Amir Omerovic Decision Making

Decision Making in Fuzzy Environments J. Jusufovic A. Omerovic M. Can

In a standard multiple goal programming, goals and constraints are defined precisely. Fuzzy goal programming has the advantage of allowing for the vague aspirations of decision makers, which are quantified by some natural language rules.

MULTIPLE FUZZY GOAL PROGRAMMING

Find x such that X – VECTOR OF VARIABLES b – VECTOR OF GOALS AND RESOURCES A – MATRIX OF THE COEFICIENT

Max such that for all i ,

PREEMPTIVE FUZZY GOAL PROGRAMMING

Let us assume the existence of K priority levels in the fuzzy goal programming problem. The problem is then partitioned in K sub problems which can be transformed into a standard goal programming problem. if only: T he first sub problem consider s the first priority goals only: Find x such that

Next the goals in the second priority level will be considered; under the condition that achievement of the first sub problem is satisfied:

Find x such that

AN APLICATION: THE PRODUCTION-MARKETING PROBLEM

Assume decision maker consider sale goals only after the profit goal is absolutely achieved. Then the optimization problem is divided into two sub problems. The first problem deals with the first priority goal, profit.

Assume profit is computed through the formula

Find such that

Fuzzy profit goal with: b 11 =7000, d 11 =1000,d 12 =2000

Maximize such that .

Next the second priority level of sales Maximize such that

First Product: b 21 =60, d 1 =10, d 2 =20 Second Product: b 22 =60, d 1 =10, d 2 =20

Maximize such that