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.

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.

SOLVING FUZZY LINEAR PROGRAMMING PROBLEMS WITH MODIFIED S-CURVE MEMBERSHIP FUNCTION

2005 ◽  
Vol 13 (01) ◽  
pp. 97-109 ◽  
Author(s):  
PANDIAN M. VASANT
Keyword(s):  
Linear Programming ◽  
Membership Function ◽  
Fuzzy Numbers ◽  
Numerical Solutions ◽  
Real Life ◽  
Optimization Method ◽  
Fuzzy Linear Programming ◽  
Membership Functions ◽  
Linear Programming Problems ◽  
S Curve

In this paper, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy resource variables and linear programming problems in which both the resource variables and the technological coefficients are fuzzy numbers. We consider here only the case of fuzzy numbers with modified s-curve membership functions. We propose here the modified s-curve membership function as a methodology for fuzzy linear programming and use it for solving these problems. We also compare the new proposed method with non-fuzzy linear programming optimization method. Finally, we provide real life application examples in production planning and their numerical solutions.

FUZZY LINEAR PROGRAMMING APPROACH TO MULTI-ATTRIBUTE DECISION-MAKING WITH LINGUISTIC VARIABLES AND INCOMPLETE INFORMATION

2007 ◽  
Vol 10 (04) ◽  
pp. 505-525 ◽  
Author(s):  
DENG-FENG LI ◽  
TAO SUN
Keyword(s):  
Decision Making ◽  
Linear Programming ◽  
Programming Model ◽  
Fuzzy Linear Programming ◽  
Programming Approach ◽  
Final Decision ◽  
Linguistic Variables ◽  
Information Structures ◽  
Decision Matrix ◽  
Multi Attribute Decision Making

The aim of this paper is to develop a new fuzzy linear programming technique for solving multi-attribute decision-making (MADM) problems with incomplete weight preference information under fuzzy environments. In this methodology, linguistic variables are used to capture fuzziness in decision information and decision-making processes by means of a fuzzy decision matrix. Consistency and inconsistency indices are defined on the basis of preference relations between alternatives given by the decision maker under uncertain environments. Each alternative is assessed on the basis of its distance to a fuzzy ideal solution (FIS) which is unknown a priori. Then the FIS and the weights of attributes are estimated using a new linear programming model based upon the consistency and inconsistency indices defined. The fuzzy distance of each alternative to the FIS can be calculated to determine the ranking order of all alternatives. An extended illustrative example on the selection of air-fighters is presented to demonstrate the implementation process of this methodology. The methodology proposed in this paper can deal with MADM problems under not only fuzzy environments but also crisp environments. Also it has been proven that different weight information structures may result in different final decision results.

FUZZY MULTI-OBJECTIVE LINEAR PROGRAMMING APPROACH FOR SOLVING PROBLEM OF FOOD INDUSTRY

2018 ◽  
Vol 6 (2) ◽  
pp. 13-19
Author(s):  
Mukesh Kumar Sinha ◽  
Arun Prasad Burnwal ◽  
Chitra Singh
Keyword(s):  
Decision Making ◽  
Fuzzy Logic ◽  
Linear Programming ◽  
Food Industry ◽  
Programming Model ◽  
Fuzzy Linear Programming ◽  
Programming Approach ◽  
Market Uncertainty ◽  
Surrounding Environment ◽  
Different Types

Enterprises and industrial centers need current decision for making products in fast changing market. Uncertainty and yield defined goals make decision making more difficult. In this situation fuzzy logic is used for coping surrounding environment. This paper deals with a fuzzy linear programming model for a problem of food industry. The different types of achievement function such as compensatory and weighted compensatory form 

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.

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