The textbook presents fuzzy sets and their applications. It is suitable for undergraduate liberal arts and sciences programs.
The introductory overview covers classical logic, classical set theory and classical binary relations. Basic concepts of fuzzy set theory: fuzzy set, membership function, operations on fuzzy sets, \(\alpha\)-cuts, measurement of fuzziness, are given. Fuzzy relations and operations with them, some classes of fuzzy relations (equivalence, partial ordering), projections and cylindric extensions are studied. Fuzzy arithmetic covers fuzzy numbers and arithmetic operations on fuzzy numbers. Fuzzy logic as a system of concepts, principles and methods for dealing with models of reasoning is considered. A short survey of applications (historical, established and prospective) completes the exposition.