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 portfolio allocation models through a new risk measure and fuzzy sharpe ratio

A new portfolio risk measure that is the uncertainty of portfolio fuzzy return is introduced in this paper. Beyond the well-known Sharpe ratio (i.e., the reward-to-variability ratio) in modern portfolio theory, we initiate the so-called fuzzy Sharpe ratio in the fuzzy modeling context. In addition to the introduction of the new risk measure, we also put forward the reward-to-uncertainty ratio to assess the portfolio performance in fuzzy modeling. Corresponding to two approaches based on TM and TW fuzzy arithmetic, two portfolio optimization models are formulated in which the uncertainty of portfolio fuzzy returns is minimized, while the fuzzy Sharpe ratio is maximized. These models are solved by the fuzzy approach or by the genetic algorithm (GA). Solutions of the two proposed models are shown to be dominant in terms of portfolio return uncertainty compared with those of the conventional mean-variance optimization (MVO) model used prevalently in the financial literature. In terms of portfolio performance evaluated by the fuzzy Sharpe ratio and the reward-to-uncertainty ratio, the model using TW fuzzy arithmetic results in higher performance portfolios than those obtained by both the MVO and the fuzzy model, which employs TM fuzzy arithmetic. We also find that using the fuzzy approach for solving multiobjective problems appears to achieve more optimal solutions than using GA, although GA can offer a series of well-diversified portfolio solutions diagrammed in a Pareto frontier.

Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model

When using linguistic approaches to solve decision problems, we need the techniques for computing with words (CW). Together with the 2-tuple fuzzy linguistic representation models (i.e., the Herrera and Mart´ınez model and the Wang and Hao model), some computational techniques for CW are also developed. In this paper, we define the concept of numerical scale and extend the 2-tuple fuzzy linguistic representation models under the numerical scale.We find that the key of computational techniques
based on linguistic 2-tuples is to set suitable numerical scale with
the purpose of making transformations between linguistic 2-tuples
and numerical values. By defining the concept of the transitive
calibration matrix and its consistent index, this paper develops an optimization model to compute the numerical scale of the linguistic term set. The desired properties of the optimization model are also presented. Furthermore, we discuss how to construct the transitive calibration matrix for decision problems using linguistic preference relations and analyze the linkage between the consistent index of the transitive calibration matrix and one of the linguistic preference relations. The results in this paper are pretty helpful to complete the fuzzy 2-tuple representation models for CW.

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.

Building monotonicity-preserving fuzzy inference models with optimization-based similarity reasoning and a monotonicity index

In this paper, a novel approach to building a Fuzzy Inference System (FIS) that preserves the monotonicity property is proposed. A new fuzzy re-labeling technique to re-label the consequents of fuzzy rules in the database (before the Similarity Reasoning process) and a monotonicity index for use in FIS modeling are introduced. The proposed approach is able to overcome several restrictions in our previous work that uses mathematical conditions in building monotonicity-preserving FIS models. Here, we show that the proposed approach is applicable to different FIS models, which include the zero-order Sugeno FIS and Mamdani models. Besides, the proposed approach can be extended to undertake problems related to the local monotonicity property of FIS models. A number of examples to demonstrate the usefulness of the proposed approach are presented. The results indicate the usefulness of the proposed approach in constructing monotonicity-preserving FIS models.

On the use of fuzzy inference techniques in assessment models : part I — theoretical properties

An assessment model is a mathematical model that produces a measuring index, either in the form of a numerical score or a category to a situation/object, with respect to the subject of measure. From the numerical score, decision can be made and action can be taken. To allow valid and useful comparisons among various situations/objects according to their associated numerical scores to be made, the monotone output property and the output resolution property are essential in fuzzy inference-based assessment problems. We investigate the conditions for a fuzzy assessment model to fulfill the monotone output property 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 its input. This derivative should be greater than the minimum resolution required. From the derivative, we suggest improvements to the output resolution property by refining the fuzzy production rules.

On the use of fuzzy inference techniques in assessment models : part II : industrial applications

In this paper, we study the applicability of the monotone output property and the output resolution property in fuzzy assessment models to two industrial Failure Mode and Effect Analysis (FMEA) problems. First, the effectiveness of the monotone output property in a single-input fuzzy assessment model is demonstrated with a proposed fuzzy occurrence model. Then, the usefulness of the two properties to a multi-input fuzzy assessment model, i.e., the Bowles fuzzy Risk Priority Number (RPN) model, is assessed. The experimental results indicate that both the fuzzy occurrence model and Bowles fuzzy RPN model are able to fulfill the monotone output property, with the derived conditions (in Part I) satisfied. In addition, the proposed rule refinement technique is able to improve the output resolution property of the Bowles fuzzy RPN model.

Sliding mode-like learning control for SISO complex systems with T-S fuzzy models

In this paper, a sliding mode-like learning control scheme is developed for a class of single input single output (SISO) complex systems. First, the Takagi-Sugeno (T-S) fuzzy modelling technique is employed to model the uncertain complex dynamical systems. Second, a sliding mode-like learning control is designed to drive the sliding variable to converge to the sliding surface, and the system states can then asymptotically converge to zero on the sliding surface. The advantages of this scheme are that: 1) the information about the uncertain system dynamics and the system model structure is not required for the design of the learning controller; 2) the closed-loop system behaves with a strong robustness with respect to uncertainties; 3) the control input is chattering-free. The sufficient conditions for the sliding mode-like learning control to stabilise the global fuzzy model are discussed in detail. A simulation example for the control of an inverted pendulum cart is presented to demonstrate the effectiveness of the proposed control scheme.

Australian forex market anaylsis using connectionist models

The need for intelligent monitoring systems has become a necessity to keep track of the complex forex market. The forex market is difficult to understand by an average individual. However, once the market is broken down into simple terms, the average individual can begin to understand the foreign exchange market and use it as a financial instrument for future investing. This paper is an attempt to compare the performance of a Takagi-Sugeno type neuro-fuzzy system and a feed forward neural network trained using the scaled conjugate gradient algorithm to predict the average monthly forex rates. The exchange values of Australian dollar are considered with respect to US dollar, Singapore dollar, New Zealand dollar, Japanese yen and United Kingdom pound. The connectionist models were trained using 70% of the data and remaining was used for testing and validation purposes. It is observed that the proposed connectionist models were able to predict the average forex rates one month ahead accurately. Experiment results also reveal that neuro-fuzzy technique performed better than the neural network.

Short term load forecasting using interval type-2 fuzzy logic systems

Accurate Short Term Load Forecasting (STLF) is essential for a variety of decision making processes. However, forecasting accuracy may drop due to presence of uncertainty in the operation of energy systems or unexpected behavior of exogenous variables. This paper proposes the application of Interval Type-2 Fuzzy Logic Systems (IT2 FLSs) for the problem of STLF. IT2 FLSs, with extra degrees of freedom, are an excellent tool for handling prevailing uncertainties and improving the prediction accuracy. Experiments conducted with real datasets show that IT2 FLS models appropriately approximate future load demands with an acceptable accuracy. Furthermore, they demonstrate an encouraging degree of accuracy superior to feedforward neural networks used in this study.

Interval type-2 fuzzy logic systems for load forecasting : a comparative study

Accurate short term load forecasting (STLF) is essential for a variety of decision-making processes. However, forecasting accuracy can drop due to the presence of uncertainty in the operation of energy systems or unexpected behavior of exogenous variables. This paper proposes the application of Interval Type-2 Fuzzy Logic Systems (IT2 FLSs) for the problem of STLF. IT2 FLSs, with additional degrees of freedom, are an excellent tool for handling uncertainties and improving the prediction accuracy. Experiments conducted with real datasets show that IT2 FLS models precisely approximate future load demands with an acceptable accuracy. Furthermore, they demonstrate an encouraging degree of accuracy superior to feedforward neural networks and traditional type-1 Takagi-Sugeno-Kang (TSK) FLSs.

An empirical analysis of colour image segmentation using fuzzy c-means clustering

In this paper, an empirical analysis to examine the effects of image segmentation with different colour models using the fuzzy c-means (FCM) clustering algorithm is conducted. A qualitative evaluation method based on human perceptual judgement is used. Two sets of complex images, i.e., outdoor scenes and satellite imagery, are used for demonstration. These images are employed to examine the characteristics of image segmentation using FCM with eight different colour models. The results obtained from the experimental study are compared and analysed. It is found that the CIELAB colour model yields the best outcomes in colour image segmentation with FCM.

Enhancing the failure mode and effect analysis methodology with fuzzy inference techniques

Traditional Failure Mode and Effect Analysis (FMEA) adopts the Risk Priority Number (RPN) ranking model to evaluate failure risks, to rank failures, as well as to prioritize actions. Although this approach is simple, it suffers from several shortcomings. In this paper, we investigate a number of fuzzy inference techniques for determining the RPN scores, in an attempt to overcome the weaknesses associated with the traditional RPN model. The main objective is to examine the possibility of using fuzzy rule interpolation and reduction techniques to design new fuzzy RPN models. The performance of the fuzzy RPN models is evaluated using a real-world case study pertaining to the test handler process in a semiconductor manufacturing plant. The FMEA procedure for the test handler is performed, and a fuzzy RPN model is developed. In addition, improvement to the fuzzy RPN model is proposed by refining the weights of the fuzzy production rules, hence a new weighted fuzzy RPN model. The ability of the weighted fuzzy RPN model in failure risk evaluation with a reduced rule base is also demonstrated.

Fuzzy ARTMAP and hybrid evolutionary programming for pattern classification

In this paper, an Evolutionary Artificial Neural Network (EANN) that combines the Fuzzy ARTMAP (FAM) network and a Hybrid Evolutionary Programming (HEP) model is introduced. The proposed FAM-HEP model, which combines the strengths of FAM and HEP, is able to construct its network structure autonomously as well as to perform learning and evolutionary search and adaptation concurrently. The effectiveness of the proposed FAM-HEP network is assessed empirically using several benchmark data sets and a real medical diagnosis problem. The performance of FAM-HEP is analyzed, and the results are compared with those of FAM-EP, FAM, and other classification models. In general, the results of FAM-HEP are better than those of FAM-EP and FAM, and are comparable with those from other classification models. The study also reveals the potential of FAM-HEP as an innovative EANN model for undertaking pattern classification problems in general, and a promising computerized decision support tool for tackling medical diagnosis tasks in particular.

Authenticating the identity of computer users with typing biometrics and the fuzzy min-max neural network

In this paper, typing biometrics is applied as an additional security measure to the password-based or Personal Identification Number (PIN)-based systems to authenticate the identity of computer users. In particular, keystroke pressure and latency signals are analyzed using the Fuzzy Min-Max (FMM) neural network for authentication purposes. A special pressure-sensitive keyboard is designed to collect keystroke pressure signals, in addition to the latency signals, from computer users when they type their passwords. Based on the keystroke pressure and latency signals, the FMM network is employed to classify the computer users into two categories, i.e., genuine users or impostors. To assess the effectiveness of the proposed approach, two sets of experiments are conducted, and the results are compared with those from statistical methods and neural network models. The experimental outcomes positively demonstrate the potentials of using typing biometrics and the FMM network to provide an additional security layer for the current password-based or PIN-based methods in authenticating the identity of computer users.