Fuzzy Logic And Mathematics A Historical Perspective Pdf
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Fuzzy Logic and Mathematics: A Historical Perspective
Radim Belohlavek, Joseph W. Dauben, and George J. Klir
Abstract
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 connect ... More
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.
Keywords: bivalence principle, many-valued logic, fuzzy set theory, fuzzy logic, mathematics based on fuzzy logic, history, paradigm
Bibliographic Information
| Print publication date: 2017 | Print ISBN-13: 9780190200015 |
| Published to Oxford Scholarship Online: June 2017 | DOI:10.1093/oso/9780190200015.001.0001 |
Authors
Affiliations are at time of print publication.
Radim Belohlavek, author
Professor of Computer Science, Palacky University, Olomouc, Czech Republic
Joseph W. Dauben, author
Professor of History and the History of Science, City University of New York, New York, NY, USA
George J. Klir, author
Professor of Systems Science, State University of New York, Binghamton, NY, USA
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Fuzzy Logic And Mathematics A Historical Perspective Pdf
Source: https://oxford.universitypressscholarship.com/view/10.1093/oso/9780190200015.001.0001/oso-9780190200015
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