Abstract
In this paper, a fully rough integer linear fractional programmingproblem is introduced, in which all coefficients and decision variablesin the objective function and the constraints are rough intervals. Theoptimal value of decision rough variables is rough interval. In order tosolve this problem, we will construct four crisp integer linear fractionalprogramming problems. Via these four crisp problems the roughoptimal integer solution is obtained. An illustrative numerical exampleis given for the developed theory.
Highlights
The main interest in fractional programming was generated by the fact that a lot of optimization problem from engineering, natural resources and economics require the optimization between physical and / or economic functions
The problems, where the objective function is a ratio of two linear functions subject to a set of linear constraints and nonnegative integer variables constitute an integer linear fractional programming problem
Hamazehee et al [8] introduced a new class of Linear Programming (LP) problems in which some or all of the coefficients are rough intervals and showed that each one of them can be transformed into two LP problems with interval coefficients
Summary
The main interest in fractional programming was generated by the fact that a lot of optimization problem from engineering, natural resources and economics require the optimization between physical and / or economic functions. Borza et al [3]proposed the method to solve linear fractional programming problem with interval coefficients in objective function. Jayalakshmi and Pandian, Proposed a new Article title method namely, denominator objective restriction method for finding an optimal solution to linear fractional programming problems [4]. [9] introduced a rough linear fractional programming problem They are considered a rough interval in the objective function coefficient. Emam et al [10] presented a solution of fully rough three level large scaler linear programming problem, in which all decision parameters and decision variables in the objective functions and the constraints are rough intervals. Algorithm for solving fuzzy rough linear fractional programming problems (FRLFP) is introduced, All the variables and coefficients of the objective function and constraints are fuzzy rough number [11]. A Large-Scale three level fractional problem is introduced with random rough coefficient in the objective function in [12]
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