Optimal way of selecting cities and conveyances for supplying coal in uncertain environment

Abstract

In this paper, the limitations and shortcomings of the existing methods for solving fuzzy solid transportation problem are pointed out and to overcome these shortcomings, a new method is proposed for solving fuzzy solid transportation problem. The advantages of the proposed method over the existing methods are discussed. To illustrate the proposed method, an existing fuzzy solid transportation problem is solved. Also, to show the application of the proposed method in real life problems an existing real life fuzzy solid transportation problem is solved by the proposed method. Keywords. Fuzzy solid transportation problem; ranking function;LR flat fuzzy number.Fuzzy solid transportation problem 167 If m = n then A = (m, n, α, β) LR will be converted into A = (m, α, β) LR and is said to be LR fuzzy number. L and R are called reference functions, which are continuous, non-increasing functions that defines the left and right shapes of μ A (x), respectively and L(0) = R(0) = 1.If L(x) = R(x) = maximum {0, 1 − x} then an LR flat fuzzy number (m, n, α, β) LR and an LR fuzzy number (m, α, β) LR are said to be trapezoidal and triangular fuzzy numbers and denoted by (m, n, α, β) and (m, α, β), respectively. A = (m, n, α, β) LR be an LR flat fuzzy number and λ be a real number in the interval [0, 1] then the crisp set Definition 2 (Dubois & Prade 1980). LetDefinition 3 (Dubois & Prade 1980). An LR flat fuzzy numberà = (m, n, α, β) LR is said to be zero LR flat fuzzy number if and only if m = 0, n = 0, α = 0, β = 0.Definition 4 (Dubois & Prade 1980). Two LR flat fuzzy numbersà 1 = (m 1 , n 1 , α 1 , β 1 ) LR and A 2 = (m 2 , n 2 , α 2 , β 2 ) LR are said to be equal i.e.,à 1 =à 2 if and only if m 1 = m 2 , n 1 = n 2 , α 1 = α 2 , β 1 = β 2 .Definition 5 (Dehghan et al 2006). An LR flat fuzzy numberà = (m, n, α, β) LR is said to be non-negative LR flat fuzzy number if m − α ≥ 0.Remark 1. If m = n then an LR flat fuzzy number (m, n, α, β) LR is said to be an LR fuzzy number and is denoted as (m, m, α, β) LR or (n, n, α, β) LR or (m, α, β) LR or (n, α, β) LR .

Uncertain multi-objective multi-product solid transportation problems

“…This method is also applicable to the problems considered in Gen et al [25], [10,[20][21][22][23]. We have also solved the examples in Kumar and Kaur [19] by the method proposed by us. The results obtained are same as shown in table 6.…”

“…The obtained results are thus real numbers, while the method proposed in this paper provides the fuzzy optimal compromise solution. (ii) Kumar and Kaur [19] pointed out the limitations of existing methods [10,[20][21][22][23]25] and the shortcomings of the method proposed by Liu [24] to solve the single and multi-objective solid transportation problems. To overcome these limitations and resolve the shortcomings, they have proposed a method to obtain the fuzzy optimal solution of the fuzzy solid transportation problem.…”

“…w 0 À v 0 and a À w ! a 0 À w 0 is met and so according to Subcase 2b of Step 2, we introduce a dummy conveyance having capacity e e 3 = (9,19,27,39…”

On Fuzzy Multiobjective Multi-Item Solid Transportation Problem

“…Baidya et al have discussed the multi-item interval valued solid transportation problem in [16,17]. A method to solve multiobjective solid transportation problems in uncertain environment has been presented in [18]. Kundu et al [19,20] have proposed methods to solve fuzzy MOMISTP.…”