Computer Engineering and Intelligent Systems ISSN 2222-1719 (Paper) ISSN 2222-2863 (Online) Vol.4, No.3, 2013
www.iiste.org
of membership of an element x in a set A is mA(x), and therefore we denote the fuzzy set by the pair (A, mA (x)), or A(x) for short [4, 12]. 2.2 Fuzzy Operators The basic operations defined on crisp sets, namely intersection (AND), union (OR) and complement (NOT), can be generalized to fuzzy sets. The generalization to fuzzy sets can be achieved in more than one possible way. The most widely used fuzzy set operations that will be adopted in this work are called standard operations. They are; standard fuzzy intersection, standard fuzzy union, and standard fuzzy complement [3][6][7]. Let A(x) and B(x) denote two fuzzy sets, that is the degree to which x belongs to A is mA(x), and the degree to which x belongs to B is mB(x). The standard fuzzy complement for set A(x) denoted by cA(x) is defined as 1 – mA(x). The standard fuzzy intersection for two set A(x) and B(x) denoted by (A ∩ B)(x) is defined as min[ mA(x), mB(x) ]. The standard fuzzy union for two set A(x) and B(x) denoted by (A ∪ B)(x) is defined as max[ mA(x), mB(x) ]. 2.3 Fuzzy Rules A fuzzy rule has the form If x is A then y is B in which A and B are fuzzy sets, defined on universes X and Y, respectively. In fuzzy logic, logic rules are represented by a collection of IF-THEN statements. Interpreting an if–then rule is a three part process: (a) Resolve all fuzzy statements in the antecedent to a degree of membership between 0 and 1; (b) if there are multiple parts to the antecedent, apply fuzzy logic operators and resolve the antecedent to a single number between 0 and 1, is the result being the degree of support for the rule; and (c) apply the implication method, using the degree of support for the entire rule to shape the output fuzzy set. If the rule has more than one antecedent, the fuzzy operator is applied to obtain one number that represents the result of applying that rule [8,4]. Examples of such rules in everyday conversation are •
If you are hungry then eat.
•
If the room is cold, then increase the heat
A single assignment statement has the general form of “x is Ai” and a compound assignment statement is constructed from single assignments and set operations for example “orientation is HORIZONTAL AND height is HIGH”. Fuzzy rules facilitate the representation of linguistic rules. In order to make the representation of such rules even easier, we use fuzzy hedges, which are equivalent of the adverbs in natural languages. The most common types of fuzzy hedges are “very” and “somewhat” which are defined as follows. Let (A, mA(x)) denote a fuzzy set defined on the universe of discourse x, then: Very A(x) ≡ (very A, mvery A(x))
where mvery A(x) = [mA (x)]2
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