The Principles of Fuzzy Logic: Its Mathematical and Computational Aspects
Our aim in this chapter is to give a brief overview of the main aspects of fuzzy logic. We introduce the concept of fuzzy logic and discuss its philosophical background. We argue that people encounter a phenomenon of indeterminacy which has two complementary facets, namely uncertainty and vagueness. Fuzzy logic is then considered as a mathematical model useful for modelling of the latter. Furthermore, we outline the theory of special structures, which are suitable for representation of the structure of truth values.
KeywordsFuzzy Logic Normal Form Classical Logic Residuated Lattice Conjunctive Normal Form
Unable to display preview. Download preview PDF.
- 1.Black, M. (1937). “Vagueness: An Exercise in Logical Analysis,” Philosophy of Science 4, 427–455. Reprinted in Int. J. of General Systems 17 (1990), 107–128.Google Scholar
- 4.Cohen, P. M. (1965), Universal algebra, New York: Harper and Row.Google Scholar
- 6.Gottwald, S. (1993). Fuzzy Sets and Fuzzy Logic. Wiesbaden: Vieweg.Google Scholar
- 7.Gottwald, S.: A Treatise on Many-Valued Logics. Research Studies Press Ltd., Baldock, Herfordshire, UK (to appear)Google Scholar
- 14.Vopénka, P. (1979). Mathematics In the Alternative Set Theory. Leipzig: Teubner.Google Scholar