A Fuzzy Approach for Solving a Three-Level Linear Programming Problem with Neutrosophic Parameters in the Objective Functions and Constraints

2021 ◽  
Vol 10 (3) ◽  
pp. 677-686
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Approach ◽  
Objective Functions

scholarly journals Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Aihong Ren
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Function Method ◽  
Optimal Solution ◽  
Ranking Function ◽  
Objective Functions ◽  
Bilevel Linear Programming ◽  
Fuzzy Optimal Solution ◽  
Deviation Degree

This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solution of the problem, we apply deviation degree measures to deal with the fuzzy constraints and use a ranking function method of fuzzy numbers to rank the upper and lower level fuzzy objective functions. Then the fully fuzzy bilevel linear programming problem can be transformed into a deterministic bilevel programming problem. Considering the overall balance between improving objective function values and decreasing allowed deviation degrees, the computational procedure for finding a fuzzy optimal solution is proposed. Finally, a numerical example is provided to illustrate the proposed approach. The results indicate that the proposed approach gives a better optimal solution in comparison with the existing method.

A METHOD FOR GENERATING ALL THE EFFICIENT SOLUTIONS OF A 0-1 MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEM

2004 ◽  
Vol 21 (01) ◽  
pp. 127-139 ◽  
Author(s):  
G. R. JAHANSHAHLOO ◽  
F. HOSSEINZADEH LOTFI ◽  
N. SHOJA ◽  
G. TOHIDI
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Feasible Solution ◽  
Efficient Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multi Objective ◽  
Feasible Solutions ◽  
Single Objective

In this paper, a method using the concept of l1-norm is proposed to find all the efficient solutions of a 0-1 Multi-Objective Linear Programming (MOLP) problem. These solutions are specified without generating all feasible solutions. Corresponding to a feasible solution of a 0-1 MOLP problem, a vector is constructed, the components of which are the values of objective functions. The method consists of a one-stage algorithm. In each iteration of this algorithm a 0-1 single objective linear programming problem is solved. We have proved that optimal solutions of this 0-1 single objective linear programming problem are efficient solutions of the 0-1 MOLP problem. Corresponding to efficient solutions which are obtained in an iteration, some constraints are added to the 0-1 single objective linear programming problem of the next iteration. Using a theorem we guarantee that the proposed algorithm generates all the efficient solutions of the 0-1 MOLP problem. Numerical results are presented for an example taken from the literature to illustrate the proposed algorithm.

scholarly journals Fuzzy Multi Objective Linear Programming Problem with Imprecise Aspiration Level and Parameters

2015 ◽  
Vol 5 (2) ◽  
pp. 81-86 ◽  
Author(s):  
Zahra Shahraki ◽  
Mehdi Allahdadi ◽  
Hassan Mishmast Nehi
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Aspiration Level ◽  
Membership Functions ◽  
Objective Functions ◽  
Multi Objective ◽  
Fuzzy Goals ◽  
Linear Programming Problems

This paper considers the multi-objective linear programming problems with fuzzygoal for each of the objective functions and constraints. Most existing works deal withlinear membership functions for fuzzy goals. In this paper, exponential membershipfunction is used.

scholarly journals THE LINEAR-FRACTIONAL PROGRAMMING PROBLEM UNDER UNCERTAINTY CONDITIONS

2021 ◽  
pp. 20-28
Author(s):  
Oleksandr Pavlov ◽  
Oleksandra Vozniuk ◽  
Olena Zhdanova
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fractional Programming ◽  
Linear Programming Problem ◽  
Original Problem ◽  
Graphical Form ◽  
Compromise Solution ◽  
Objective Functions ◽  
Linear Fractional Programming ◽  
Optimal Values

This paper addresses the problem of linear-fractional programming under uncertainty. The uncertainty here is understood as the ambiguity of the coefficients’ values in the optimized functional. We give two mathematical formulations of the problem. In the first one, the uncertainty refers to the numerator: there are several sets of objective function coefficients, each coefficient can determine the numerator of the problem’s criterion at the stage of its solution implementation. The uncertainty in the second formulation refers to the denominator of the functional. We propose several compromise criteria for evaluating solutions to the problem we consider. We study the following two criterions in detail: 1) finding a compromise solution in which the deviation of the values of the partial functionals from their optimal values is within the specified limits; 2) finding a compromise solution according to the criterion of minimizing the total weighted excess of the values of partial functionals in relation to the specified feasible deviations from their optimal values (the values of concessions). We formulate an auxiliary linear programming problem to find a compromise solution to the linear-fractional programming problems by these two criteria. The constraints of the auxiliary problem depend on the optimization direction in the original problem. We carried out a series of experiments of four types to study the properties of the problem. The purposes of the experiments were: 1) to study how changes in the values of the specified feasible deviations of partial objective functions impact the values of actual deviations and the values of concessions; 2) to study how changes in the expert weights of partial objective functions impact the values of actual deviations and the values of concessions for the compromise solutions we obtain. We propose in this work the schemes of experiments and present their results in graphical form. We have found that the obtained relations depend on the optimization direction in the original problem. Keywords: optimization, uncertainty, convolution, linear-fractional programming, linear programming problem, compromise solution

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.

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