Topic
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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01 Jul 2001
TL;DR: The design problem of output feedback controllers for Takagi–Sugeno fuzzy models is considered and sufficient conditions for the asymptotic convergence of the fuzzy observers are given.
Abstract: In this paper the design problem of output feedback controllers for Takagi–Sugeno fuzzy models is considered. As for the premise variables, we consider two cases: the outputs and the state variables. In each case, we first consider the design of observers. In the first case we give sufficient conditions for the asymptotic convergence of the fuzzy observers. In the second case we give observers for an approximation of the original system. We then propose the output feedback controllers based on state feedback controllers and observers. Two design examples are given to illustrate the theory.
131 citations
TL;DR: Empirical comparisons indicate that the proposed approach yields comparable or better accuracy than fuzzy or neuro-fuzzy models based on fuzzy rules bases, as well as other soft computing methods.
Abstract: Although traditional fuzzy models have proven to have high capacity of approximating the real-world systems, they have some challenges, such as computational complexity, optimization problems, subjectivity, etc. In order to solve some of these problems, this paper proposes a new fuzzy system modeling approach based on improved fuzzy functions to model systems with continuous output variable. The new modeling approach introduces three features: i) an improved fuzzy clustering (IFC) algorithm, ii) a new structure identification algorithm, and iii) a nonparametric inference engine. The IFC algorithm yields simultaneous estimates of parameters of c-regression models, together with fuzzy c-partitioning of the data, to calculate improved membership values with a new membership function. The structure identification of the new approach utilizes IFC, instead of standard fuzzy c-means clustering algorithm, to fuzzy partition the data, and it uses improved membership values as additional input variables along with the original scalar input variables for two different choices of regression methods: least squares estimation or support vector regression, to determine ldquofuzzy functionsrdquo for each cluster. With novel IFC, one could learn the system behavior more accurately compared to other FSM models. The nonparametric inference engine is a new approach, which uses the alike -nearest neighbor method for reasoning. Empirical comparisons indicate that the proposed approach yields comparable or better accuracy than fuzzy or neuro-fuzzy models based on fuzzy rules bases, as well as other soft computing methods.
131 citations
18 Aug 1985
TL;DR: Prolog-ELF incorporating fuzzy logic and several useful functions into Prolog has been implemented as a basic language for building knowledge systems with uncertainty or fuzziness.
Abstract: Prolog-ELF incorporating fuzzy logic and several useful functions into Prolog has been implemented as a basic language for building knowledge systems with uncertainty or fuzziness. Prolog-ELF inherits all the desirable basic features of Prolog. In addition to assertions with truth-values between 1.0 and 0.5 (0 for exceptional cases), fuzzy sets can be very easily manipulated. An application of fuzzy logical database is illustrated.
131 citations
01 Jan 1990
TL;DR: In this paper some results on group decision making under fuzzy preferences are reviewed and how to represent fuzzy preferences is discussed.
Abstract: In this paper some results on group decision making under fuzzy preferences are reviewed. Since preferences of men are often “fuzzy” and the direct interpersonal comparison of preferences is not easy, the above topic is inevitable and quite important. First we discuss how to represent fuzzy preferences. They might be represented by fuzzy choice sets, fuzzy binary relations or fuzzy utility functions. Secondly group decision making situations are classified according to the above levels in representing both individual and group preferences. Some methods are explained in each category.
131 citations
TL;DR: The concept of a membership function used in fuzzy set theory for representing imprecise data is adopted and the smallest possible, most possible, and largest possible values of the missing data are derived from the observed data to construct a triangular membership function.
Abstract: In measuring the relative efficiencies of a set of decision making units (DMUs) via data envelopment analysis (DEA), detailed inputs and outputs are usually involved. However, there are cases where some DMUs are unable to provide all the necessary data. This paper adopts the concept of a membership function used in fuzzy set theory for representing imprecise data. The smallest possible, most possible, and largest possible values of the missing data are derived from the observed data to construct a triangular membership function. With the membership function, a fuzzy DEA model can be utilized to calculate the efficiency scores. Since the efficiency scores are fuzzy numbers, they are more informative than crisp efficiency scores calculated by assuming crisp values for the missing data. As an illustration, the efficiency scores of the 24 University libraries in Taiwan, with three missing values, are calculated to show the extent that the actual amount of resources and services provided by each University is away from the technically efficient amount of resources and services. This methodology can also be applied to calculate the relative efficiencies of the DMUs with imprecise linguistic data.
130 citations