Tanmoy Som

Some fixed point theorems for fuzzy mappings

In the present work we extend the concept of weakly dissipative multi-valued map of Aubin and Siegel [1] for a fuzzy mapping and derive a fixed point theorem for such a mapping. We also generalize a result of Heilpern [5] on fuzzy contraction mappings for a fuzzy nonexpansive mapping. Further, we extend a theorem of Kirk and Downing [6] on fixed points of a multi-valued mapping for a fuzzy mapping on a metric space. Finally a fixed point theorem for a generalized nonexpansive fuzzy mapping is given which extends a result of Bose and Sahani [3].

An Automated Vehicle License Plate Recognition System

License plate recognition is a computer vision method that identifies vehicles from their license plates. The most crucial step of such a system is accurate localization of the plate. The authors propose a system for automatic recognition that has three phases: image capture, plate localization, and license plate number recognition. They tested their methodology on 40 different car models with different types of license plates.

Using Radon Transform to Recognize Skewed Images of Vehicular License Plates

An algorithm that projects image intensity along a radial line oriented at a specific angle enables the recognition of vehicular license plates at odd angles. The algorithm determines orientation angle, rotates the image to a horizontal perspective, and removes image noise from rotation to achieve recognition accuracy as high as 98 percent.

Tolerance-based intuitionistic fuzzy-rough set approach for attribute reduction

Abstract Due to technological advancement and the explosive growth of electrically stored information, automated methods are required to aid users in maintaining and processing this huge amount of information. Experts, as well as machine learning processes on large volumes of data, are the main sources of knowledge. Knowledge extraction is an important step in framing expert and intelligent systems. However, the knowledge extraction phase is very slow or even impossible due to noise and large size of data. To enhance the productivity of machine learning algorithms, feature selection or attribute reduction plays a key role in the selection of relevant and non-redundant features to improve the performance of classifiers and interpretability of data. Many areas like machine learning, image processing, data mining, natural language processing and Bioinformatics, etc., which have high relevancy to expert and intelligent systems, are applications of feature selection. Rough set theory has been successfully applied for attribute reduction, but this theory is inadequate in the case of attribute reduction of real-valued data set as it may lose some information during the discretization process. Fuzzy and rough set theories have been combined and various attribute selection techniques were proposed, which can easily handle the real-valued data. An intuitionistic fuzzy set possesses a strong ability to represent information and better describing the uncertainty when compared to the classical fuzzy set theory as it considers positive, negative and hesitancy degree simultaneously for an object to belong to a set. This paper proposes a novel mechanism of attribute selection using tolerance-based intuitionistic fuzzy rough set theory. For this, we present tolerance-based intuitionistic fuzzy lower and upper approximations and formulate a degree of dependency of decision features over the set of conditional features. Moreover, the basic results on lower and upper approximations based on rough sets are extended for intuitionistic fuzzy rough sets and analogous results are established. In the end, the proposed algorithm is applied to an example data set and the comparison between tolerance-based fuzzy rough and intuitionistic fuzzy rough sets approaches for feature selection is presented. The proposed concept is found to be better performing in the form of selected attributes.

An introduction towards automated parameterization reduction of soft set

In this paper, we introduce seven correlated algorithms for reduction of decision making parameters. This reduction framework is heuristic function based. The reduction of soft set decision parameters, those are collectively sufficient and individually necessary for keeping any special characteristic of a given information system. There has been very few works done on the algorithmic reduction techniques of decision parameter of soft set To the best of our knowledge, the computing complexities of available methods are of exponential order. We claim that our method is the first such kind of algorithms having polynomial time of computation. Illustrative example demonstrates the process elaborately.

Feature Subset Selection of Semi-supervised Data: An Intuitionistic Fuzzy-Rough Set-Based Concept

We are surrounded by a spate of data generating from various sources. To extract some relevant information from these data sets, many pre-processing techniques have been proposed, in which feature selection technique is widely used. However, most of the feature selection approaches focus on supervised learning, which operates on labelled data only. In real-world applications, such as medical diagnosis, forensic science, both labelled and unlabelled data instances are available. Semi-supervised learning handles these types of situations. Some of the researchers have presented rough set as well as fuzzy-rough set-based methods for feature selection of semi-supervised data sets but these approaches have their own limitations. Intuitionistic fuzzy sets maintain a stronger potency of exhibiting information and better drawing and representing intricate ambiguities of the uncertain character of the objective world when compared with fuzzy sets, as it considers positive, the negative and hesitancy degree simultaneously. In this paper, we have proposed a novel feature selection technique for partially labelled data set based on intuitionistic fuzzy-rough set theory. Moreover, we have presented supporting theorems and proposed a novel algorithm to compute reduct based on our method. Finally, we have presented supremacy of our approach over fuzzy-rough technique by considering a partially labelled information system.

Convergence of Generalized Mann Type of Iterates to Common Fixed Point

The present paper deals with the convergence of two modified Mann type of iteration schemes for a single and a finite family of mappings to the fixed and common fixed point, respectively, of a single and a finite family of quasi-nonexpansive mappings on a uniformly convex Banach space. An example is added in support of our main result. The results obtained generalize the earlier results of Rhoades (J Math Anal Appl 56:741–750, [6]), Som et al. (Proc Nat Acad Sci (India) 70(A)(II):185–189, [8]), and others in turn.

Enhanced Prediction for Piezophilic Protein by Incorporating Reduced Set of Amino Acids Using Fuzzy-Rough Feature Selection Technique Followed by SMOTE

In this paper, the learning performance of different machine learning algorithms is investigated by applying fuzzy-rough feature selection (FRFS) technique on optimally balanced training and testing sets, consisting of the piezophilic and nonpiezophilic proteins. By experimenting using FRFS technique followed by Synthetic Minority Over-sampling Technique (SMOTE) at optimal balancing ratios, we obtain the best results by achieving sensitivity of 79.60%, specificity of 74.50%, average accuracy of 77.10%, AUC of 0.841, and MCC of 0.542 with random forest algorithm. The ranking of input features according to their differentiating ability of piezophilic and nonpiezophilic proteins is presented by using fuzzy-rough attribute evaluator. From the results, it is observed that the performance of classification algorithms can be improved by selecting the reduced optimally balanced training and testing sets. This can be obtained by selecting the relevant and non-redundant features from training sets using FRFS approach followed by suitably modifying the class distribution.

Fixed Point Results for \((\phi ,\psi )\)-Weak Contraction in Fuzzy Metric Spaces

In the present work, a fixed point result for generalized weakly contractive mapping in fuzzy metric space has been established. An example is cited to illustrate the obtained result.

Vehicular License Plate Localization Using Principal Component Analysis

ABSTRACT The need of vehicular license plate recognition system (VLPR) has arisen based on the need to implement traffic control on transportation systems, since early 1970s. Since then, researchers are continuously proposing various approaches and solutions. One of the significant and challenging tasks is to localize the license plate of the moving car. Since the license plate standards are not strictly practiced in world, a large amount of variations are obtained like, size, location, type of font used, background and foreground colour, and so on. The principal component analysis (PCA) is one of the widely used and most successful techniques that have been used in image recognition and compression. In this paper, we propose a novel approach to identify the license plate using PCA.