Fuzzy Logic of Quasi-Truth: An Algebraic Treatment [electronic resource] / by Antonio Di Nola, Revaz Grigolia, Esko Turunen.
By: Di Nola, Antonio [author.].
Contributor(s): Grigolia, Revaz [author.] | Turunen, Esko [author.] | SpringerLink (Online service).
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BookSeries: Studies in Fuzziness and Soft Computing: 338Publisher: Cham : Springer International Publishing : Imprint: Springer, 2016Edition: 1st ed. 2016.Description: VI, 116 p. 3 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319304069.Subject(s): Engineering | Computer science -- Mathematics | Algebra | Computational intelligence | Engineering | Computational Intelligence | General Algebraic Systems | Symbolic and Algebraic ManipulationAdditional physical formats: Printed edition:: No titleDDC classification: 006.3 Online resources: Click here to access online
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Springer eBooksSummary: This book presents the first algebraic treatment of quasi-truth fuzzy logic and covers the algebraic foundations of many-valued logic.  It offers a comprehensive account of basic techniques and reports on important results showing the pivotal role played by perfect many-valued algebras (MV-algebras). It is well known that the first-order predicate �ukasiewicz logic is not complete with respect to the canonical set of truth values.  However, it is complete with respect to all linearly ordered MV -algebras.  As there are no simple linearly ordered MV-algebras in this case, infinitesimal elements of an MV-algebra are allowed to be truth values. The book presents perfect algebras as an interesting subclass of local MV-algebras and provides readers with the necessary knowledge and tools for formalizing the fuzzy concept of quasi true and quasi false. All basic concepts are introduced in detail to promote a better understanding of the more complex ones. It is an advanced and inspiring reference-guide for graduate students and researchers in the field of non-classical many-valued logics.
This book presents the first algebraic treatment of quasi-truth fuzzy logic and covers the algebraic foundations of many-valued logic.  It offers a comprehensive account of basic techniques and reports on important results showing the pivotal role played by perfect many-valued algebras (MV-algebras). It is well known that the first-order predicate �ukasiewicz logic is not complete with respect to the canonical set of truth values.  However, it is complete with respect to all linearly ordered MV -algebras.  As there are no simple linearly ordered MV-algebras in this case, infinitesimal elements of an MV-algebra are allowed to be truth values. The book presents perfect algebras as an interesting subclass of local MV-algebras and provides readers with the necessary knowledge and tools for formalizing the fuzzy concept of quasi true and quasi false. All basic concepts are introduced in detail to promote a better understanding of the more complex ones. It is an advanced and inspiring reference-guide for graduate students and researchers in the field of non-classical many-valued logics.
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