913 research outputs found
Measuring Relations Between Concepts In Conceptual Spaces
The highly influential framework of conceptual spaces provides a geometric
way of representing knowledge. Instances are represented by points in a
high-dimensional space and concepts are represented by regions in this space.
Our recent mathematical formalization of this framework is capable of
representing correlations between different domains in a geometric way. In this
paper, we extend our formalization by providing quantitative mathematical
definitions for the notions of concept size, subsethood, implication,
similarity, and betweenness. This considerably increases the representational
power of our formalization by introducing measurable ways of describing
relations between concepts.Comment: Accepted at SGAI 2017 (http://www.bcs-sgai.org/ai2017/). The final
publication is available at Springer via
https://doi.org/10.1007/978-3-319-71078-5_7. arXiv admin note: substantial
text overlap with arXiv:1707.05165, arXiv:1706.0636
New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems
This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of TakagiâSugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2âdecades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parametersâ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use
Fuzzy Interpolation Systems and Applications
Fuzzy inference systems provide a simple yet effective solution to complex non-linear problems, which have been applied to numerous real-world applications with great success. However, conventional fuzzy inference systems may suffer from either too sparse, too complex or imbalanced rule bases, given that the data may be unevenly distributed in the problem space regardless of its volume. Fuzzy interpolation addresses this. It enables fuzzy inferences with sparse rule bases when the sparse rule base does not cover a given input, and it simplifies very dense rule bases by approximating certain rules with their neighbouring ones. This chapter systematically reviews different types of fuzzy interpolation approaches and their variations, in terms of both the interpolation mechanism (inference engine) and sparse rule base generation. Representative applications of fuzzy interpolation in the field of control are also revisited in this chapter, which not only validate fuzzy interpolation approaches but also demonstrate its efficacy and potential for wider applications
Scale and move transformation-based fuzzy interpolative reasoning:A revisit
This paper generalises the previously proposed
interpolative reasoning method 151 to cover interpolations involving
complex polygon, Gaussian or other bell-shaped fuzzy
membership functions. This can be achieved by the generality
of the proposed scale and move transformations. The method
works by first constructing a new inference rule via manipulating
two given adjacent rules, and then by using scale and move
transformations to convert the intermediate inference results into
the final derived conclusions. This generalised method has two
advantages thanks to the elegantly proposed transformations: I)
It can easily handle interpolation of multiple antecedent variables
with simple computation; and 2) It guarantees the uniqueness as
well as normality and convexity of the resulting interpolated fuzzy
sets. Numerical examples are provided to demonstrate the use of
this method
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