Topic
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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TL;DR: This paper proposes two goal programming models, based on additive consistent incomplete fuzzy preference relation and multiplicative consistent incomplete fuzziest preference relation respectively, for obtaining the priority vector of incomplete fuzzy preferences.
241 citations
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TL;DR: New learning laws for Mamdani and Takagi-Sugeno-Kang type fuzzy neural networks based on input-to-state stability approach are suggested, which employ a time-varying learning rate that is determined from input-output data and model structure.
Abstract: In general, fuzzy neural networks cannot match nonlinear systems exactly. Unmodeled dynamic leads parameters drift and even instability problem. According to system identification theory, robust modification terms must be included in order to guarantee Lyapunov stability. This paper suggests new learning laws for Mamdani and Takagi-Sugeno-Kang type fuzzy neural networks based on input-to-state stability approach. The new learning schemes employ a time-varying learning rate that is determined from input-output data and model structure. Stable learning algorithms for the premise and the consequence parts of fuzzy rules are proposed. The calculation of the learning rate does not need any prior information such as estimation of the modeling error bounds. This offer an advantage compared to other techniques using robust modification.
241 citations
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TL;DR: In this article, the authors considered linear programming problems with fuzzy constraints and fuzzy coefficients in both matrix and right hand side of the constraint set are considered, and the diversity of such methods provides a lot of different models from which fuzzy solutions to the former problem can be obtained.
240 citations
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TL;DR: Based on fuzzy-rough set theory, hidden fuzzy relationships (rules) in audit data are uncovered and are some deeper "signatures" of computer users, which provide a foundation to detect abuses and misuses of computer systems.
Abstract: Computer are finite discrete machines, the set of real numbers is an infinite continuum. So real numbers in computers are approximation. Rough set theory is the underlying mathematics. A 'computer' version of Weistrass theorem states that every sequence, within the radius of error, repeats certain terms infinitely many times. In terms of applications, the theorem guarantees that the audit trail has repeating patterns. Examining further, based on fuzzy-rough set theory, hidden fuzzy relationships (rules) in audit data are uncovered. The information about the repeating data and fuzzy relationships reflect "unconscious patterns" of users' habits. They are some deeper "signatures" of computer users, which provide a foundation to detect abuses and misuses of computer systems, A "sliding window information system" is used to illustrate the detection of a 'simple' virus attack. The complexity problem is believed to be controllable via rough set representation of data.
240 citations
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TL;DR: This method for solving a multicriteria linear program where the coefficients of the objective functions and the constraints are fuzzy numbers of the L-R type is elaborated with a view to the application to the development of a water supply system.
240 citations