Antonio Di Nola - Böcker

It took many decades for Peirce's coneept of a relation to find its way into the microelectronic innards of control systems of eement kilns, subway trains, and tunnel-digging machinery. But what is amazing is that the more we leam about the basically simple coneept of a relation, the more aware we become of its fundamental importanee and wide ranging ramifications. The work by Di Nola, Pedrycz, Sanchez, and Sessa takes us a long distanee in this direction by opening new vistas on both the theory and applications of fuzzy relations - relations which serve to model the imprecise coneepts which pervade the real world. Di Nola, Pedrycz, Sanchez, and Sessa focus their attention on a eentral problem in the theory of fuzzy relations, namely the solution of fuzzy relational equations. The theory of such equations was initiated by Sanchez in 1976, ina seminal paper dealing with the resolution of composite fuzzy relational equations. Sinee then, hundreds of papers have been written on this and related topics, with major contributions originating in France, Italy, Spain, Germany, Poland, Japan, China, the Soviet Union, India, and other countries. The bibliography included in this volume highlights the widespread interest in the theory of fuzzy relational equations and the broad spectrum of its applications.

This book presents the first algebraic treatment of quasi-truth fuzzy logic and covers the algebraic foundations of many-valued logic. 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.

This book presents the first algebraic treatment of quasi-truth fuzzy logic and covers the algebraic foundations of many-valued logic. 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.

This volume offers a picture, as a job in progress, of the effort that is coming in founding and developing soft computing techniques. It contains papers aimed to report results containing genuinely logical aspects of fuzzy logic. The topics treated in this area cover Lukasiewicz logic, fuzzy logic as the logic of continuous t-norms, intuitionistic fuzzy logic. Aspects of fuzzy logic based on similarity relation are presented in connection with the problem of flexible querying in deductive database. Departing from fuzzy logic, some papers present results in probability logic treating computational aspects, results based on indishernability relation and a non commutative version of generalized effect algebras. Several strict applications of soft computing are also presented. The volume can serve as a reference work for foundational logico-algebraic aspects of soft computing and for concrete applications of coft computing techniques.