Type 2 Fully Fuzzy Linear Programming

2021 ◽  
Vol 10 (4) ◽  
pp. 37-56
Author(s):  
Mohamed El Alaoui
Keyword(s):  
Linear Programming ◽  
Real Life ◽  
Inequality Constraints ◽  
Fuzzy Linear Programming ◽  
Fuzzy Membership Function ◽  
Programming Approach ◽  
Life Problems ◽  
Comparative Results ◽  
Interval Type

Since its inception, fuzzy linear programming (FLP) has proved to be a more powerful tool than classical linear programming to optimize real-life problems dealing with uncertainty. However, the proposed models are partially fuzzy; in other words, they suppose that only some aspects can be uncertain, while others have to be crisp. Furthermore, the few methods that deal with fully fuzzy problems use Type 1 fuzzy membership function, while Type 2 fuzzy logic captures the uncertainty in a more suitable way. This work presents a fully fuzzy linear programming approach in which all parameters are represented by unrestricted Interval Type 2 fuzzy numbers (IT2FN) and variables by positive IT2FN. The treated comparative results show that the proposed achieves a better optimized function while permitting consideration of both equality and inequality constraints.

A Different Approach for Solving the Shortest Path Problem Under Mixed Fuzzy Environment

2020 ◽  
Vol 9 (2) ◽  
pp. 132-161 ◽  
Author(s):  
Ranjan Kumar ◽  
Sripati Jha ◽  
Ramayan Singh
Keyword(s):  
Linear Programming ◽  
Shortest Path ◽  
Path Length ◽  
Real Life ◽  
Shortest Path Problem ◽  
Fuzzy Linear Programming ◽  
Fuzzy Membership ◽  
Fuzzy Membership Function ◽  
Membership Functions ◽  
Fuzzy Environment

The authors present a new algorithm for solving the shortest path problem (SPP) in a mixed fuzzy environment. With this algorithm, the authors can solve the problems with different sets of fuzzy numbers e.g., normal, trapezoidal, triangular, and LR-flat fuzzy membership functions. Moreover, the authors can solve the fuzzy shortest path problem (FSPP) with two different membership functions such as normal and a fuzzy membership function under real-life situations. The transformation of the fuzzy linear programming (FLP) model into a crisp linear programming model by using a score function is also investigated. Furthermore, the shortcomings of some existing methods are discussed and compared with the algorithm. The objective of the proposed method is to find the fuzzy shortest path (FSP) for the given network; however, this is also capable of predicting the fuzzy shortest path length (FSPL) and crisp shortest path length (CSPL). Finally, some numerical experiments are given to show the effectiveness and robustness of the new model. Numerical results show that this method is superior to the existing methods.

Fuzzy Linear Programming: A Modern Tool for Decision Making

2012 ◽  
Author(s):  
Pandian M. Vasant ◽  
R. Nagarajan ◽  
Sazali Yaacob
Keyword(s):  
Decision Making ◽  
Linear Programming ◽  
Production Planning ◽  
Membership Function ◽  
Industrial Production ◽  
Real Life ◽  
Fuzzy Linear Programming ◽  
Programming Approach ◽  
Modern Trend ◽  
Application Problem

The modern trend in industrial application problem deserves modeling of all relevant vague or fuzzy information involved in a real decision making problem. In the first part of the paper, some explanations on tri partite fuzzy linear programming approach and its importance have been given. In the second part, the usefulness of the proposed S-curve membership function is established using a real life industrial production planning of a chocolate manufacturing unit. The unit produces 8 products using 8 raw materials, mixed in various proportions by 9 different processes under 29 constraints. A solution to this problem establishes the usefulness of the suggested membership function for decision making in industrial production planning. Key words: Fuzzy linear programming, Satisfactory solution; Decision maker; Implementer; Analyst; Fuzzy constraint; Vagueness.

Fuzzy Multi-objective Linear Programming Problem using DM's Perspective

2022 ◽  
Vol 14 (1) ◽  
pp. 0-0
Keyword(s):  
Linear Programming ◽  
Problem Solving ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Closed Interval ◽  
Programming Approach ◽  
Multi Objective ◽  
Mathematical Programming Approach ◽  
Interval Type

In this paper, a two-stage method has been proposed for solving Fuzzy Multi-objective Linear Programming Problem (FMOLPP) with Interval Type-2 Triangular Fuzzy Numbers (IT2TFNs) as its coefficients. In the first stage of problem solving, the imprecise nature of the problem has been handled. All technological coefficients given by IT2TFNs are first converted to a closed interval and then the objectives are made crisp by reducing a closed interval into a crisp number and constraints are made crisp by using the concept of acceptability index. The amount by which a specific constraint can be relaxed is decided by the decision maker and thus the problem reduces to a crisp multi-objective linear programming problem (MOLPP). In the second stage of problem solving, the multi-objective nature of the problem is handled by using fuzzy mathematical programming approach. In order to explain the methodology, two numerical examples of the proposed methodology in Production planning and Diet planning problems have also been worked out in this paper.

Application of Multi Objective Fuzzy Linear Programming in Supply Production Planning Problem

2012 ◽  
Author(s):  
Pandian M. Vasant
Keyword(s):  
Linear Programming ◽  
Production Planning ◽  
Membership Function ◽  
Programming Model ◽  
Real Life ◽  
Fuzzy Linear Programming ◽  
Programming Approach ◽  
Planning Problem ◽  
Production Planning Problem ◽  
S Curve

The objective of this paper is to establish the usefulness of modified s-curve membership function in a limited supply production planning problem with continuous variables. In this respect, fuzzy parameters of linear programming are modeled by non-linear membership functions such as s-curve function. This paper begins with an introduction and construction of the modified s-curve membership function. A numerical real life example of supply production planning problem is then presented. The computational results show the usefulness of the modified s-curve membership function with fuzzy linear programming technique in optimising individual objective functions, compared to non-fuzzy linear programming approach. Futhermore, the optimal solution helps to conclude that by incorporating fuzziness in a linear programming model through the objective function and constraints, a better level of satisfactory solution will be provided in respect to vagueness, compared to non-fuzzy linear programming.

scholarly journals Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
A. Srinivasan ◽  
G. Geetharamani
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Trapezoidal Fuzzy Numbers ◽  
Degree Of Satisfaction ◽  
Linear Programming Problems ◽  
Interval Type ◽  
Perfectly Normal

Interval type 2 fuzzy numbers are a special kind of type 2 fuzzy numbers. These numbers can be described by triangular and trapezoidal shapes. In this paper, first, perfectly normal interval type 2 trapezoidal fuzzy numbers with their left-hand and right-hand spreads and their core have been introduced, which are normal and convex; then a new type of fuzzy arithmetic operations for perfectly normal interval type 2 trapezoidal fuzzy numbers has been proposed based on the extension principle of normal type 1 trapezoidal fuzzy numbers. Moreover, in this proposal, linear programming problems with resources and technology coefficients are perfectly normal interval type 2 fuzzy numbers. To solve this kind of fuzzy linear programming problems, a method based on the degree of satisfaction (or possibility degree) of the constraints has been introduced. In this method the fulfillment of the constraints can be measured with the help of ranking method of fuzzy numbers. Optimal solution is obtained at different degree of satisfaction by using Barnes algorithm with the help of MATLAB. Finally, the optimal solution procedure is illustrated with numerical example.

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