Fuzzy logic and mathematics : a historical perspective

The term “fuzzy logic” (FL) is a generic one, which stands for a broad variety of logical systems. Their common ground is the rejection of the most fundamental principle of classical logic—the principle of bivalence—according to which each declarative sentence has exactly two possible truth values—t...

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Bibliographische Detailangaben
Hauptverfasser: Belohlavek, Radim, Dauben, Joseph W, Klir, George J
Format: E-Book Buch
Sprache:Englisch
Veröffentlicht: New York Oxford University Press 2017
Oxford University Press, Incorporated
Ausgabe:1
Schlagworte:
Fuzzy logic
Logic, Symbolic and mathematical
Philosophy
Philosophy of Mathematics and Logic
many-valued logic
mathematics based on fuzzy logic
paradigm
fuzzy set theory
fuzzy logic
bivalence principle
history
ISBN:0190200014, 9780190200015
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:The term “fuzzy logic” (FL) is a generic one, which stands for a broad variety of logical systems. Their common ground is the rejection of the most fundamental principle of classical logic—the principle of bivalence—according to which each declarative sentence has exactly two possible truth values—true and false. Each logical system subsumed under FL allows for additional, intermediary truth values, which are interpreted as degrees of truth. These systems are distinguished from one another by the set of truth degrees employed, its algebraic structure, truth functions chosen for logical connectives, and other properties. The book examines from the historical perspective two areas of research on fuzzy logic known as fuzzy logic in the narrow sense (FLN) and fuzzy logic in the broad sense (FLB), which have distinct research agendas. The agenda of FLN is the development of propositional, predicate, and other fuzzy logic calculi. The agenda of FLB is to emulate commonsense human reasoning in natural language and other unique capabilities of human beings. In addition to FL, the book also examines mathematics based on FL. One chapter in the book is devoted to overviewing successful applications of FL and the associated mathematics in various areas of human affairs. The principal aim of the book is to assess the significance of FL and especially its significance for mathematics. For this purpose, the notions of paradigms and paradigm shifts in science, mathematics, and other areas are introduced and employed as useful metaphors.
Bibliographie:Includes bibliographical references (p. 475-510) and indexes
ISBN:0190200014
9780190200015
DOI:10.1093/oso/9780190200015.001.0001