FUZZY LINEAR PROGRAMMING WITH GRADES OF SATISFACTION IN CONSTRAINTS

Document Type: Research Paper

Authors

1 Department of Industrial Engineering, Mazandaran University of Science and Technology, Babol, Iran

2 Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11365-9415, Tehran, Iran

Abstract

We present a new model and a new approach for solving fuzzy
linear programming (FLP) problems with various utilities for the satisfaction
of the fuzzy constraints. The model, constructed as a multi-objective linear
programming problem, provides flexibility for the decision maker (DM), and
allows for the assignment of distinct weights to the constraints and the objective
function. The desired solution is obtained by solving a crisp problem
controlled by a parameter. We establish the validity of the proposed model
and study the effect of the control parameter on the solution. We also illustrate
the efficiency of the model and present three algorithms for solving the
FLP problem, the first of which obtains a desired solution by solving a single
crisp problem. The other two algorithms, interact with the decision maker,
and compute a solution which achieves a given satisfaction level. Finally, we
present an illustrative example showing that the solutions obtained are often
even more satisfactory than asked for.

Keywords


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