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Membership function
About: Membership function is a research topic. Over the lifetime, 15795 publications have been published within this topic receiving 418366 citations.
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TL;DR: An axiomatic definition of an interval-valued fuzzy sets' inclusion measure which is different from Bustince's is introduced and six theorems are proposed showing how the similarity measure, the inclusion measure, and the entropy of interval- valued fuzzy sets can be deduced by the interval- valuation fuzzy sets’ normalized distance based on their axi automatic definitions.
164 citations
TL;DR: The proposed rule-based fuzzy modeling implements system structure and parameter identification in the efficient form of “IF …, THEN … ” statements, and exploits the theory of system optimization and fuzzy implication rules.
164 citations
TL;DR: The theoretical framework of FDT in continuous space is extended to digital cubic spaces and it is shown that for any fuzzy digital object, fuzzy distance is a metric for the support of the object.
164 citations
01 Jan 2008
TL;DR: A new concept in fuzzy set theory is introduced, that of a gradual element, that embodies the idea of fuzziness only, thus contributing to the distinction between fuzziness and imprecision.
Abstract: The notion of a fuzzy set stems from considering sets where, in the words of Zadeh, the "transition from non-membership to membership is gradual rather than abrupt". This paper introduces a new concept in fuzzy set theory, that of a gradual element. It embodies the idea of fuzziness only, thus contributing to the distinction between fuzziness and imprecision. A gradual element is to an element of a set what a fuzzy set is to a set. A gradual element is as precise as an element, but the former is flexible while the latter is fixed. The gradual nature of an element may express the idea that the choice of this element depends on a parameter expressing some relevance or describing some concept. Applications of this notion to fuzzy cardinality, fuzzy interval analysis, fuzzy optimization, and defuzzification principles are outlined.
164 citations
TL;DR: The proposed stability-analysis approach offers a nice property that includes the membership functions of both fuzzy model and fuzzy controller in the LMI-based stability conditions for a dedicated FMB control system.
Abstract: This paper presents the stability analysis of fuzzy-model-based (FMB) control systems. Staircase membership functions are introduced to facilitate the stability analysis. Through the staircase membership functions approximating those of the fuzzy model and fuzzy controller, the information of the membership functions can be brought into the stability analysis. Based on the Lyapunov-stability theory, stability conditions in terms of linear-matrix inequalities (LMIs) are derived in a simple and easy-to-understand manner to guarantee the system stability. The proposed stability-analysis approach offers a nice property that includes the membership functions of both fuzzy model and fuzzy controller in the LMI-based stability conditions for a dedicated FMB control system. Furthermore, the proposed stability-analysis approach can be applied to the FMB control systems of which the membership functions of both fuzzy model and fuzzy controller are not necessarily the same. Greater design flexibility is allowed to choose the membership functions during the design of fuzzy controllers. By employing membership functions with simple structure, it is possible to lower the structural complexity and the implementation cost. Simulation examples are given to illustrate the merits of the proposed approach.
164 citations