ABSTRACT

Fuzzy set theory is intended to introduce inaccuracies and ambiguities. Its objective is to model the human brain with artificial intelligence, and its importance is increasing day by day in the field of expert systems. Many actions and strategies are designed to deal with or reduce uncertainty to make life easier for decision makers. Every decision we make is a source of uncertainty, despite being the result of a series of negotiations working to reduce uncertainty. Fuzzy logic (FL) has led to a new architecture for problem solving. Logic is the science of formal reasoning that uses the principles of valid reasoning. FL is a formal mathematical approach for modeling complex systems that have been successfully used in many control systems. Membership features and language descriptions in the form of rules make up the model. Fuzzy logic systems (FLSs) can be defined as a nonlinear mapping of input data sets to scalar output data. FLS consists of four main parts: fuzzy fire, rules, inference engine, and defuzzifier. Quantitative measures like probability can turn out to be insufficient or misleading in many cases. Lotfi Zadeh is the founder of FL. His first treatise on fuzzy sets came out in 1965, though he started formulating ideas for it at least 4 years before. In the decades after 1965, some people, along with Zadeh, developed a strict mathematical basis for fuzzy sets and FL by a relatively small number of people. Fuzzy inference systems (FISs) map vectors from input space to output space. Similar mappings can be done in several different ways, including neural networks, mathematical functions, and conventional control systems. FL techniques can be used to complement other techniques such as neural networks and genetic algorithms. Defuzzification is the process of generating quantifiable results in crisp logic given a fuzzy set and its membership level. It is the process of mapping a fuzzy set to a crisp set typically required for fuzzy control systems. There are various set-theoretic operations on fuzzy sets such as union, intersection, and set difference. The relationship and construction of the crisp and fuzzy sets are also discussed.