By Jagdeep Kaur, Amit Kumar
The booklet provides a image of the state-of-the-art within the box of absolutely fuzzy linear programming. the focus is on exhibiting present tools for locating the bushy optimum answer of absolutely fuzzy linear programming difficulties within which all of the parameters and choice variables are represented through non-negative fuzzy numbers. It provides new equipment constructed by way of the authors, in addition to current tools built via others, and their program to real-world difficulties, together with fuzzy transportation difficulties. additionally, 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 booklet represents an invaluable reference advisor for college students and researchers, offering them with the required theoretical and useful wisdom to house linear programming difficulties less than uncertainty.
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Extra info for An Introduction to Fuzzy Linear Programming Problems: Theory, Methods and Applications
2, are pointed out and to overcome these limitations, Kaur and Kumar’s method  is presented for solving fully fuzzy linear programming problems with equality constraints. To show the application of Kaur and Kumar’s method  a real life problem, which cannot be solved by using the method, presented in Chap. 2, is solved by using the Kaur and Kumar’s method . 1 Limitations of the Previous Presented Method The method, presented in Chap. 2, can be used to find the exact fuzzy optimal solution of the following type of problems: (i) Fully fuzzy linear programming problems with equality constraints having nonnegative fuzzy coefficients and non-negative fuzzy variables.
5, over the existing method  are discussed. ’s method, presented in Sect. 5, as compared to the existing method . ’s method, presented in Sect. 5, exactly satisfy the constraints of the fully fuzzy linear programming problems. 9). ’s method, presented in Sect. 9). ’s method, presented in Sect. 1. 2, all the coefficients are not non-negative triangular fuzzy numbers. So, due to the limitations of the existing method , discussed in Sect. 1, none of these problems can be solved by using the existing method .
8) 2 qj + qj 2 −| qj − qj 2 |, |) |) = bi ∀ i = 1, 2, . . 9) |) = gi ∀ i = 1, 2, . . , 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, .