A non-linear programming-based similarity reasoning scheme for modelling of monotonicity-preserving multi-input fuzzy inference systems

In this paper, the zero-order Sugeno Fuzzy Inference System (FIS) that preserves the monotonicity property is studied. The sufficient conditions for the zero-order Sugeno FIS model to satisfy the monotonicity property are exploited as a set of useful governing equations to facilitate the FIS modelling process. The sufficient conditions suggest a fuzzy partition (at the rule antecedent part) and a monotonically-ordered rule base (at the rule consequent part) that can preserve the monotonicity property. The investigation focuses on the use of two Similarity Reasoning (SR)-based methods, i.e., Analogical Reasoning (AR) and Fuzzy Rule Interpolation (FRI), to deduce each conclusion separately. It is shown that AR and FRI may not be a direct solution to modelling of a multi-input FIS model that fulfils the monotonicity property, owing to the difficulty in getting a set of monotonically-ordered conclusions. As such, a Non-Linear Programming (NLP)-based SR scheme for constructing a monotonicity-preserving multi-input FIS model is proposed. In the proposed scheme, AR or FRI is first used to predict the rule conclusion of each observation. Then, a search algorithm is adopted to look for a set of consequents with minimized root means square errors as compared with the predicted conclusions. A constraint imposed by the sufficient conditions is also included in the search process. Applicability of the proposed scheme to undertaking fuzzy Failure Mode and Effect Analysis (FMEA) tasks is demonstrated. The results indicate that the proposed NLP-based SR scheme is useful for preserving the monotonicity property for building a multi-input FIS model with an incomplete rule base.

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.

Prediction interval construction using interval type-2 fuzzy logic systems

This study proposes a novel non-parametric method for construction of prediction intervals (PIs) using interval type-2 Takagi-Sugeno-Kang fuzzy logic systems (IT2 TSK FLSs). The key idea in the proposed method is to treat the left and right end points of the type-reduced set as the lower and upper bounds of a PI. This allows us to construct PIs without making any special assumption about the data distribution. A new training algorithm is developed to satisfy conditions imposed by the associated confidence level on PIs. Proper adjustment of premise and consequent parameters of IT2 TSK FLSs is performed through the minimization of a PI-based objective function, rather than traditional error-based cost functions. This new cost function covers both validity and informativeness aspects of PIs. A metaheuristic method is applied for minimization of the non-linear non-differentiable cost function. Quantitative measures are applied for assessing the quality of PIs constructed using IT2 TSK FLSs. The demonstrated results for four benchmark case studies with homogenous and heterogeneous noise clearly show the proposed method is capable of generating high quality PIs useful for decision-making.

A fuzzy decision support method for customer preferences analysis based on Choquet integral

The explosion of the Web 2:0 platforms, with massive volume of user generated data, has presented many new opportunities as well as challenges for organizations in understanding consumer's behavior to support for business planning process. Feature based sentiment mining has been an emerging area in providing tools for automated opinion discovery and summarization to help business managers with achieving such goals. However, the current feature based sentiment mining systems were only able to provide some forms of sentiments summary with respect to product features, but impossible to provide insight into the decision making process of consumers. In this paper, we will present a relatively new decision support method based on Choquet Integral aggregation function, Shapley value and Interaction Index which is able to address such requirements of business managers. Using a study case of Hotel industry, we will demonstrate how this technique can be applied to effectively model the user's preference of (hotel) features. The presented method has potential to extend the practical capability of sentiment mining area, while, research findings and analysis are useful in helping business managers to define new target customers and to plan more effective marketing strategies.

Fuzzy ARTMAP and a hybrid chaos genetic algorithm for medical pattern classification

In this paper, an Evolutionary Artificial Neural Network (EANN), which combines the Fuzzy ARTMAP (FAM) neural network and a hybrid Chaos Genetic Algorithm (CGA), is proposed for undertaking pattern classification tasks. The hybrid CGA is a modified version of the hybrid real-coded genetic algorithms that includes a Chaotic Mapping Operator (CMO) in its search and adaptation process. It is used to evolve the connection weights in FAM, and the resulting EANN is known as FAM-hybrid CGA. The CMO in the hybrid CGA is used to generate a group of chromosomes that incorporates the characteristics of chaos. The chromosomes are then adapted with an arbitrary small amount of variation in every generation. As the evolution procedure proceeds, chromosomes with considerable differences are produced. Such chromosomes, which are located at different regions of interest in the solution space, are able to provide good solutions to undertake search and adaption problems. The effectiveness of the proposed FAM-hybrid CGA model is first evaluated using benchmark medical data sets from the UCI machine learning repository. Its applicability to medical decision support is then demonstrated using a real database of patient records with suspected Acute Coronary Syndrome. The results indicate that FAM-hybrid CGA is able to outperform its neural network counterpart (i.e., FAM), and it can be employed as a useful pattern classification tool for tackling medical decision support tasks.

On Operating Strategies of the Fuzzy Artmap Neural Network: A Comparative Study

In this paper, the effectiveness of three different operating strategies applied to the Fuzzy ARTMAP (FAM) neural network in pattern classification tasks is analyzed and compared. Three types of FAM, namely average FAM, voting FAM, and ordered FAM, are formed for experimentation. In average FAM, a pool of the FAM networks is trained using random sequences of input patterns, and the performance metrics from multiple networks are averaged. In voting FAM, predictions from a number of FAM networks are combined using the majority-voting scheme to reach a final output. In ordered FAM, a pre-processing procedure known as the ordering algorithm is employed to identify a fixed sequence of input patterns for training the FAM network. Three medical data sets are employed to evaluate the performances of these three types of FAM. The results are analyzed and compared with those from other learning systems. Bootstrapping has also been used to analyze and quantify the results statistically. [ABSTRACT FROM AUTHOR].

Fuzzy clustering of color and texture features for image segmentation: a study on satellite image retrieval

In this paper, a new image segmentation approach that integrates color and texture features using the fuzzy c-means clustering algorithm is described. To demonstrate the applicability of the proposed approach to satellite image retrieval, an interactive region-based image query system is designed and developed. A database comprising 400 multispectral satellite images is used to evaluate the performance of the system. The results are analyzed and discussed, and a performance comparison with other methods is included. The outcomes reveal that the proposed approach is able to improve the quality of the segmentation results as well as the retrieval performance.

Enhancing fuzzy inference system based criterion-referenced assessment with an application

An important and difficult issue in designing a Fuzzy Inference System (FIS) is the specification of fuzzy sets, and fuzzy rules. The aim of this paper is to demonstrate how an additional qualitative information, i.e., monotonicity property, can be exploited and extended to be part of an FIS designing procedure (i.e., fuzzy sets and fuzzy rules design). In this paper, the FIS is employed as an alternative to the use of addition in aggregating the scores from test items/tasks in a Criterion-Referenced Assessment (CRA) model. In order to preserve the monotonicity property, the sufficient conditions of the FIS is proposed. Our proposed FIS based CRA procedure can be viewed as an enhancement for the FIS based CRA procedure, where monotonicity property is preserved. We demonstrate the applicability of the proposed approach with a case study related to a laboratory project assessment task at a university, and the results indicate the usefulness of the proposed approach in the CRA domain.

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.

Optimization of gaussian fuzzy membership functions and evaluation of the monotonicity property of fuzzy inference systems

In this paper, two issues relating to modeling of a monotonicity-preserving Fuzzy Inference System (FIS) are examined. The first is on designing or tuning of Gaussian Membership Functions (MFs) for a monotonic FIS. Designing Gaussian MFs for an FIS is difficult because of its spreading and curvature characteristics. In this study, the sufficient conditions are exploited, and the procedure of designing Gaussian MFs is formulated as a constrained optimization problem. The second issue is on the testing procedure for a monotonic FIS. As such, a testing procedure for a monotonic FIS model is proposed. Applicability of the proposed approach is demonstrated with a real world industrial application, i.e., Failure Mode and Effect Analysis. The results obtained are analysis and discussed. The outcomes show that the proposed approach is useful in designing a monotonicity-preserving FIS model.