Investigating The Piece-Wise Linearity And Benchmark Related To Koczy-Hirota Fuzzy Linear Interpolation

arXiv.org Artificial Intelligence

Fuzzy Rule Interpolation (FRI) reasoning methods have been introduced to address sparse fuzzy rule bases and reduce complexity. The first FRI method was the Koczy and Hirota (KH) proposed "Linear Interpolation". Besides, several conditions and criteria have been suggested for unifying the common requirements FRI methods have to satisfy. One of the most conditions is restricted the fuzzy set of the conclusion must preserve a Piece-Wise Linearity (PWL) if all antecedents and consequents of the fuzzy rules are preserving on PWL sets at {\alpha}-cut levels. The KH FRI is one of FRI methods which cannot satisfy this condition. Therefore, the goal of this paper is to investigate equations and notations related to PWL property, which is aimed to highlight the problematic properties of the KH FRI method to prove its efficiency with PWL condition. In addition, this paper is focusing on constructing benchmark examples to be a baseline for testing other FRI methods against situations that are not satisfied with the linearity condition for KH FRI.


New Movement and Transformation Principle of Fuzzy Reasoning and Its Application to Fuzzy Neural Network

arXiv.org Artificial Intelligence

In this paper, we propose a new fuzzy reasoning principle, so called Movement and Transformation Principle(MTP). This Principle is to obtain a new fuzzy reasoning result by Movement and Transformation the consequent fuzzy set in response to the Movement, Transformation, and Movement-Transformation operations between the antecedent fuzzy set and fuzzificated observation information. And then we presented fuzzy modus ponens and fuzzy modus tollens based on MTP. We compare proposed method with Mamdani fuzzy system, Sugeno fuzzy system, Wang distance type fuzzy reasoning method and Hellendoorn functional type method. And then we applied to the learning experiments of the fuzzy neural network based on MTP and compared it with the Sugeno method. Through prediction experiments of fuzzy neural network on the precipitation data and security situation data, learning accuracy and time performance are clearly improved. Consequently we show that our method based on MTP is computationally simple and does not involve nonlinear operations, so it is easy to handle mathematically.


Optimal Fuzzy Model Construction with Statistical Information using Genetic Algorithm

arXiv.org Artificial Intelligence

Fuzzy rule based models have a capability to approximate any continuous function to any degree of accuracy on a compact domain. The majority of FLC design process relies on heuristic knowledge of experience operators. In order to make the design process automatic we present a genetic approach to learn fuzzy rules as well as membership function parameters. Moreover, several statistical information criteria such as the Akaike information criterion (AIC), the Bhansali-Downham information criterion (BDIC), and the Schwarz-Rissanen information criterion (SRIC) are used to construct optimal fuzzy models by reducing fuzzy rules. A genetic scheme is used to design Takagi-Sugeno-Kang (TSK) model for identification of the antecedent rule parameters and the identification of the consequent parameters. Computer simulations are presented confirming the performance of the constructed fuzzy logic controller.


A qualitative-fuzzy framework for nonlinear black-box system identification

AAAI Conferences

System Identification (sl) deals with the development and analysis of methods which infer a quantitative model of the system dynamics from observed data (Haber & Unbehauen 1990; Juditsky et al. 1995; Ljung 1987; S6derstrSm & Stoiea 1989).


On the Functional Equivalence of TSK Fuzzy Systems to Neural Networks, Mixture of Experts, CART, and Stacking Ensemble Regression

arXiv.org Artificial Intelligence

Fuzzy systems have achieved great success in numerous applications. However, there are still many challenges in designing an optimal fuzzy system, e.g., how to efficiently train its parameters, how to improve its performance without adding too many parameters, how to balance the trade-off between cooperations and competitions among the rules, how to overcome the curse of dimensionality, etc. Literature has shown that by making appropriate connections between fuzzy systems and other machine learning approaches, good practices from other domains may be used to improve the fuzzy systems, and vice versa. This paper gives an overview on the functional equivalence between Takagi-Sugeno-Kang fuzzy systems and four classic machine learning approaches -- neural networks, mixture of experts, classification and regression trees, and stacking ensemble regression -- for regression problems. We also point out some promising new research directions, inspired by the functional equivalence, that could lead to solutions to the aforementioned problems. To our knowledge, this is so far the most comprehensive overview on the connections between fuzzy systems and other popular machine learning approaches, and hopefully will stimulate more hybridization between different machine learning algorithms.