Possibilistic linear programming with triangular fuzzy numbers

1988 ◽  
Vol 26 (1) ◽  
pp. 135-138 ◽  
Author(s):  
J.J. Buckley
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Numbers ◽  
Possibilistic Linear Programming

scholarly journals A fuzzy multi-objective linear programming with interval-typed triangular fuzzy numbers

2019 ◽  
Vol 17 (1) ◽  
pp. 607-626 ◽  
Author(s):  
Chunquan Li
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Optimal Solution ◽  
Objective Functions ◽  
Triangular Fuzzy Numbers ◽  
Matlab Toolbox ◽  
Multi Objective ◽  
Cut Set ◽  
The Stability

Abstract A multi-objective linear programming problem (ITF-MOLP) is presented in this paper, in which coefficients of both the objective functions and constraints are interval-typed triangular fuzzy numbers. An algorithm of the ITF-MOLP is provided by introducing the cut set of interval-typed triangular fuzzy numbers and the dominance possibility criterion. In particular, for a given level, the ITF-MOLP is converted to the maximization of the sum of membership degrees of each objective in ITF-MOLP, whose membership degrees are established based on the deviation from optimal solutions of individual objectives, and the constraints are transformed to normal inequalities by utilizing the dominance possibility criterion when compared with two interval-typed triangular fuzzy numbers. Then the equivalent linear programming model is obtained which could be solved by Matlab toolbox. Finally several examples are provided to illuminate the proposed method by comparing with the existing methods and sensitive analysis demonstrates the stability of the optimal solution.

scholarly journals A Novel Approach to Solve Fully Fuzzy Linear Programming Problems with Modified Triangular Fuzzy Numbers

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2937
Author(s):  
Saeid Jafarzadeh Ghoushchi ◽  
Elnaz Osgooei ◽  
Gholamreza Haseli ◽  
Hana Tomaskova
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Number ◽  
Fuzzy Linear Programming ◽  
Fuzzy Decision ◽  
Triangular Fuzzy Numbers ◽  
Novel Approach ◽  
Decision Variables ◽  
Linear Programming Problems ◽  
Fuzzy Solution

Recently, new methods have been recommended to solve fully fuzzy linear programming (FFLP) issues. Likewise, the present study examines a new approach to solve FFLP issues through fuzzy decision parameters and variables using triangular fuzzy numbers. The strategy, which is based on alpha-cut theory and modified triangular fuzzy numbers, is suggested to obtain the optimal fully fuzzy solution for real-world problems. In this method, the problem is considered as a fully fuzzy problem and then is solved by applying the new definition presented for the triangular fuzzy number to optimize decision variables and the objective function. Several numerical examples are solved to illustrate the above method.

LEXICOGRAPHIC METHOD FOR MATRIX GAMES WITH PAYOFFS OF TRIANGULAR FUZZY NUMBERS

2008 ◽  
Vol 16 (03) ◽  
pp. 371-389 ◽  
Author(s):  
DENG-FENG LI
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Order Relation ◽  
Programming Models ◽  
Matrix Game ◽  
Triangular Fuzzy Numbers ◽  
Matrix Games ◽  
Lexicographic Method

The purpose of the paper is to study how to solve a type of matrix games with payoffs of triangular fuzzy numbers. In this paper, the value of a matrix game with payoffs of triangular fuzzy numbers has been considered as a variable of the triangular fuzzy number. First, based on two auxiliary linear programming models of a classical matrix game and the operations of triangular fuzzy numbers, fuzzy optimization problems are established for two players. Then, based on the order relation of triangular fuzzy numbers the fuzzy optimization problems for players are decomposed into three-objective linear programming models. Finally, using the lexicographic method maximin and minimax strategies for players and the fuzzy value of the matrix game with payoffs of triangular fuzzy numbers can be obtained through solving two corresponding auxiliary linear programming problems, which are easily computed using the existing Simplex method for the linear programming problem. It has been shown that the models proposed in this paper extend the classical matrix game models. A numerical example is provided to illustrate the methodology.

scholarly journals Evaluating fuzzy inequalities and solving fully fuzzified linear fractional programs

2012 ◽  
Vol 22 (1) ◽  
pp. 41-50 ◽  
Author(s):  
B. Stanojevic ◽  
I.M. Stancu-Minasian
Keyword(s):  
Linear Programming ◽  
Fractional Programming ◽  
Fuzzy Numbers ◽  
Multiple Objective ◽  
Multiple Objective Linear Programming ◽  
Triangular Fuzzy Numbers ◽  
Linear Fractional Programming ◽  
Numerical Examples ◽  
Fractional Programs ◽  
Linear Fractional Programming Problem

In our earlier articles, we proposed two methods for solving the fully fuzzified linear fractional programming (FFLFP) problems. In this paper, we introduce a different approach of evaluating fuzzy inequalities between two triangular fuzzy numbers and solving FFLFP problems. First, using the Charnes-Cooper method, we transform the linear fractional programming problem into a linear one. Second, the problem of maximizing a function with triangular fuzzy value is transformed into a problem of deterministic multiple objective linear programming. Illustrative numerical examples are given to clarify the developed theory and the proposed algorithm.

scholarly journals Mehar method for finding exact fuzzy optimal solution of fully fuzzy linear programming problems

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Gourav Gupta
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Triangular Fuzzy Number ◽  
Fuzzy Linear Programming ◽  
Decision Making Under Uncertainty ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Optimal Solution ◽  
Linear Programming Problems ◽  
Fuzzy Solutions

There are several methods in the literature to find the fuzzy optimal solution of fully fuzzy linear programming (FFLP) problems. However, in all these methods, it is assumed that the product of two trapezoidal (triangular) fuzzy numbers will also be a trapezoidal (triangular) fuzzy number. Fan et al. (“Generalized fuzzy linear programming for decision making under uncertainty: Feasibility of fuzzy solutions and solving approach”, Information Sciences, Vol. 241, pp. 12–27, 2013) proposed a method for finding the fuzzy optimal solution of FFLP problems without considering this assumption. In this paper, it is shown that the method proposed by Fan et al. (2013) suffer from errors and to overcome these errors, a new method (named as Mehar method) is proposed for solving FFLP problems by modifying the method proposed by Fan et al. (2013) . To illustrate the proposed method, some numerical problems are solved.

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