Minimum about fuzzy logic
Introduction

Fuzzy logic is a part of artificial intelligence. Her mission is inflicts natural indeterminateness around us and indeterminateness of human thinking and locution. That way is possible to make accessible to realization by usual facilities for described phenomena and make possible their usage in technical practice.

There exist many fuzzy logic applications in various branches – technical and also untechnical from regulation, technical diagnostic to geology, linguistics, biology, social sciences etc.

## We don’t say „yes, yes, no, no“

„Let your language be yes, yes - no, no!”, such should be the expressing style of a good man according to Rudyard Kipling. Usually we expect to hear such unambiguous language from statesmen and politicians; it is however only rarely encountered at our place (at most with populist promises). Our way of thinking is influenced by the Greek philosophy (particularly by the teaching of Aristotle and his logic) far more than we realize. Logical thinking facilitated incredible boom of science and technology since the Middle Ages up until now. All computers, control and communication systems, and other digital devices operate on the basis of two-valued logic.

The situation is, however, more complex. It is indeed fixed in our rational thinking that clear questions should get clear answers – either yes, or no. But our actual language and the way of thinking significantly differ from strictly unambiguous rules of mathematical logic. For example, try to analyze what you are saying in the statement nothing is impossible. Far too often do we use “fuzzy” and “uncertain” words about, I’m not sure, maybe, approximately, likely, probably, supposedly, presumably, in my opinion, more or less, almost, rather not, basically yes, at 70% yes, sometimes even the quaint almost exactly. Sometimes it is indolence in thinking and poor culture of expressing oneself. It might be even deliberate effort to “conceal” the fact, to avoid telling the whole truth and to complicate its understanding – this is particularly remarkable in the speech of lawyers, diplomats, politicians and their press secretaries.

## False declaration subjective evaluation

In our vision, interpretation of the percepts, and subsequent assessment, we unknowingly use our own “filters and templates” which are individual and depend on the past experience and bearings. Consequently we also judge something uncommon with comments such as “my eyes are playing tricks”, or “I must be dreaming” – but it is frequently only our misconception or misinterpretation of the sighted experience without deliberate comment. If our knowledge and opinions are biased with uncertainty, it is natural and correct to communicate them with “rating” of such uncertainty.

Fig. 6.1: Sharp distinction.

Another problem occurs when trying to assess exact and explicit data. The picture illustrates an attempt to distinguish data about water temperature in a subjective view of a person intending to take a bath. The boundary between zones assessed as pleasant and warm is shown here at 36 °C. Such sharp transition seems to be natural. We could possibly discuss the values for the individual zone boundaries because everyone judges temperature and its “congeniality” differently.

## Fuzzy logic – mathematical branch

Consequently, an apparatus of fuzzy sets and fuzzy logic was created. The author is Lotfi Zadeh, who published his first article thereof in the fifties of the twentieth century. It raised hot interest, developed quickly and “cultivated” in a great thematic extent, especially in its application fields. There are comprehensive monographs and textbooks written on this topic. The general explanation is too complicated for the fuzzy logic to become a routine apparatus for the PLC programmers, who could use it and its advantages in their practice.

Logic is a science field concerned with the mechanisms of human thought and reasoning. Its roots stretch back to philosophers of the Ancient Greece. In this regard, the most popular is Aristotle who is considered the founder of two-valued logic and resulting way of thought, which has influenced the evolution of our entire Western (Euro-American) civilization. Logic became the basis of mathematics and mathematical thought in other technical fields; mathematical logic became independent (and relatively sophisticated) branch of mathematics. One part of mathematical logic is Boolean algebra, which has found its use in technical application.

The traditional logic is two-valued and deals with statements (logical variables) that have two values: true – false, logical 1 – logical 0. Composite statements (logical functions) are constructed by linking fundamental logical statements via logical conjunctions (e.g. and, or, either – or, neither – nor, it is not true that). Using certain rules of mathematical logic, it is possible to determine the value of a composite statement based on the truth or falsity (value) of the sub-statements.