Infinite-Level Interpolation for Inference with Sparse Fuzzy Rules: Fundamental Analysis Toward Practical Use

2013 ◽  
Vol 17 (1) ◽  
pp. 44-59 ◽  
Author(s):  
Kiyohiko Uehara ◽  
◽  
Kaoru Hirota ◽  
Keyword(s):  
Feasibility Study ◽  
Infinite Number ◽  
Fuzzy Rule ◽  
Fuzzy Rules ◽  
Nonlinear Mapping ◽  
Fundamental Analysis ◽  
Mapping Accuracy ◽  
Multi Level

Infinite-level interpolation is proposed for inference with sparse fuzzy rules. It is based onmulti-level interpolation where fuzzy rule interpolation is performed at a number of multi-level points. Multi-level points are defined by the bounds of α-cuts of each given fact. As a feasibility study, fundamental analysis is focused on in order to theoretically derive convergent consequences in increasing the number of the levels of α for the α-cuts. By increasing the number of the levels, nonlinear mapping by the inference is made more precise in reflecting the distribution forms of sparse fuzzy rules to consequences. The convergent consequences make it unnecessary to examine the number of the levels for improving the mapping accuracy. It is confirmed that each of the consequences deduced with simulations converges to one theoretically derived with an infinite number of the levels of α. It is thereby proved that the fundamental analysis has its validity. Toward the practical use of the convergent consequences, further discussions may be possible to extend the fundamental analysis, considering practical conditions.

Inference with Fuzzy Rule Interpolation at an Infinite Number of Activating Points

2015 ◽  
Vol 19 (1) ◽  
pp. 74-90 ◽  
Author(s):  
Kiyohiko Uehara ◽  
◽  
Kaoru Hirota ◽  
Keyword(s):  
Lower Bounds ◽  
Infinite Number ◽  
Fuzzy Rule ◽  
Fuzzy Rules ◽  
Nonlinear Mapping ◽  
Membership Functions ◽  
Inference Method ◽  
Generalized Mean ◽  
Simulation Results ◽  
Α Level

An inference method for sparse fuzzy rules is proposed which interpolates fuzzy rules at an infinite number of activating points and deduces consequences based on α-GEMII (α-level-set and generalized-mean-based inference). The activating points, proposed in this paper, are determined so as to activate interpolated fuzzy rules by each given fact. The proposed method is named α-GEMINAS (α-GEMII-based inference with fuzzy rule interpolation at an infinite number of activating points). α-GEMINAS solves the problem in infinite-level interpolation where fuzzy rules are interpolated at the least upper and greatest lower bounds of an infinite number of α-cuts of each given fact. The infinite-level interpolation can nonlinearly transform the shapes of given membership functions to those of deduced ones in accordance even with sparse fuzzy rules under some conditions. These conditions are, however, strict from a practical viewpoint. α-GEMINAS can deduce consequences without these conditions and provide nonlinear mapping comparable with infinite-level interpolation. Simulation results demonstrate these properties of α-GEMINAS. Thereby, it is found that α-GEMINAS is practical and applicable to a wide variety of fields.

Inference for Nonlinear Mapping with Sparse Fuzzy Rules Based on Multi-Level Interpolation

2011 ◽  
Vol 15 (3) ◽  
pp. 264-287 ◽  
Author(s):  
Kiyohiko Uehara ◽  
◽  
Shun Sato ◽  
Kaoru Hirota ◽  
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Rules ◽  
Nonlinear Mapping ◽  
Mean Square ◽  
Inference Method ◽  
Multi Level ◽  
Simulation Results ◽  
Conventional Methods ◽  
Rule Bases ◽  
Mean Square Errors

An inference method is proposed for sparse fuzzy rules on the basis of interpolations at a number of points determined by α-cuts of given facts. The proposed method can perform nonlinear mapping even with sparse rule bases when each given fact activates a number of fuzzy rules which represent nonlinear relations. The operations for the nonlinear mapping are exactly the same as for the case when given facts activate no fuzzy rules due to the sparseness of rule bases. Such nonlinear mapping cannot be provided by conventional methods for sparse fuzzy rules. In evaluating the proposed method, mean square errors are adopted to indicate difference between deduced consequences and fuzzy sets transformed by nonlinear fuzzy-valued functions to be represented with sparse fuzzy rules. Simulation results show that the proposed method can follow the nonlinear fuzzy-valued functions. The proposed method contributes to both reducing the number of fuzzy rules and providing nonlinear mapping with sparse rule bases.

scholarly journals Multi-Level Interpolation for Inference with Sparse Fuzzy Rules: An Extended Way of Generating Multi-Level Points

2013 ◽  
Vol 17 (2) ◽  
pp. 127-148 ◽  
Author(s):  
Kiyohiko Uehara ◽  
◽  
Kaoru Hirota ◽  
Keyword(s):  
Fuzzy Rules ◽  
Simulation Studies ◽  
Mapping Accuracy ◽  
Basic Study ◽  
Adaptive Inference ◽  
Core Sets ◽  
Multi Level ◽  
Support Sets ◽  
Rules Changes ◽  
Effective Use

As an extended way for inference based on multi-level interpolation, the number of multi-level points, generated with the α-cuts of given facts, is increased by making larger the number of levels of α. The conventional way uses the number of the levels adopted to define each given fact by α-cuts. A basic study is performed with triangular membership functions, where it is examined how the accuracy of mapping with fuzzy rules changes in increasing the number of the levels. It is also examined how deduced consequences behave when the number is increased. Moreover, convergent core sets of consequences are theoretically derived in the increase by the effective use of non-adaptive inference operations for core sets. They are used as references in simulation studies. Increasing the number of the levels provides nonlinear mapping with more precise reflection of distribution forms of sparse fuzzy rules to consequences. The basic study here contributes to improving the reflection accuracy. In simulations for the basic study, it is found that the mapping accuracy improves when the number of levels of α is increased. It is also confirmed that deduced core sets converge to those theoretically derived. Support sets are also found to converge in increasing the number of the levels. The core sets and support sets of deduced consequences do not, however, monotonically converge. This property causes difficulty in determining the optimized number of the levels so as to satisfy required mapping accuracy. In order to solve this problem, further discussions may be possible to theoretically derive convergent consequences and to use them in practical fields, in accordance with the theoretically derived core sets mentioned above.

Multi-Level Control of Fuzzy-Constraint Propagation in Inference Based on α-Cuts and Generalized Mean

2013 ◽  
Vol 17 (4) ◽  
pp. 647-662 ◽  
Author(s):  
Kiyohiko Uehara ◽  
◽  
Kaoru Hirota ◽  
Keyword(s):  
Fuzzy Sets ◽  
Level Set ◽  
Constraint Propagation ◽  
Fuzzy Rules ◽  
Nonlinear Mapping ◽  
Fuzzy Input ◽  
Fuzzy Constraint ◽  
Multi Level ◽  
Generalized Mean ◽  
Α Level

An inference method is proposed, which can perform nonlinear mapping between convex fuzzy sets and present a scheme of various fuzzy-constraint propagation from given facts to deduced consequences. The basis of nonlinear mapping is provided by α-GEMII (α-level-set and generalized-mean-based inference) whereas the control of fuzzy-constraint propagation is based on the compositional rule of inference (CRI). The fuzzy-constraint propagation is controlled at the multi-level of α in its α-cut-based operations. The proposed method is named α-GEMS (α-level-set and generalized-mean-based inference in synergy with composition). Although α-GEMII can perform the nonlinear mapping according to a number of fuzzy rules in parallel, it has limitations in the control of fuzzy-constraint propagation and therefore has difficulty in constructing models of various given systems. In contrast, CRI-based inference can rather easily control fuzzy-constraint propagation with high understandability especially when a single fuzzy rule is used. It is difficult, however, to perform nonlinear mapping between convex fuzzy sets by using a number of fuzzy rules in parallel. α-GEMS can solve both of these problems. Simulation results show that α-GEMS is performed well in the nonlinear mapping and fuzzy-constraint propagation. α-GEMS is expected to be applied to modeling of given systems with various fuzzy input-output relations.

Multi-Level Control of Fuzzy-Constraint Propagation in Inference with Fuzzy Rule Interpolation at an Infinite Number of Activating Points

2017 ◽  
Vol 21 (3) ◽  
pp. 425-447 ◽  
Author(s):  
Kiyohiko Uehara ◽  
◽  
Kaoru Hirota ◽  
Keyword(s):  
Fuzzy Rule ◽  
Constraint Propagation ◽  
Nonlinear Mapping ◽  
Level Control ◽  
Inference Method ◽  
Fuzzy Constraints ◽  
Fuzzy Input ◽  
Fuzzy Constraint ◽  
Multi Level ◽  
Α Level

An inference method is proposed, which can control the degree to which the fuzzy constraints of given facts are propagated to those of consequences via the nonlinear mapping represented by fuzzy rules. The conventional method, α-GEMST (α-level-set and generalized-mean-based inference in synergy with composition via linguistic-truth-value control), has limitations in the control of the propagation degree. In contrast, the proposed method can fully control the fuzzy-constraint propagation to a different degree with each fuzzy rule. After the nonlinear mapping, the proposed method performs fuzzy-logic-based control for further fuzzy-constraint propagation wherein evaluations are conducted via linguistic truth values to suppress the excessive specificity decrease in deduced consequences. Thereby, fuzzy constraints can be propagated in various ways by selecting one pair from the widely available implications and compositional operations. The proposed method controls the fuzzy-constraint propagation at the multi-levels of α in its α-cut-based operations. This scheme contributes to fast computation with parallel processing for each level of α. Simulation results illustrate that the proposed method can properly control the propagation degree. The proposed method is expected to be applied to the modeling of given systems with various fuzzy input-output relations.

A Multi-Level Fuzzy Rule Based Control Strategy for Maglev System

EPE Journal ◽  
2000 ◽  
Vol 10 (1) ◽  
pp. 26-31 ◽  
Author(s):  
Moinuddin ◽  
A.S. Siddiqui ◽  
A.K. Sharma ◽  
J.P. Gupta
Keyword(s):  
Control Strategy ◽  
Fuzzy Rule ◽  
Rule Based ◽  
Maglev System ◽  
Multi Level

Corner Detection Using Fuzzy Principles

2013 ◽  
pp. 498-512
Author(s):  
Erik Cuevas ◽  
Daniel Zaldivar ◽  
Marco Perez-Cisneros
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Systems ◽  
Fuzzy Rule ◽  
Important Task ◽  
Fuzzy Rules ◽  
Corner Detection ◽  
Illumination Change ◽  
Benchmark Test ◽  
Rule Based ◽  
Rule Based System

Reliable corner detection is an important task in pattern recognition applications. In this chapter an approach based on fuzzy-rules to detect corners even under imprecise information is presented. The uncertainties arising due to various types of imaging defects such as blurring, illumination change, noise, et cetera. Fuzzy systems are well known for efficient handling of impreciseness. In order to handle the incompleteness arising due to imperfection of data, it is reasonable to model corner properties by a fuzzy rule-based system. The robustness of the proposed algorithm is compared with well known conventional detectors. The performance is tested on a number of benchmark test images to illustrate the efficiency of the algorithm in noise presence.

Support Vector Machine based Hybrid Classifiers and Rule Extraction thereof

2010 ◽  
pp. 404-426 ◽  
Author(s):  
M. A.H. Farquad ◽  
V. Ravi ◽  
Raju S. Bapi
Keyword(s):  
Radial Basis Function Network ◽  
Hybrid Approach ◽  
Fuzzy Rule ◽  
Rule Extraction ◽  
Bankruptcy Prediction ◽  
Fuzzy Rules ◽  
Machine Learning Techniques ◽  
Support Vector ◽  
Support Vectors ◽  
Hybrid Classifiers

Support vector machines (SVMs) have proved to be a good alternative compared to other machine learning techniques specifically for classification problems. However just like artificial neural networks (ANN), SVMs are also black box in nature because of its inability to explain the knowledge learnt in the process of training, which is very crucial in some applications like medical diagnosis, security and bankruptcy prediction etc. In this chapter a novel hybrid approach for fuzzy rule extraction based on SVM is proposed. This approach handles rule-extraction as a learning task, which proceeds in two major steps. In the first step the authors use labeled training patterns to build an SVM model, which in turn yields the support vectors. In the second step extracted support vectors are used as input patterns to fuzzy rule based systems (FRBS) to generate fuzzy “if-then” rules. To study the effectiveness and validity of the extracted fuzzy rules, the hybrid SVM+FRBS is compared with other classification techniques like decision tree (DT), radial basis function network (RBF) and adaptive network based fuzzy inference system. To illustrate the effectiveness of the hybrid developed, the authors applied it to solve a bank bankruptcy prediction problem. The dataset used pertain to Spanish, Turkish and US banks. The quality of the extracted fuzzy rules is evaluated in terms of fidelity, coverage and comprehensibility.

Optimal Design for Fuzzy Controller by Ant Colony Algorithm

2010 ◽  
Vol 439-440 ◽  
pp. 1190-1196 ◽  
Author(s):  
Bao Jiang Zhao
Keyword(s):  
Ant Colony Algorithm ◽  
Inverted Pendulum ◽  
Fuzzy Controller ◽  
Fuzzy Rule ◽  
Ant Colony ◽  
Fuzzy Rules ◽  
Real Time Control ◽  
Time Control ◽  
Information Updating ◽  
Fuzzy Logical

Fuzzy logical controller is one of the most important applications of fuzzy-rule-based system that models the human decision processing with a collection of fuzzy rules. In this paper, an adaptive ant colony algorithm is proposed based on dynamically adjusting the strategy of selection of the paths and the strategy of the trail information updating. The algorithm is used to design a fuzzy logical controller automatically for real-time control of an inverted pendulum. In order to avoid the combinatorial explosion of fuzzy rules due to multivariable inputs, state variable synthesis scheme is employed to reduce the number of fuzzy rules greatly. Experimental results show that the designed controller can control actual inverted pendulum successfully.

New classification technique: fuzzy oblique decision tree

2018 ◽  
Vol 41 (8) ◽  
pp. 2185-2195
Author(s):  
Yuliang Cai ◽  
Huaguang Zhang ◽  
Qiang He ◽  
Shaoxin Sun
Keyword(s):  
Decision Tree ◽  
Decision Trees ◽  
Main Idea ◽  
Fuzzy Rule ◽  
Decision Function ◽  
Fuzzy Rules ◽  
Leaf Node ◽  
Biomedical Data ◽  
Data Set ◽  
Afs Theory

Based on axiomatic fuzzy set (AFS) theory and fuzzy information entropy, a novel fuzzy oblique decision tree (FODT) algorithm is proposed in this paper. Traditional axis-parallel decision trees only consider a single feature at each non-leaf node, while oblique decision trees partition the feature space with an oblique hyperplane. By contrast, the FODT takes dynamic mining fuzzy rules as a decision function. The main idea of the FODT is to use these fuzzy rules to construct leaf nodes for each class in each layer of the tree; the samples that cannot be covered by the fuzzy rules are then put into an additional node – the only non-leaf node in this layer. Construction of the FODT consists of four major steps: (a) generation of fuzzy membership functions automatically by AFS theory according to the raw data distribution; (b) extraction of dynamically fuzzy rules in each non-leaf node by the fuzzy rule extraction algorithm (FREA); (c) construction of the FODT by the fuzzy rules obtained from step (b); and (d) determination of the optimal threshold [Formula: see text] to generate a final tree. Compared with five traditional decision trees (C4.5, LADtree (LAD), Best-first tree (BFT), SimpleCart (SC) and NBTree (NBT)) and a recently obtained fuzzy rules decision tree (FRDT) on eight UCI machine learning data sets and one biomedical data set (ALLAML), the experimental results demonstrate that the proposed algorithm outperforms the other decision trees in both classification accuracy and tree size.

Sign in / Sign up

Export Citation Format

Share Document