Page 50 - Decision Making Applications in Modern Power Systems

Multicriteria decision-making methodologies Chapter | 1 25

Input Fuzzification Rule base Defuzzification Output

FIGURE 1.5 A fuzzy logic system.

constraints can be represented symmetrically as fuzzy sets. The decision is to
be well defined such that the union between the constraints and the goals is
satisfied. The maximum value of the membership function is to be defined at
the point with maximized decision. Few other approaches are proposed by
Bass and Kwakernaak (1977) and Yager (1978) [81,82]. The phase-wise
approach was proposed by Dubois and Prade (1980), Zimmermann (1987),
Chen and Hwang (1992), and Ribeiro (1996) [83 86]. The first phase is
meant to determine the performance rating of the alternatives or calculating
the degree of satisfaction w.r.t. all the attributes of respective alternatives.
The second phase calculates the order of ranking of all alternatives based on
the results of the first phase.
Although fuzzy-based MCDM solves a major issue of uncertainty or
fuzziness in a decision-making problem, there are many drawbacks based on
the literature. There is no standard solution technique to solve, mathematical
model to represent a problem, increased complexity, and ambiguity. It is not
possible to incorporate any quantitative factor, and the determined solution is
very difficult to be analyzed.

1.3.1 Fuzzy analytical hierarchical process

AHP is one of the most commonly used methods in the MADM procedure.
It is considered to be one of the most systematic and logical approaches to
determine the solution. It is noticed that decision maker finds it more rele-
vant to give a conclusion that is in any range of values rather than exact
numbers. There are various approaches proposed in the literature to jointly
use fuzzy with AHP. Few of them are listed in Table 1.7.
The Buckley approach is described here in six steps.
Step 1: Fuzzification
Saaty proposed a scale to prioritize alternatives [26]. The scale is based
on crisp values ranging between 1 and 8. Since fuzzy logic is based on lin-
guistic variable, a range is defined for the same scale. The corresponding
fuzzy triangular scale and the equivalent Saaty scale are given in Table 1.8.
The pairwise decision matrix is created using the fuzzy triangular scale.
k
Let the elements of the matrix be f that is a fuzzy number depicting the
ij
preference of the kth decision maker in selecting i over j. The complete
matrix is given in the following equation: