 # Introduction

## Rule-Based Fuzzy Logic Systems

Fuzzy logic (FL) is a type of logic that contains more and more than true or false values. It deals with situations where you can't reciprocate for yes/no (true/false) answers. In FL, propositions are expressed to a degree of truth or falsehood. In other words, FL uses a continuous range of truth values at intervals [0,1] that are not simply true or false values. In FL, you can break both basic laws of classical logic. So, as Zadeh's Hamlet have said, "To some extent, it's a mystery." FL is a special case and contains a classic double-value logic.

According to the Encyclopedia Britannica, "Logic is the study of propositions and is used in arguments." This is the same as in Webster's list of English words: "Logic is the science of formal reasoning that uses the principles of valid reasoning," and "Logic has its main purpose. It can be applied to uncover the principles on which all valid reasoning depends and to test the justification of any conclusions drawn from the premise." Although multivalued logic exists, we are most familiar with two-valued (double-valued) logic where the proposition is true or false. This kind of logic is called "clear logic."

Traditional (sometimes written in Western) logic was first systematized in Athens, where Aristotle propounded thousands of years ago. There are two basic laws of classical logic:

Excluded middle law: The set and its complement must contain the universe of discourse.

Law of contradiction: Elements can be sets or complementary elements. You can't have both at the same time.

These two laws sound similar, but the law of contradiction simultaneously prohibits facts that are not true, while the excluded intermediate law prohibits anything other than true or not. Shakespeare's Hamlet exemplified the law of contradiction by saying, "It's a matter of existence or not."

FL led to a new tracery for problem solving. This tracery treats inputs non- linearly and is based on rules that are logical propositions. You can extract the rules from the experts and then quantify them using FL's math you will learn in this course. This forms the tracery of fuzzy logic system (FLS), or FL's math gives the FLS the structure of a tracery from which we can tweak and use appropriate parameters to solve a problem. This helps in solving problems using neural networks (NNs). NNs' tracery is a time superiority that cannot be supported, and its parameters are tuned for troubleshooting. By combining the two approaches, you can learn a tracery that can be based on a combination of linguistic and numeric information. Both approaches play an important role in solving the problem.

An assertion that examines only in the correct case loses all gravity if the underlying assumptions change slightly, whereas an inaccurate paper can be stable even with small perturbations of the underlying axioms.

Schwartz (1962)

All traditional logic habitually assumes that the correct symbols are used. Therefore, it is not possible in this earthly life, only in the imagined Godhead.

Russell (1923)

As the complexity of the system increases, our value in making accurate, yet important statements closer to policy, diminishes until accuracy and importance (or relevance) reaches the threshold for scrutinizing the nature of the cross-sectional area.

This is classified as a principle of incompatibility.

As we enter the information age, human knowledge is becoming more and more important. We need a theory to systematically formulate human knowledge and apply it to engineering systems along with other information such as mathematical models and sensory measurements.

L.-X. Wang (1999)

1.2 A New Direction for FLSs

Rule-based FLS is built on the basis of logic's IF-TFIEN proposal, while NNs are built on simple biological models of neurons. Just as today's NN is different from biological neurons, today's rule-based FLS is different from propositional logic.

Today, fuzzy and nerve are a combination. A fuzzy NN is an NN that uses FL in some way. For example, NN's weights can be modeled as fuzzy sets. The neural fuzzy system is an FLS that uses the NN concept in some way protected by FLS.