Fuzzy number

About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.

The canonical representation of multiplication operation on triangular fuzzy numbers

Abstract: The representation of multiplication operation on fuzzy numbers is very useful and important in the fuzzy system such as the fuzzy decision making. In this paper, we propose a new arithmetical principle and a new arithmetical method for the arithmetical operations on fuzzy numbers. The new arithmetical principle is the L−1-R−1 inverse function arithmetic principle. Based on the L−1-R−1 inverse function arithmetic principle, it is easy to interpret the multiplication operation with the membership functions of fuzzy numbers. The new arithmetical method is the graded multiple integrals representation method. Based on the graded multiple integrals representation method, it is easy to compute the canonical representation of multiplication operation on fuzzy numbers. Finally, the canonical representation is applied to a numerical example of fuzzy decision.

Genetic fuzzy learning

Abstract: A hybrid approach to fuzzy supervised learning is presented. It is based on a genetic-neuro learning algorithm. The mixed-genetic coding adopted involves only the premises of the fuzzy rules. The conclusions are derived through a least-squares solution of an over-determined system using the singular value decomposition (SVD) algorithm. The paper presents the results obtained with C++ software called GEFREX that implements the proposed algorithm. The main characteristic of the algorithm is the compactness of the fuzzy systems extracted. Several comparisons ranging from approximation problems, classification problems, and time series predictions show that GEFREX reaches a smaller error than found in previous works with the same or a smaller number of rules. Further, it succeeds in identifying significant features. Although the SVD is used extensively, the learning time is decidedly reduced in comparison with previous work.

Distance-based fuzzy MCDM approach for evaluating flexible manufacturing system alternatives

Abstract: Considering the high required capital outlay and moderate risk of a flexible manufacturing system (FMS) investment, economic justification techniques are insufficient by themselves since they cannot cope with the benefits such as flexibility and enhanced quality offered by advanced manufacturing technologies. A robust decision-making procedure for evaluating FMS requires the consideration of both economic and strategic investment measures. A distance-based fuzzy multicriteria decision-making (MCDM) framework based on the concepts of ideal and anti-ideal solutions is presented for the selection of an FMS from a set of mutually exclusive alternatives. The proposed method provides the means for integrating the economic figure of merit with the strategic performance variables. The multicriteria decision approach presented here enables us to incorporate data in the forms of linguistic variables, triangular fuzzy numbers and crisp numbers into the evaluation process of FMS alternatives. Linguistic variables are...

Control Synthesis of Discrete-Time T–S Fuzzy Systems Based on a Novel Non-PDC Control Scheme

Abstract: This paper proposes relaxed stabilization conditions of discrete-time nonlinear systems in the Takagi-Sugeno (T-S) fuzzy form. By using the algebraic property of fuzzy membership functions, a novel nonparallel distributed compensation (non-PDC) control scheme is proposed based on a new class of fuzzy Lyapunov functions. Thus, relaxed stabilization conditions for the underlying closed-loop fuzzy system are developed by applying a new slack variable technique. In particular, some existing fuzzy Lyapunov functions and non-PDC control schemes are special cases of the new Lyapunov function and fuzzy control scheme, respectively. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.