Fuzzy Relational Systems
Fuzzy Relational Systems: Foundations and Principles presents a general theory of fuzzy relational systems and concentrates on selected general issues of fuzzy relational modeling in the framework of the developed theory. The text discusses phenomena hidden in the ordinary bivalent case, as well as new topics in fuzzy relational systems, such as object-attribute fuzzy relations and fuzzy concept latices, similarity, and fuzzy closure operators. Both mathematicians and engineers will find...
Search in google:
Fuzzy Relational Systems: Foundations and Principles presents a general theory of fuzzy relational systems and concentrates on selected general issues of fuzzy relational modeling in the framework of the developed theory. The text discusses phenomena hidden in the ordinary bivalent case, as well as new topics in fuzzy relational systems, such as object-attribute fuzzy relations and fuzzy concept latices, similarity, and fuzzy closure operators. Both mathematicians and engineers will find Fuzzy Relational Systems to be an invaluable teaching and reference resource in modeling and fuzzy logic.
1Preliminaries11.1Sets, relations, mappings11.2Ordered sets, lattices31.3Tolerances, equivalences51.4Algebras62Fuzzy Approach, Graded Truth, and Structures of Truth Values112.1Fuzzy approach: from resolving paradoxes to engineering applications122.2Graded truth and structures of truth values252.3Residuated lattices272.4Residuated lattices and t-norms623Fuzzy Structures753.1Fuzzy sets and fuzzy relations763.2Fuzzy logic: syntax and semantics963.3Similarity issues1103.4Morphisms, products, substructures1253.5Representation by crisp structures: cutlike semantics1543.6Algebras with fuzzy equalities1593.7Many-sorted case1734Binary Fuzzy Relations1814.1Operations and properties of binary fuzzy relations1824.2Similarity: fuzzy equivalences1934.3Hierarchy: fuzzy order2035Object-Attribute Fuzzy Relations and Fuzzy Concept Lattices2155.1Conceptual granulation: fuzzy context, fuzzy concepts, and fuzzy concept lattice2155.2Similarity and logical precision2225.3Fuzzy Galois connections2445.4Main theorem of fuzzy concept lattices2616Composition and Decomposition of Fuzzy Relations2736.1Composition of fuzzy relations2736.2Decomposition: fuzzy relational equations2797Miscellanea2997.1Fuzzy closure operators and similarity spaces2997.2Applications of selected results to some problems and models3397.3Fuzzy logic with truth degrees in residuated lattices350References357Index367
