CHAPTER ONE
1.0 INTRODUCTION
Logic in its literal meaning could mean the ability of a system to make a rational decision which can be regarded as the theory of reasoning in decision making. Mathematically, logic generates two results which can be either TRUE or FALSE, 0 or 1, ON or OFF, or any other applicable representation. This concept is referred to as Boolean logic.
Unfortunately, Boolean logic has its limitations. This is due to the fact that it is limited to a set of (0, 1) only, meaning Boolean logic is too precise. This also means that a condition can either be true or false only. For example, Boolean logic cannot differentiate between something that is “good” and that which is “very good”. This limitation is being eliminated by the concept of fuzzy logic.
Fuzzy logic is a branch of logical systems and artificial intelligence. Although it has being studied since 1920,as infinite-valued logics notably by Łukasiewicz and Tarski, the concept was fully developed in 1965 by Lofti A. Zadeh in one of his seminar works regarded as the “fuzzy set theory”. Fuzzy logic is a kind of logic that allows for imprecise or ambiguous answers to questions, forming the basis of computer programming designed to mimic human intelligence (Microsoft Encarta Encyclopedia, 2009). Unlike Boolean logic, fuzzy logic extends its set elements to [0.0, 1.0] and appliesmembership function to each of the elements contained in the set.
From the above, it could be seen that fuzzy logic compared to Boolean logic, is more complex and it is not too precise, giving a wider range of results to a condition. Rather than mere producing true of false, fuzzy logic can produce very true, true, false, very false. This concept is regarded as degree of truth, where; 0.0 is represented as absolute falseness, and; 1.0 is represented as absolute truth.
Before we go deeper into fuzzy logic, we should not neglect a concept known as defuzzification. Defuzzification is the process of producing a quantifiable result in fuzzy logic, given fuzzy sets and corresponding membership degrees. It is typically needed in fuzzy control systems. These will have a number of rules that transform a number of variables into a fuzzy result, that is, the result is described in terms of membership in fuzzy sets. For example, rules designed to decide how much pressure to apply might result in “Decrease Pressure (15%), Maintain Pressure (34%), and Increase Pressure (72%)”. Defuzzification is interpreting the membership degrees of the fuzzy sets into a specific decision or real value.