A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers

Abstract

In this paper, an efficient method is introduced to solve fully fuzzy linear programming problems. The proposed method is derived from the multi-objective linear programming problem and lexicographic ordering method. Theoretical analysis for the proposed method has been provided. Moreover, some numerical experiments are given to show the preference of the proposed methods and are compared with some available methods.

An epsilon‐constraint method for fully fuzzy multiobjective linear programming

“…To make this property hold for the fuzzy case, it is necessary that the order relation ≼ establish a complete order on R ( ). To this aim, several authors, for example, 11,17,[24][25][26][27][28] have defined the order relation ≼ lexicographically by using a set of three or four ranking indices, guaranteeing to meet at least properties 1 to 4. However, in the existing methods, such an order relation has been used only to compare objective function values, mostly in FFLP problems having only equality constraints.…”

“…To handle fuzzy inequality constraints, some authors suggest to transform them into equalities by introducing nonnegative fuzzy slack and surplus variables 7,11,29,30 ; this is, however, incorrect as shown by Bhardwaj and Kumar 31 and Gupta et al 32 Other authors, for example, 6,8,14,26,33 use a partial order to handle the fuzzy inequality constraints and a linear ranking function or lexicographic ranking criterion with the objective function. Thus, it can be observed that, for both approaches in the literature, two different order relations are used for the inequality of fuzzy numbers in the same problem.…”

“…Data of fully fuzzy multiobjective project crashing problem (E3) t 78 (0, 0, 0) LR (0, 0, 0) LR (0, 0, 0) LR (0, 0, 2) LR t 89 (7, 3.00, 8) LR (7, 4.6, 8) LR (7, 3.6, 9) LR (7, 3, 2) LR t 1 (0, 0, 0) LR (0, 0, 0) LR (0, 0, 0) LR (0, 0, 0) LR t 2 (7, 0, 2) LR (7, 0, 2) LR (7, 0, 2) LR (7, 0, 1.6) LR , we obtain t = (0, 0, 0) ij LR for all (i, j) ∈ A; hence no crashing cost and no CO 2 emission. Event times are as follows: t t t t = (0, 0, 0) ,˜= (12,2,4) ,˜= (26,5,7) ,˜= (28,0,11) , (27,4,6) ,˜= (43,7,10) ,˜= (46,2,13) LR LR LR 5 6 7 , and t = (62, 9, 12) LR 8 , with project completion time t = (77, 14, 15) LR 9 . However, on solving FFMOPC problem (E3) by using the proposed fuzzy epsilon-constraint method, we obtain another solution t = (0, 0, 0)…”

A Fully Fuzzy Linear Programming Model to the Berth Allocation Problem

“…When the parameters and decision variables are fuzzy, the problem is formulated as a Fully Fuzzy Lineal Programming Problem (FFLP). There are many methodologies of solution to a FFLP [12]. Mostly of them, convert the original fuzzy model in a classical satisfactory model.…”

A new interactive approach for solving fully fuzzy mixed integer linear programming

“…An algorithm to solve the FFLP problem based on a new lexicographic ordering on triangular fuzzy numbers is suggested by Ezzati et al [17]. An efficient method to solve FFLP is introduced by Das et al [18]. Some well-known approaches for solving FLP problems is reviewed by Skandari and Ghaznavi [19] and some of their difficulties is shown by some numerical examples.…”