Image Processing Reference
In-Depth Information
3
Fuzzy and Intuitionistic Fuzzy Operators
with Applic
ation in Decision-Making
3.1 Introduction
With the demand for knowledge handling systems capable of dealing with
imprecision, a formal mathematical tool is quiet necessary. In real decision-
making, decision-making problems are fuzzy and uncertain, and the attri-
bute values are not expressed always as real numbers; rather, some of them
are more suitable to be denoted as fuzzy numbers. The theory of fuzzy logic
provides a mathematical strength to capture the uncertainties and is suit-
able to process human information and reasoning. Fuzzy logic operators are
used to decide multi-criteria decision-making problem. Decision-making is
defined as making choices between future and uncertain alternatives. It is
a difficult process due to incomplete and imprecise information, vagueness
and uncertainty of the situation. These factors show that decisions can take
place in a fuzzy logic environment.
Aggregating criterion functions to form decision functions is of great
importance in all disciplines. At one extreme of the situation, we desire that
all the criteria are fulfilled, and in another extreme, we desire that any of the
criteria is fulfilled. These two extremes lead to the use of 'and' and 'or' opera-
tors to combine the criterion function.
3.2 Fuzzy Operators
Since the introduction of fuzzy sets by Zadeh, fuzzy set theory is extended
from ordinary set theory and the operators in ordinary set theory can be
extended to operators that are capable of realization of the same union,
intersection and complement logical operators in a multi-valued logic. In
propositional logic, the operators OR, AND and NOT are used to build new
propositions.
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