Page 45 - Decision Making Applications in Modern Power Systems

22 Decision Making Applications in Modern Power Systems

Step 4: Calculation of net outranking
This is the final step of ranking all the alternatives or possible decisions.
It is calculated as the difference of positive and negative outranking flows.
FaðÞ is the net outranking of the decision a.
1 2
FaðÞ5F aðÞ 2 F aðÞ ð1:33Þ
The selected applications of PROMETHE in the area of energy planning
are given in Table 1.6.

1.3 Fuzzy logic in multicriteria decision-making

Conventional MCDM methods are based on the assigning values, which act
as weights. These values are always a fixed number, generally called crisp
values. The ranking and all other procedures are carried out based on the
assigned crisp values. In a practical world application involving a real-world
scenario, most of the quantities cannot be defined quantitatively in terms of
numbers. They are expressed as a function or any linguistic variable. The
real-world decision problems are dependent on multiple constraints of which
the significance and consequences are not exactly defined and determined.
Another situation is when the available data or information is not sufficient
to judge or the crisp values are incompetent to determine the model of a real
situation. Thus, in the situations mentioned previously, it becomes very diffi-
cult to use the classical MCDM methods. The MCDM models are
suitable for dealing with situations and problems in which it is assumed that
the performance or the outputs of any operation is known and can be further
represented in the form of crisp numbers.
Fuzzy logic developed by Zadeh in the 1960s has established its applica-
tion in various fields [76].ItisanIF THEN rule based controller. It is use-
ful for solving complex systems whose behaviors cannot be understood. The
solutions can be approximate, but a fast output solution is warranted [77].
The output of fuzzy logic is based on three basic processes—fuzzification,
rule base, and defuzzification—as given in Fig. 1.5.
The fuzzification process converts the input variables in fuzzy variables,
which is a form of membership function. This is given as an input to the rule
base, which is the list of rules based on the number of inputs and outputs.
Based on the logic defined in the rule base, output is given for defuzzifica-
tion. The defuzzification process converts the fuzzy variables to crisp values
[77,78].
The use of fuzzy in MCDM increases the complexity, but the use is justi-
fied for the cases when the goal and final output of the problem statement is
not a crisp value. Bellman and Zadeh, and Zimmermann introduced the
application of fuzzy in the field of MCDM in the years 1970 and 1978,
respectively [79,80]. According to Bellman and Zadeh, the fuzzy goals and