Intuitionistic fuzzy similarity measures based on min–max operators

Pattern Analysis and Applications - Intuitionistic fuzzy sets, introduced by Atanassov, offer a new possibility to describe in a more adequate way many real problems. An important tool for...     

Fuzzy min–max neural networks: a bibliometric and social network analysis

Neural Computing and Applications - The amount of digital data in the universe is growing at an exponential rate with the rapid development of digital information, and this reveals new machine...     

Max–plus matrix method and cycle time assignability and feedback stabilizability for min–max–plus systems

A variety of problems arising in nonlinear systems with timing constraints such as manufacturing plants, digital circuits, scheduling managements, etc., can be modeled as min–max–plus systems described by the expressions in which the operations minimum, maximum and addition appear. This paper applies the max–plus matrix method to analyze the cycle time assignability and feedback stabilizability of min–max–plus systems with min–max–plus inputs and max–plus outputs, which are nonlinear extensions of the systems studied in recent years. The max–plus projection matrix representation of closed-loop systems is introduced to establish some structural and quantitative relationships between reachability, observability, cycle time assignability and feedback stabilizability. The necessary and sufficient conditions for the cycle time assignability with respect to a state feedback and an output feedback, respectively, and the sufficient condition for the feedback stabilizability with respect to an output feedback are derived. Furthermore, one output feedback stabilization policy is designed so that the closed-loop systems take the maximal Lyapunov exponent as an eigenvalue. The max–plus matrix method based on max–plus algebra and directed graph is constructive and intuitive, and several numerical examples are given to illustrate this method.     

Fuzzy min–max neural networks: from classification to regression

 In this paper we show two new learning algorithms for a fuzzy min–max neural network. The top down fuzzy min–max (TDFMM) algorithm modifies the classic Simpson's learning algorithm overcoming its main difficulties: the dependence on the presentation order of the patterns and the poor resolutive adaptation to the characteristics of input space. The top down fuzzy min–max regressor (TDFMMR) algorithm extends our neural network to solve regression problems by using a hybrid fuzzy classifier and a gradient descent algorithm.     

Feature selection based on max–min-associated indices for classification of remotely sensed imagery

This article proposes two novel feature selection methods for dimension reduction according to max–min-associated indices derived from Cramer's V-test coefficient. The proposed methods incrementally select features simultaneously satisfying the criteria of a statistically maximal association (A) between target labels and features and a minimal association (R) among selected features with respect to Cramer's V-test value. Two indices are developed by different combinations of the A and R conditions. One index is to maximize A/R and the other is to maximize A–λR, which are referred to as the MMAIQ and MMAIS methods, respectively. Since the proposed feature selection algorithms are feature filter methods, how to determine the best number of features is another important issue. This article adopts an information lost criterion by measuring the variation between χ² and β statistics to optimize the number of features selected associated with the Gaussian maximal likelihood classifier (GMLC). To validate the proposed methods, experiments are conducted with both a hyperspectral image data set and a high spatial resolution image data set. The results demonstrate that the proposed methods can provide an effective tool for feature selection and improve classification accuracy significantly. Furthermore, the proposed methods with well-known feature selection methods, i.e. mutual information-based max-dependency criterion (mRMR) and sequential forward selection (SFS), are evaluated and compared. The experiments demonstrate that the proposed methods can offer better results in terms of kappa coefficient and overall classification accuracy measurements.     

Sequential multi-criteria feature selection algorithm based on agent genetic algorithm

A multi-criteria feature selection method-sequential multi-criteria feature selection algorithm (SMCFS) has been proposed for the applications with high precision and low time cost. By combining the consistency and otherness of different evaluation criteria, the SMCFS adopts more than one evaluation criteria sequentially to improve the efficiency of feature selection. With one novel agent genetic algorithm (chain-like agent GA), the SMCFS can obtain high precision of feature selection and low time cost that is similar as filter method with single evaluation criterion. Several groups of experiments are carried out for comparison to demonstrate the performance of SMCFS. SMCFS is compared with different feature selection methods using three datasets from UCI database. The experimental results show that the SMCFS can get low time cost and high precision of feature selection, and is very suitable for this kind of applications of feature selection.     

Scenario relaxation algorithm for finite scenario-based min–max regret and min–max relative regret robust optimization

Most practical decision-making problems are compounded in difficulty by the degree of uncertainty and ambiguity surrounding the key model parameters. Decision makers may be confronted with problems in which no sufficient historical information is available to make estimates of the probability distributions for uncertain parameter values. In these situations, decision makers are not able to search for the long-term decision setting with the best long-run average performance. Instead, decision makers are searching for the robust long-term decision setting that performs relatively well across all possible realizations of uncertainty without attempting to assign an assumed probability distribution to any ambiguous parameter. In this paper, we propose an iterative algorithm for solving min–max regret and min–max relative regret robust optimization problems for two-stage decision-making under uncertainty (ambiguity) where the structure of the first-stage problem is a mixed integer (binary) linear programming model and the structure of the second-stage problem is a linear programming model. The algorithm guarantees termination at an optimal robust solution, if one exists. A number of applications of the proposed algorithm are demonstrated. All results illustrate good performance of the proposed algorithm.     

Fuzzy decision-making framework for treatment selection based on the combined QUALIFLEX–TODIM method

Treatment selection is a multi-criteria decision-making problem of significant concern in the medical field. In this study, a fuzzy decision-making framework is established for treatment selection. The framework mitigates information loss by introducing single-valued trapezoidal neutrosophic numbers to denote evaluation information. Treatment selection has multiple criteria that remarkably exceed the alternatives. In consideration of this characteristic, the framework utilises the idea of the qualitative flexible multiple criteria method. Furthermore, it considers the risk-averse behaviour of a decision maker by employing a concordance index based on TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method. A sensitivity analysis is performed to illustrate the robustness of the framework. Finally, a comparative analysis is conducted to compare the framework with several extant methods. Results indicate the advantages of the framework and its better performance compared with the extant methods.     

A modified fuzzy min–max neural network with rule extraction and its application to fault detection and classification

The fuzzy min–max (FMM) network is a supervised neural network classifier that forms hyperboxes for classification and prediction. In this paper, we propose modifications to FMM in an attempt to improve its classification performance when a small number of large hyperboxes are formed in the network. Given a new input pattern, in addition to measuring the fuzzy membership function of the input pattern to the hyperboxes formed in FMM, an Euclidean distance measure is introduced for predicting the target class associated with the new input pattern. A rule extraction algorithm is also embedded into the modified FMM network. A confidence factor is calculated for each FMM hyperbox, and a user-defined threshold is used to prune the hyperboxes with low confidence factors. Fuzzy if–then rules are then extracted from the pruned network. The benefits of the proposed modifications are twofold, viz., to improve the performance of FMM when large hyperboxes are formed in the network; to facilitate the extraction of a compact rule set from FMM to justify its predictions. To assess the effectiveness of modified FMM, two benchmark pattern classification problems are experimented, and the results from different methods published in the literature are compared. In addition, a fault detection and classification problem with a set of real sensor measurements collected from a power generation plant is evaluated using modified FMM. The results obtained are analyzed and explained, and implications of the modified FMM network as a useful fault detection and classification tool in real environments are discussed.     

Dynamic visual tracking based on multiple feature matching and g–h filter

The area-based matching approach has been used extensively in many dynamic visual tracking systems to detect moving targets because it is computation efficient and does not require an object model. Unfortunately, area-based matching is sensitive to occlusion and illumination variation. In order to improve the robustness of visual tracking, two image cues, i.e., target template and target contour, are used in the proposed visual tracking algorithm. In particular, the target contour is represented by the active contour model that is used in combination with the fast greedy algorithm. However, to use the conventional active contour method, the initial contour needs to be provided manually. In order to facilitate the use of contour matching, a new approach that combines the adaptive background subtraction method with the border tracing technique was developed and is used to automatically generate the initial contour. In addition, a g–h filter is added to the visual loop to deal with the latency problem of visual feedback so that the performance of dynamic visual tracking can be improved. Experimental results demonstrate the effectiveness of the proposed approach.     

Classification through incremental max–min separability

Piecewise linear functions can be used to approximate non-linear decision boundaries between pattern classes. Piecewise linear boundaries are known to provide efficient real-time classifiers. However, they require a long training time. Finding piecewise linear boundaries between sets is a difficult optimization problem. Most approaches use heuristics to avoid solving this problem, which may lead to suboptimal piecewise linear boundaries. In this paper, we propose an algorithm for globally training hyperplanes using an incremental approach. Such an approach allows one to find a near global minimizer of the classification error function and to compute as few hyperplanes as needed for separating sets. We apply this algorithm for solving supervised data classification problems and report the results of numerical experiments on real-world data sets. These results demonstrate that the new algorithm requires a reasonable training time and its test set accuracy is consistently good on most data sets compared with mainstream classifiers.     

GRASP and path relinking for the max–min diversity problem

The max–min diversity problem (MMDP) consists in selecting a subset of elements from a given set in such a way that the diversity among the selected elements is maximized. The problem is NP-hard and can be formulated as an integer linear program. Since the 1980s, several solution methods for this problem have been developed and applied to a variety of fields, particularly in the social and biological sciences. We propose a heuristic method—based on the GRASP and path relinking methodologies—for finding approximate solutions to this optimization problem. We explore different ways to hybridize GRASP and path relinking, including the recently proposed variant known as GRASP with evolutionary path relinking. Empirical results indicate that the proposed hybrid implementations compare favorably to previous metaheuristics, such as tabu search and simulated annealing.     

Fuzzy min–max neural networks for categorical data: application to missing data imputation

The fuzzy min–max neural network classifier is a supervised learning method. This classifier takes the hybrid neural networks and fuzzy systems approach. All input variables in the network are required to correspond to continuously valued variables, and this can be a significant constraint in many real-world situations where there are not only quantitative but also categorical data. The usual way of dealing with this type of variables is to replace the categorical by numerical values and treat them as if they were continuously valued. But this method, implicitly defines a possibly unsuitable metric for the categories. A number of different procedures have been proposed to tackle the problem. In this article, we present a new method. The procedure extends the fuzzy min–max neural network input to categorical variables by introducing new fuzzy sets, a new operation, and a new architecture. This provides for greater flexibility and wider application. The proposed method is then applied to missing data imputation in voting intention polls. The micro data—the set of the respondents’ individual answers to the questions—of this type of poll are especially suited for evaluating the method since they include a large number of numerical and categorical attributes.     

Mission-oriented ant-team ACO for min–max MTSP

The multiple traveling salesman problem (mTSP) is a combinatorial optimization problem and an extension of the famous traveling salesman problem (TSP). Not only does the mTSP possess academic research value, but its application is extensive. For example, the vehicle routing problem and operations scheduling can all be reduced to mTSP solutions. The mTSP is an NP-hard problem, and multifaceted discussions of its solutions are worthwhile. This study assigned ants to teams with mission-oriented approaches to enhance ant colony optimization algorithms. Missions were appointed to ant teams before they departed (each ant had a different focal search direction). In addition to attempting to complete its own mission, each ant used the Max–Min strategy to work together to optimize the solution. The goal of appointing missions is to reduce the total distance, whereas the goal of using the max–min search method for paths was to achieve Min–Max , or the goal of labor balance. Four main elements were involved in the search process of the ant teams: mission pheromone, path pheromone, greedy factor, and Max–Min ant firing scheme. The experimental results revealed this novel approach to be constructive and effective.     

Feature subset selection Filter–Wrapper based on low quality data

Today, feature selection is an active research in machine learning. The main idea of feature selection is to choose a subset of available features, by eliminating features with little or no predictive information, as well as redundant features that are strongly correlated. There are a lot of approaches for feature selection, but most of them can only work with crisp data. Until now there have not been many different approaches which can directly work with both crisp and low quality (imprecise and uncertain) data. That is why, we propose a new method of feature selection which can handle both crisp and low quality data. The proposed approach is based on a Fuzzy Random Forest and it integrates filter and wrapper methods into a sequential search procedure with improved classification accuracy of the features selected. This approach consists of the following main steps: (1) scaling and discretization process of the feature set; and feature pre-selection using the discretization process (filter); (2) ranking process of the feature pre-selection using the Fuzzy Decision Trees of a Fuzzy Random Forest ensemble; and (3) wrapper feature selection using a Fuzzy Random Forest ensemble based on cross-validation. The efficiency and effectiveness of this approach is proved through several experiments using both high dimensional and low quality datasets. The approach shows a good performance (not only classification accuracy, but also with respect to the number of features selected) and good behavior both with high dimensional datasets (microarray datasets) and with low quality datasets.     

High performance iris recognition based on 1-D circular feature extraction and PSO–PNN classifier

In this paper, a novel iris feature extraction technique with intelligent classifier is proposed for high performance iris recognition. We use one dimensional circular profile to represent iris features. The reduced and significant features afterward are extracted by Sobel operator and 1-D wavelet transform. So as to improve the accuracy, this paper combines probabilistic neural network (PNN) and particle swarm optimization (PSO) for an optimized PNN classifier model. A comparative experiment of existing methods for iris recognition is evaluated on CASIA iris image databases. The experimental results reveal the proposed algorithm provides superior performance in iris recognition.     

A feature selection method based on improved fisher’s discriminant ratio for text sentiment classification

Owing to its openness, virtualization and sharing criterion, the Internet has been rapidly becoming a platform for people to express their opinion, attitude, feeling and emotion. As the subjectivity texts are often too many for people to go through, how to automatically classify them into different sentiment orientation categories (e.g. positive/negative) has become an important research problem. In this paper, based on Fisher’s discriminant ratio, an effective feature selection method is proposed for subjectivity text sentiment classification. In order to validate the proposed method, we compared it with the method based on Information Gain while Support Vector Machine is adopted as the classifier. Two experiments are conducted by combining different feature selection methods with two kinds of candidate feature sets. Under 2739 subjectivity documents of COAE2008s and 1006 car-related subjectivity documents, the experimental results indicate that the Fisher’s discriminant ratio based on word frequency estimation has the best performance respectively with accuracy 86.61% and 82.80% under two corpus while the candidate features are the words which appear in both positive and negative texts.