By Jagdeep Kaur, Amit Kumar

ISBN-10: 3319312731

ISBN-13: 9783319312736

ISBN-10: 331931274X

ISBN-13: 9783319312743

The publication offers a photo of the cutting-edge 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 the entire parameters and selection variables are represented through non-negative fuzzy numbers. It provides new tools built by way of the authors, in addition to current equipment constructed by way of others, and their software to real-world difficulties, together with fuzzy transportation difficulties. additionally, it compares the results of different tools and discusses their advantages/disadvantages. because the first paintings to gather at one position crucial tools for fixing fuzzy linear programming difficulties, the e-book represents an invaluable reference advisor for college students and researchers, offering them with the mandatory theoretical and sensible wisdom to accommodate linear programming difficulties below uncertainty.

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

**Sample text**

Fuzzy Sets Syst. 50, 247–255 (1992) 5. : Operations Research: An Introduction. Prentice-Hall, New Jersey (2003) Chapter 3 Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems with Equality Constrains In this chapter, the limitations of the method, presented in Chap. 2, are pointed out and to overcome these limitations, Kaur and Kumar’s method [1] is presented for solving fully fuzzy linear programming problems with equality constraints. To show the application of Kaur and Kumar’s method [1] a real life problem, which cannot be solved by using the method, presented in Chap.

M 2 +| ci j − ci j |) = h i ∀ i = 1, 2, . . , m 2 +| di j − di j |) = ki ∀ i = 1, 2, . . , m 2 y j − x j ≥ 0, z j − y j ≥ 0, w j − z j ≥ 0 ∀ j = 1, 2, . . 10) by using an appropriate existing method [2] to find the optimal solution {x ∗j , y ∗j , z ∗j , w ∗j }. 2) by putting the values of x ∗j , y ∗j , z ∗j and w ∗j in x˜ ∗j = (x ∗j , y ∗j , z ∗j , w ∗j ). Step 11 Find the fuzzy optimal value by putting the values of x˜ ∗j , obtained from Step n 10, in j=1 c˜ j ⊗ x˜ ∗j . 4 Illustrative Examples In this section, the method, presented in Sect.

2 Maximize ((−2, −1, 3, 6) ⊗ x˜1 ⊕ (2, 4, 6, 8) ⊗ x˜2 ) subject to (−3, 2, 5, 7) ⊗ x˜1 ⊕ (−2, −1, 5, 7) ⊗ x˜2 = (−42, −17, 45, 91) (1, 2, 3, 4) ⊗ x˜1 ⊕ (−4, −3, −2, −1) ⊗ x˜2 = (−48, −27, −4, 28) where x˜1 and x˜2 are unrestricted trapezoidal fuzzy numbers. , the method, presented in Chap. 2, cannot be used for solving such fully fuzzy linear programming problems with equality constraints in which all or some of the variables are represented by unrestricted fuzzy numbers. 2 Product of Unrestricted Trapezoidal Fuzzy Numbers In this section, the product of two unrestricted trapezoidal fuzzy numbers is presented [1].

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

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