Fuzzy sets and applications
Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view
Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view
Fuzzy Sets and Systems - Special issue: fuzzy sets: where do we stand? Where do we go?
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
Foundations of Fuzzy Systems
On isomorphisms between the lattice of tolerance relations and lattices of clusterings
ISMVL '96 Proceedings of the 26th International Symposium on Multiple-Valued Logic
On Some Classes of Fuzzy Information Granularity and Their Representations
ISMVL '99 Proceedings of the Twenty Ninth IEEE International Symposium on Multiple-Valued Logic
On the Concept of Qualitative Fuzzy Set
ISMVL '99 Proceedings of the Twenty Ninth IEEE International Symposium on Multiple-Valued Logic
On Algebraic Foundations of Information Granulation III Investigating the HATA-MUKAIDONO Approach
ISMVL '00 Proceedings of the 30th IEEE International Symposium on Multiple-Valued Logic
On the Mutual Definability of Fuzzy Tolerance Relations and Fuzzy Tolerance Coverings
ISMVL '95 Proceedings of the 25th International Symposium on Multiple-Valued Logic
Fuzzy logic = computing with words
IEEE Transactions on Fuzzy Systems
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In his paper "Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic" L.A. ZADEH writes "There are three basic concepts that underline human cognition: granulation, organisation and causation. Informally, granulation involves decomposition of whole into parts; organisation involves integration of parts into whole; and causation involves association of causes with effects.Granulation of an object A leads to a collection of granules of A, with a granule being a clump of points (objects) drawn together by indistinguishability, similarity, proximity or functionality?"Furthermore, he writes: "Modes of information granulation (IG) in which the granules are crisp (c-granular) play important roles in a wide variety of methods, approaches and techniques. Crisp IG, however, does not reflect the fact that in almost all of human reasoning and concept formation the granules are fuzzy (f-granular)."The contribution presented contains first steps to develop a systematic mathematical theory fitting ZADEH's approach. Because of lacking space we restrict our considerations to the generation of granulations by equivalence, tolerance, S4, partial order, and linear order relations, however, in the crisp as well as in the fuzzy case.