Author | Bฤlohlรกvek, Radim. author |
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Title | Fuzzy Relational Systems [electronic resource] : Foundations and Principles / by Radim Bฤlohlรกvek |
Imprint | Boston, MA : Springer US : Imprint: Springer, 2002 |
Connect to | http://dx.doi.org/10.1007/978-1-4615-0633-1 |
Descript | XII, 369 p. online resource |
1. Preliminaries -- 1.1 Sets, relations, mappings -- 1.2 Ordered sets, lattices -- 1.3 Tolerances, equivalences -- 1.4 Algebras -- 2. Fuzzy Approach, Graded Truth, and Structures of Truth Values -- 2.1 Fuzzy approach: from resolving paradoxes to engineering applications -- 2.2 Graded truth and structures of truth values -- 2.3 Residuated lattices -- 2.4 Residuated lattices and t-norms -- 2.5 Bibliographical remarks -- 3. Fuzzy Structures -- 3.1 Fuzzy sets and fuzzy relations -- 3.2 Fuzzy logic: syntax and semantics -- 3.3 Similarity issues -- 3.4 Morphisms, products, substructures -- 3.5 Representation by crisp structures: cutlike semantics -- 3.6 Algebras with fuzzy equalities -- 3.7 Many-sorted case -- 3.8 Bibliographical remarks -- 4. Binary Fuzzy Relations -- 4.1 Operations and properties of binary fuzzy relations -- 4.2 Similarity: fuzzy equivalences -- 4.3 Hierarchy: fuzzy order -- 4.4 Bibliographical remarks -- 5. Object-Attribute Fuzzy Relations and Fuzzy Concept Lattices -- 5.1 Conceptual granulation: fuzzy context, fuzzy concepts, and fuzzy concept lattice -- 5.2 Similarity and logical precision -- 5.3 Fuzzy Galois connections -- 5.4 Main theorem of fuzzy concept lattices -- 5.5 Bibliographical remarks -- 6. Composition and Decomposition of Fuzzy Relations -- 6.1 Composition of fuzzy relations -- 6.2 Decomposition: fuzzy relational equations -- 6.3 Bibliographical remarks -- 7. Miscellanea -- 7.1 Fuzzy closure operators and similarity spaces -- 7.2 Applications of selected results to some problems and models -- 7.3 Fuzzy logic with truth degrees in residuated lattices -- 7.4 Bibliographical remarks -- References