated fully fuzzy transportation problem can be solved by using the tabular method [3]. , there is no tabular method in the literature to solve the crisp capacitated minimal cost flow problems which can be extended to propose a new method for solving fully fuzzy capacitated minimal cost flow problems but such problems can be formulated as a fuzzy linear programming problem and then can be solved by using the proposed method.

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

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