On the use of fuzzy rule interpolation techniques for monotonic multi-input fuzzy rule base models

Constructing a monotonicity relating function is important, as many engineering problems revolve around a monotonicity relationship between input(s) and output(s). In this paper, we investigate the use of fuzzy rule interpolation techniques for monotonicity relating fuzzy inference system (FIS). A mathematical derivation on the conditions of an FIS to be monotone is provided. From the derivation, two conditions are necessary. The derivation suggests that the mapped consequence fuzzy set of an FIS to be of a monotonicity order. We further evaluate the use of fuzzy rule interpolation techniques in predicting a consequent associated with an observation according to the monotonicity order. There are several findings in this article. We point out the importance of an ordering criterion in rule selection for a multi-input FIS before the interpolation process; and hence, the practice of choosing the nearest rules may not be true in this case. To fulfill the monotonicity order, we argue with an example that conventional fuzzy rule interpolation techniques that predict each consequence separately is not suitable in this case. We further suggest another class of interpolation techniques that predicts the consequence of a set of observations simultaneously, instead of separately. This can be accomplished with the use of a search algorithm, such as the brute force, genetic algorithm or etc.

Fuzzy rule base assessment models : theoretical analyses and a case study

An assessment model is usually a mathematical model that produces a measuring index, in the form of a numerical score to a situation/object, with respect to the subject of measure. To allow a valid and useful comparison among various situations/objects according to their associated numerical scores to be made, two important properties, i.e., the monotone output property and output resolution properties, are essential in fuzzy inference-based assessment problems. In this paper, the conditions for a fuzzy assessment model to fulfill the monotone output property is investigated using a derivative approach. A guideline on how the input membership functions should be tuned is also provided. Besides, the output resolution property is defined as the derivative of the output of the assessment model with respect to the input, whereby the derivative should be greater than a minimum resolution. Based on the derivative, improvements to the output resolution property by refining the fuzzy production rules are suggested. A case study on the Bowles fuzzy RPN model to demonstrate the effectiveness of the properties is also included.

A recursive rule base adjustment algorithm for a fuzzy logic controller

This paper introduces a recursive rule base adjustment to enhance the performance of fuzzy logic controllers. Here the fuzzy controller is constructed on the basis of a decision table (DT), relying on membership functions and fuzzy rules that incorporate heuristic knowledge and operator experience. If the controller performance is not satisfactory, it has previously been suggested that the rule base be altered by combined tuning of membership functions and controller scaling factors. The alternative approach proposed here entails alteration of the fuzzy rule base. The recursive rule base adjustment algorithm proposed in this paper has the benefit that it is computationally more efficient for the generation of a DT, and advantage for online realization. Simulation results are presented to support this thesis. (c) 2005 Elsevier B.V. All rights reserved.

Bacterial algorithm applied for fuzzy rule extraction

This paper presents a method of using the so-colled "bacterial algorithm" (4,5) for extracting a fuzzy rule base from a training set. The bewly proposed bacterial evolutionary algorithm (BEA) is shown. In our application one bacterium corresponds to a fuzzy rule system.

Robust neurofuzzy rule base knowledge extraction and estimation using subspace decomposition combined with regularization and D-optimality

A new robust neurofuzzy model construction algorithm has been introduced for the modeling of a priori unknown dynamical systems from observed finite data sets in the form of a set of fuzzy rules. Based on a Takagi-Sugeno (T-S) inference mechanism a one to one mapping between a fuzzy rule base and a model matrix feature subspace is established. This link enables rule based knowledge to be extracted from matrix subspace to enhance model transparency. In order to achieve maximized model robustness and sparsity, a new robust extended Gram-Schmidt (G-S) method has been introduced via two effective and complementary approaches of regularization and D-optimality experimental design. Model rule bases are decomposed into orthogonal subspaces, so as to enhance model transparency with the capability of interpreting the derived rule base energy level. A locally regularized orthogonal least squares algorithm, combined with a D-optimality used for subspace based rule selection, has been extended for fuzzy rule regularization and subspace based information extraction. By using a weighting for the D-optimality cost function, the entire model construction procedure becomes automatic. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

A new framework with similarity reasoning and monotone fuzzy rule relabeling for fuzzy inference systems

A complete and monotonically-ordered fuzzy rule base is necessary to maintain the monotonicity property of a Fuzzy Inference System (FIS). In this paper, a new monotone fuzzy rule relabeling technique to relabel a non-monotone fuzzy rule base provided by domain experts is proposed. Even though the Genetic Algorithm (GA)-based monotone fuzzy rule relabeling technique has been investigated in our previous work [7], the optimality of the approach could not be guaranteed. The new fuzzy rule relabeling technique adopts a simple brute force search, and it can produce an optimal result. We also formulate a new two-stage framework that encompasses a GA-based rule selection scheme, the optimization based-Similarity Reasoning (SR) scheme, and the proposed monotone fuzzy rule relabeling technique for preserving the monotonicity property of the FIS model. Applicability of the two-stage framework to a real world problem, i.e., failure mode and effect analysis, is further demonstrated. The results clearly demonstrate the usefulness of the proposed framework.

A new monotonicity index for fuzzy rule-based systems

A search in the literature reveals that mathematical conditions (usually sufficient conditions) for the Fuzzy Inference System (FIS) models to satisfy the monotonicity property have been developed. A monotonically-ordered fuzzy rule base is important to maintain the monotonicity property of an FIS. However, it may difficult to obtain a monotonically-ordered fuzzy rule base in practice. We have previously introduced the idea of fuzzy rule relabeling to tackle this problem. In this paper, we further propose a monotonicity index for the FIS system, which serves as a metric to indicate the degree of a fuzzy rule base fulfilling the monotonicity property. The index is useful to provide an indication whether a fuzzy rule base should (or should not) be used in practice, even with fuzzy rule relabeling. To illustrate the idea, the zero-order Sugeno FIS model is exemplified. We add noise as errors into the fuzzy rule base to formulate a set of non-monotone fuzzy rules. As such, the metric also acts as a measure of noise in the fuzzy rule base. The results show that the proposed metric is useful to indicate the degree of a fuzzy rule base fulfilling the monotonicity property.

Fuzzy rule-based system for evaluation of uncertainty transaction in cassava chain

A fuzzy ruled-based system was developed in this study and resulted in an index indicating the level of uncertainty related to commercial transactions between cassava growers and their dealers. The fuzzy system was developed based on Transaction Cost Economics approach. The fuzzy system was developed from input variables regarding information sharing between grower and dealer on “Demand/purchase Forecasting”, “Production Forecasting” and “Production Innovation”. The output variable is the level of uncertainty regarding the transaction between seller and buyer agent, which may serve as a system for detecting inefficiencies. Evidences from 27 cassava growers registered in the Regional Development Offices of Tupa and Assis, São Paulo, Brazil, and 48 of their dealers supported the development of the system. The mathematical model indicated that 55% of the growers present a Very High level of uncertainty, 33% present Medium or High. The others present Low or Very Low level of uncertainty. From the model, simulations of external interferences can be implemented in order to improve the degree of uncertainty and, thus, lower transaction costs.

Data-driven fuzzy rule generation and its application for student academic performance evaluation

K. Rasmani and Q. Shen. Data-driven fuzzy rule generation and its application for student academic performance evaluation. Applied Intelligence, 25(3):305-319, 2006.

Iterative vs Simultaneous Fuzzy Rule Induction

M. Galea and Q. Shen. Iterative vs Simultaneous Fuzzy Rule Induction. Proceedings of the 14th International Conference on Fuzzy Systems, pages 767-772.

Subsethood-based Fuzzy Rule Models and their Application to Student Performance

K. Rasmani and Q. Shen. Subsethood-based Fuzzy Rule Models and their Application to Student Performance Classification. Proceedings of the 14th International Conference on Fuzzy Systems, pages 755-760, 2005.

Adaptive Measurement-Based Policy-Driven QoS Management with Fuzzy-Rule-based Resource Allocation

Fixed and wireless networks are increasingly converging towards common connectivity with IP-based core networks. Providing effective end-to-end resource and QoS management in such complex heterogeneous converged network scenarios requires unified, adaptive and scalable solutions to integrate and co-ordinate diverse QoS mechanisms of different access technologies with IP-based QoS. Policy-Based Network Management (PBNM) is one approach that could be employed to address this challenge. Hence, a policy-based framework for end-to-end QoS management in converged networks, CNQF (Converged Networks QoS Management Framework) has been proposed within our project. In this paper, the CNQF architecture, a Java implementation of its prototype and experimental validation of key elements are discussed. We then present a fuzzy-based CNQF resource management approach and study the performance of our implementation with real traffic flows on an experimental testbed. The results demonstrate the efficacy of our resource-adaptive approach for practical PBNM systems

Estimating fuzzy membership functions parameters by the levenberg-marquardt algorithm

In previous papers from the authors fuzzy model identification methods were discussed. The bacterial algorithm for extracting fuzzy rule base from a training set was presented. The Levenberg-Marquardt algorithm was also proposed for determining membership functions in fuzzy systems. In this paper the Levenberg-Marquardt technique is improved to optimise the membership functions in the fuzzy rules without Ruspini-partition. The class of membership functions investigated is the trapezoidal one as it is general enough and widely used. The method can be easily extended to arbitrary piecewise linear functions as well.