Читать книгу Introduction to Fuzzy Logic - James K. Peckol - Страница 15

Building on the work of those who opened the path and set the trail for us, the next two chapters introduce and study the fundamental concepts, properties, and operations of sets and set membership first for classic sets and then for fuzzy sets.

Chapter 3 introduces the fundamental concept of sets, focusing on what are known as classical or crisp sets. The chapter begins with an introduction of some of the elementary vocabulary and terminology and then reviews the principle definitions and concepts of the theory of ordinary or classical sets. The concepts of subsets and set membership are then presented and explored. Set membership naturally leads to the concept of membership functions.

With the fundamentals of sets and set membership established, we study the basic theory of classic or crisp logic. We then move to the details of the properties and logical operations of using crisp sets and of developing crisp membership applications. Crisp sets and crisp membership applications are a prelude to the introduction of fuzzy logic, fuzzy sets, fuzzy set membership, and threshold logic.

Chapter 4 moves to the fuzzy world introducing and focusing on what are termed fuzzy sets. The chapter reviews some of the principle definitions and concepts of the theory of ordinary or classical sets and illustrates how these are identical to fuzzy subsets when the degree of membership in the subset is expanded to include all real numbers in the interval [0.0, 1.0]. We learned that vagueness and imprecision are common in everyday life. Very often, the kind of information we encounter may be placed into two major categories: statistical and nonstatistical.

The fundamental fuzzy terminology is presented and followed by the introduction of the basic fuzzy set properties and applications. With properties and applications understood, the focus shifts to membership functions and the grade of membership. Up to this point, data has been expressed in numerical form. Often a graphical presentation is a more effective and convenient tool. Such graphs can be expressed in both linear and curved graphical format.