A parametric approach to fuzzy multi-objective linear fractional program: An alpha cut based method

2021 ◽  
pp. 1-14
Author(s):  
Mojtaba Borza ◽  
Azmin Sham Rambely
Keyword(s):  
Programming Problem ◽  
Efficient Solution ◽  
Fuzzy Numbers ◽  
Parametric Approach ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Multi Objective Programming ◽  
Linear Fractional Program ◽  
Interval Valued ◽  
Linear Fractional Programming Problem

In the multi-objective programming problem (MOPP), finding an efficient solution is challenging and partially encompasses some difficulties in practice. This paper presents an approach to address the multi-objective linear fractional programing problem with fuzzy coefficients (FMOLFPP). In the method, at first, the concept of α - cuts is used to change the fuzzy numbers into intervals. Therefore, the fuzzy problem is further changed into an interval-valued linear fractional programming problem (IVLFPP). Afterward, this problem is transformed into a linear programming problem (LPP) using a parametric approach and the weighted sum method. It is proven that the solution resulted from the LPP is at least a weakly ɛ - efficient solution. Two examples are given to illustrate the method.

scholarly journals A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

2017 ◽  
Vol 27 (3) ◽  
pp. 563-573 ◽  
Author(s):  
Rajendran Vidhya ◽  
Rajkumar Irene Hepzibah
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Method ◽  
Arithmetic Operations ◽  
Intuitionistic Fuzzy Numbers ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

AbstractIn a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming differentαandβcut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.

Solving the multi-objective stochastic interval-valued linear fractional integer programming problem

2021 ◽  
pp. 2250022
Author(s):  
Leila Younsi-Abbaci ◽  
Mustapha Moulaï
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Probabilistic Constraints ◽  
Chance Constrained Programming ◽  
Integer Programming Problem ◽  
Objective Functions ◽  
Programming Technique ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Interval Valued

In this paper, we consider a Multi-Objective Stochastic Interval-Valued Linear Fractional Integer Programming problem (MOSIVLFIP). We especially deal with a multi-objective stochastic fractional problem involving an inequality type of constraints, where all quantities on the right side are log-normal random variables, and the objective functions coefficients are fractional intervals. The proposed solving procedure is divided in three steps. In the first one, the probabilistic constraints are converted into deterministic ones by using the chance constrained programming technique. Then, the second step consists of transforming the studied problem objectives on an optimization problem with an interval-valued objective functions. Finally, by introducing the concept of weighted sum method, the equivalent converted problem obtained from the two first steps is transformed into a single objective deterministic fractional problem. The effectiveness of the proposed procedure is illustrated through a numerical example.

scholarly journals Stochastic Multi-Objective Programming Problem: A Two-Phase Weighted Coefficient Approach

2021 ◽  
Vol 8 (6) ◽  
pp. 854-860
Author(s):  
Hamiden Abd El-Wahed Khalifa ◽  
Pavan Kumar ◽  
Sultan S. Alodhaibi
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Efficient Solution ◽  
Stochastic Linear Programming ◽  
Two Phase ◽  
Multi Objective ◽  
Deterministic Problem ◽  
Multi Objective Programming ◽  
Decision Variables ◽  
The Right

This paper deals with multi-objective stochastic linear programming problem. The problem is considered by introducing the coefficients of the decision variables and the right-hand-side parameters in the constraints as normal random variables. A method for converting the problem into its deterministic problem is proposed and hence two- phase approach with equal weights is proposed for finding an efficient solution. The advantages of the approach are: as weights which is positive, not necessarily equal and generate an efficient solution. A numerical example is given to illustrate the suggested methodology.

scholarly journals A Multi-Level Multi-Objective Quadratic Programming Problem with Fuzzy Parameters on Objective Functions

2016 ◽  
Vol 15 (5) ◽  
pp. 6738-6748 ◽  
Author(s):  
Usama Emam
Keyword(s):  
Quadratic Programming ◽  
Programming Problem ◽  
Decision Model ◽  
Fuzzy Numbers ◽  
Quadratic Programming Problem ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Multi Level ◽  
Fuzzy Parameters

This paper proposes an algorithm to solve multi-level multi-objective quadratic programming problem with fuzzy parameters in the objective functions, This algorithm uses the tolerance membership function concepts and multi-objective optimization at each level to develop a fuzzy Max-Min decision model for generating satisfactory solution after applying linear ranking method on trapezoidal fuzzy numbers in the objective functions, An illustrative example is included to explain the results.

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