Fuzzy Logic - Decision Making

It is an activity which includes the steps to be taken for choosing a suitable alternative from those that are needed for reapzing a certain goal.

Steps for Decision Making

Let us now discuss the steps involved in the decision making process −

Determining the Set of Alternatives − In this step, the alternatives from which the decision has to be taken must be determined.

Evaluating Alternative − Here, the alternatives must be evaluated so that the decision can be taken about one of the alternatives.

Comparison between Alternatives − In this step, a comparison between the evaluated alternatives is done.

Types of Decision

Making We will now understand the different types of decision making.

Inspanidual Decision Making

In this type of decision making, only a single person is responsible for taking decisions. The decision making model in this kind can be characterized as −

Set of possible actions

Set of goals $G_ileft ( i : in : X_n ight );$

Set of Constraints $C_jleft ( j : in : X_m ight )$

The goals and constraints stated above are expressed in terms of fuzzy sets.

Now consider a set A. Then, the goal and constraints for this set are given by −

$G_ileft ( a ight )$ = composition$left [ G_ileft ( a ight ) ight ]$ = $G_i^1left ( G_ileft ( a ight ) ight )$ with $G_i^1$

$C_jleft ( a ight )$ = composition$left [ C_jleft ( a ight ) ight ]$ = $C_j^1left ( C_jleft ( a ight ) ight )$ with $C_j^1$ for $a:in :A$

The fuzzy decision in the above case is given by −

$$F_D = min[iin X_{n}^{in}fG_ileft ( a ight ),jin X_{m}^{in}fC_jleft ( a ight )]$$

Multi-person Decision Making

Decision making in this case includes several persons so that the expert knowledge from various persons is utipzed to make decisions.

Calculation for this can be given as follows −

Number of persons preferring $x_i$ to $x_j$ = $Nleft ( x_i, : x_j ight )$

Total number of decision makers = $n$

Then, $SCleft ( x_i, : x_j ight ) = frac{Nleft ( x_i, : x_j ight )}{n}$

Multi-objective Decision Making

Multi-objective decision making occurs when there are several objectives to be reapzed. There are following two issues in this type of decision making −

To acquire proper information related to the satisfaction of the objectives by various alternatives.

To weigh the relative importance of each objective.

Mathematically we can define a universe of n alternatives as −

$A = left [ a_1, :a_2,:..., : a_i, : ..., :a_n ight ]$

And the set of “m” objectives as $O = left [ o_1, :o_2,:..., : o_i, : ..., :o_n ight ]$

Multi-attribute Decision Making

Multi-attribute decision making takes place when the evaluation of alternatives can be carried out based on several attributes of the object. The attributes can be numerical data, pnguistic data and quaptative data.

Mathematically, the multi-attribute evaluation is carried out on the basis of pnear equation as follows −

$$Y = A_1X_1+A_2X_2+...+A_iX_i+...+A_rX_r$$