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Fuzzy number
About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.
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Book•
31 Dec 1998
TL;DR: Rodabaugh as mentioned in this paper proposed Axiomatic Foundations of Fixed-Based Fuzzy Topology U.E. Rodabaugh, A.H. Hoehle, S.P. Sostak, and S. Weber.
Abstract: 1. Many-Valued Logic and Fuzzy Set Theory S. Gottwald. 2. Powerset Operator Foundations for Poslat Fuzzy Set Theories and Topologies S.E. Rodabaugh. 3. Axiomatic Foundations of Fixed-Based Fuzzy Topology U. Hoehle, A.P. Sostak. 4. Categorical Foundations of Variable-Basis Fuzzy Topology S.E. Rodabaugh. 5. Characterization of L-Topologies by L-Valued Neighborhoods U. Hoehle. 6. Separation Axioms: Extension of Mappings and Embedding of Spaces T. Kubiak. 7. Separation Axioms: Representation Theorems, Compactness, and Compactifications S.E. Rodabaugh. 8. Uniform Spaces W. Kotze. 9. Extensions of Uniform Space Notions M.H. Burton, J. Gutierrez Garcia. 10. Fuzzy Real Lines and Dual Real Lines as Poslat Topological, Uniform, and Metric Ordered Semirings with Unity S.E. Rodabaugh. 11. Fundamentals of Generalized Measure Theory E.P. Klement, S. Weber. 12. On Conditioning Operators U. Hoehle, S. Weber. 13. Applications of Decomposable Measures E. Pap. 14. Fuzzy Random Variables Revisited D.A. Ralescu.
248 citations
Book•
31 Aug 1997
TL;DR: This chapter introduces the author's fuzzy logic system, which combines the Additive and the Multiplicative AHP with Stochastic and Fuzzy PERT to achieve multi-Objective Optimization.
Abstract: 1. Introduction. 2. Basic Concepts of Fuzzy Logic. 3. Stochastic and Fuzzy PERT. 4. Fuzzy SMART. 5. The Additive and the Multiplicative AHP. 6. The ELECTRE Systems. 7. Fuzzy Multi-Objective Optimization. 8. Colour Perception. Subject Index. About the Author.
247 citations
TL;DR: This paper discusses the voting by multiple fuzzy if-then rules, which is used as a fuzzy reasoning method for classifying input patterns in a single fuzzy rule-based classification system, and compares it with other classification methods such as neural networks and statistical techniques by computer simulations on some well-known test problems.
247 citations
TL;DR: This paper deals with the design of control systems using type-2 fuzzy logic for minimizing the effects of uncertainty produced by the instrumentation elements, environmental noise, etc.
247 citations
TL;DR: A theory about fuzzy probabilistic approximation spaces is proposed in this paper, which combines three types of uncertainty: probability, fuzziness, and roughness into a rough set model.
Abstract: Rough set theory has proven to be an efficient tool for modeling and reasoning with uncertainty information. By introducing probability into fuzzy approximation space, a theory about fuzzy probabilistic approximation spaces is proposed in this paper, which combines three types of uncertainty: probability, fuzziness, and roughness into a rough set model. We introduce Shannon's entropy to measure information quantity implied in a Pawlak's approximation space, and then present a novel representation of Shannon's entropy with a relation matrix. Based on the modified formulas, some generalizations of the entropy are proposed to calculate the information in a fuzzy approximation space and a fuzzy probabilistic approximation space, respectively. As a result, uniform representations of approximation spaces and their information measures are formed with this work
246 citations