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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: In this article, the authors present relaxed LMI conditions for fuzzy control that incorporate shape information in the form of polynomial constraints, generalizing previous works by the authors, and apply these conditions to fuzzy control of Takagi-Sugeno fuzzy systems.
Abstract: Most linear matrix inequality (LMI) fuzzy control results in literature are valid for any membership function, i.e., independent of the actual membership shape. Hence, they are conservative (with respect to other nonlinear control approaches) when specific knowledge of the shapes is available. This paper presents relaxed LMI conditions for fuzzy control that incorporate such shape information in the form of polynomial constraints, generalizing previous works by the authors. Interesting particular cases are overlap (product) bounds and ellipsoidal regions. Numerical examples illustrate the achieved improvements, as well as the possibilities of solving some multiobjective problems. The results also apply to polynomial-in-membership Takagi-Sugeno fuzzy systems.

135 citations

Journal ArticleDOI
TL;DR: The total cost of the backorder inventory problem with fuzzy backorder is slightly higher than that in the crisp model; however, it permits better use of the economic fuzzy quantities arising with changes in orders, deliveries, and sales.

135 citations

Journal ArticleDOI
01 Jan 1974
TL;DR: The methods of constrained maximum likelihood are used to derive consensus estimates of grades of membership given a set of categorical data and an a priori set of specified pure types.
Abstract: This paper discusses the applicability of the ideas of fuzzy sets and grades of membership to problems encountered in the quantification of clinical (i.e., diagnostic and prognostic) judgment. The methods of constrained maximum likelihood are used to derive consensus estimates of grades of membership given a set of categorical data and an a priori set of specified pure types. A numerical example is given.

135 citations

Journal ArticleDOI
TL;DR: A hybrid fuzzy weights-of-evidence (WofE) model for mineral potential mapping that generates fuzzy predictor patterns based on knowledge-based fuzzy membership values and data-based conditional probabilities is described.
Abstract: This paper describes a hybrid fuzzy weights-of-evidence (WofE) model for mineral potential mapping that generates fuzzy predictor patterns based on (a) knowledge-based fuzzy membership values and (b) data-based conditional probabilities. The fuzzy membership values are calculated using a knowledge-driven logistic membership function, which provides a framework for treating systemic uncertainty and also facilitates the use of multiclass predictor maps in the modeling procedure. The fuzzy predictor patterns are combined using Bayes’ rule in a log-linear form (under an assumption of conditional independence) to update the prior probability of target deposit-type occurrence in every unique combination of predictor patterns. The hybrid fuzzy WofE model is applied to a regional-scale mapping of base-metal deposit potential in the south-central part of the Aravalli metallogenic province (western India). The output map of fuzzy posterior probabilities of base-metal deposit occurrence is classified subsequently to delineate zones with high-favorability, moderate favorability, and low-favorability for occurrence of base-metal deposits. An analysis of the favorability map indicates (a) significant improvement of probability of base-metal deposit occurrence in the high-favorability and moderate-favorability zones and (b) significant deterioration of probability of base-metal deposit occurrence in the low-favorability zones. The results demonstrate usefulness of the hybrid fuzzy WofE model in representation and in integration of evidential features to map relative potential for mineral deposit occurrence.

134 citations

Journal ArticleDOI
TL;DR: An approach for selecting and blending bio-optical algorithms is demonstrated using an ocean color satellite image of the northwest Atlantic shelf based on a fuzzy logic classification scheme applied to the satellite-derived water-leaving radiance data and it is used to select and blend class-specific algorithms.
Abstract: An approach for selecting and blending bio-optical algorithms is demonstrated using an ocean color satellite image of the northwest Atlantic shelf. This approach is based on a fuzzy logic classification scheme applied to the satellite-derived water-leaving radiance data, and it is used to select and blend class-specific algorithms. Local in situ bio-optical data were used to characterize optically-distinct water classes a priori and to parameterize algorithms for each class. Although the algorithms can be of any type (empirical or analytical), this demonstration involves class-specific semi-analytic algorithms, which are the inverse of a radiance model. The semi-analytic algorithms retrieve three variables related to the concentrations of optically active constituents. When applied to a satellite image, the fuzzy logic approach involves three steps. First, a membership function is computed for each pixel and each class. This membership function expresses the likelihood that the measured radiance belongs to a class, with a known reflectance distribution. Thus, for each pixel, class memberships are assigned to the predetermined classes on the basis of the derived membership functions. Second, three variables are retrieved from each of the class-specific algorithms for which the pixel has membership. Third, the class memberships are used to weight the class specific retrievals to obtain a final blended retrieval for each pixel. This approach allows for graded transitions between water types, and blends separately tuned algorithms for different water masses without suffering from the "patchwork quilt" effect associated with hard-classification schemes.

134 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202353
2022123
2021340
2020354
2019385
2018433