Membership function

About: Membership function is a research topic. Over the lifetime, 15795 publications have been published within this topic receiving 418366 citations.

From a Gaussian Mixture Model to Nonadditive Fuzzy Systems

Abstract: This work explores how a kind of probabilistic system, namely the Gaussian mixture model (GMM), can be translated to an additive fuzzy system. We will prove the mathematical equivalence between the conditional mean of a GMM, and the defuzzified output of a generalized fuzzy model (GFM). The relationship between a GMM and a GFM, and the conditions for GMM to GFM translation will be made explicit in the form of theorems. The work will then extend to special cases of the GFM, specifically the Mamdani-Larsen and Takagi-Sugeno fuzzy models. The possibility of reverse translation, that is, from a GFM to a GMM will also be discussed. Finally, we will consider the generality of a GMM, specifically how it can approximate other distribution functions.

Wavelet Fuzzy Neural Network With Asymmetric Membership Function Controller for Electric Power Steering System via Improved Differential Evolution

Abstract: A wavelet fuzzy neural network using asymmetric membership function (WFNN-AMF) with improved differential evolution (IDE) algorithm is proposed in this study to control a six-phase permanent magnet synchronous motor (PMSM) for an electric power steering (EPS) system. First, the dynamics of a steer-by-wire EPS system and a six-phase PMSM drive system are described in detail. Moreover, the WFNN-AMF controller, which combines the advantages of wavelet decomposition, fuzzy logic system, and asymmetric membership function (AMF), is developed to achieve the required control performance of the EPS system for the improvement of stability of the vehicle and the comfort of the driver. Furthermore, the online learning algorithm of WFNN-AMF is derived using back-propagation method. However, degenerated or diverged responses will be resulted due to the inappropriate selection of small or large learning rates of the WFNN-AMF. Therefore, an IDE algorithm is proposed to online adapt the learning rates of WFNN-AMF. In addition, a 32-bit floating-point digital signal processor, TMS320F28335, is adopted for the implementation of the proposed intelligent controlled EPS system. Finally, the feasibility of the proposed WFNN-AMF controller with IDE for the EPS system is verified through experimental results.

Three-way decision spaces based on partially ordered sets and three-way decisions based on hesitant fuzzy sets

Abstract: Three-way decisions on three-way decision spaces are based on fuzzy lattices, i.e. complete distributive lattices with involutive negators. However, now some popular structures, such as hesitant fuzzy sets and type-2 fuzzy sets, do not constitute fuzzy lattices. It limits applications of the theory of three-way decision spaces. So this paper attempts to generalize measurement on decision conclusion in three-way decision spaces from fuzzy lattices to partially ordered sets. First three-way decision spaces and three-way decisions are discussed based on general partially ordered sets. Then this paper points out that the collection of non-empty subset of 0, 1 and the family of hesitant fuzzy sets are both partially ordered sets. Finally this paper systematically discusses three-way decision spaces and three-way decisions based on hesitant fuzzy sets and interval-valued hesitant fuzzy sets and obtains many useful decision evaluation functions.

Intuitionistic fuzzy sets: past, present and future.

Abstract: Remarks on history, theory, and applications of intuitionistic fuzzy sets are given. Some open problems are introduced.