Heart disease is a danger to people’s health because of its prevalence and high mortality risk. Predicting cardiac disease early using a few simple physical indications collected from a routine physical examination has become difficult. Clinically, it is critical and sensitive for the signs of heart disease for accurate forecasts and concrete steps for future diagnosis. The manual analysis and prediction of a massive volume of data are challenging and time-consuming. In this paper, a unique heart disease prediction model is proposed to predict heart disease correctly and rapidly using a variety of bodily signs. A heart disease prediction algorithm based on the analysis of the predictive models’ classification performance on combined datasets and the train-test split technique is presented. Finally, the proposed technique’s training results are compared with the previous works. For the Cleveland, Switzerland, Hungarian, and Long Beach VA heart disease datasets, accuracy, precision, recall, F1-score, and ROC-AUC curves are used as the performance indicators. The analytical outcomes for Random Forest Classifiers (RFC) of the combined heart disease datasets are F1-score 100%, accuracy 100%, precision 100%, recall 100%, and the ROC-AUC 100%. The Decision Tree Classifiers for pooled heart disease datasets are F1-score 100%, accuracy 98.80%, precision 98%, recall 99%, ROC-AUC 99%, and for RFC and Gradient Boosting Classifiers (GBC), the ROC-AUC gives 100% performance. The performances of the machine learning algorithms are improved by using five-fold cross validation. Again, the Stacking CV Classifier is also used to improve the performances of the individual machine learning algorithms by combining two and three techniques together. In this paper, several reduction methods are incorporated. It is found that the accuracy of the RFC classification algorithm is high. Moreover, the developed method is efficient and reliable for predicting heart disease.

In 1986, Atanassov introduced the concept of intuitionistic fuzzy set theory which is based on the extensions of definitions of fuzzy set theory given by Zadeh. This theory provides a variable model to elaborate uncertainty and vagueness involved in decision making problems. In this chapter, we concentrate our study on the ideal convergence of sequence spaces with respect to intuitionistic fuzzy norm and discussed their topological and algebraic properties.

After the pioneering work of Zadeh[35], a huge number of research papers have been appeared on fuzzy theory and its applications as well as fuzzy analogues of the classical theories. Fuzzy set theory is a powerful hand set for modelling uncertainty and vagueness in various problems arising in field of science and engineering. It has a wide range of applications in various fields: population dynamics[1], chaos control[4], computer programming[5], nonlinear dynamical system[6], etc. Fuzzy topology is one of the most important and useful tools and it proves to be very useful for dealing with such situations where the use of classical theories breaks down.In this paper, we introduce ideal convergence of double sequences in intuitionistic fuzzy sequences defined by compact operator and study the fuzzy topology on the said spaces.

In the theory of classes of sequence, a wonderful application of Hahn-Banach extension theorem gave rise to the concept of Banach limit, i.e., the limit functional defined on c can be extended to the whole space l ∞ and this extended functional is called as the Banach limit. After that, in 1948 Lorentz used this concept of a week limit to introduce a new type of convergence, named as the almost convergence. Later on, Raimi generalized the concept of almost convergence known as σ − convergence and the sequence space BV σ was introduced and studied by Mursaleen. The main aim of this chapter is to study some new double sequence spaces of invariant means defined by ideal, modulus function and Orlicz function. Furthermore, we also study several properties relevant to topological structures and inclusion relations between these spaces.

We have great pleasure in presenting this text book of mathematics. This book is intended primarily for students of science and engineering. Its aims are, first, to present the fundamental mathematical ideas which underlie the notion of a convergent sequences, and secondly to develop, as far as the small spaces allows, a body of technique and a familiarity with particular examples sufficient to make the reader feel at home with such applications of infinite series as he is likely to meet in his scientific studies. Every topic has been explained in details and supported by a number of examples. This book is intended for students and researchers with a (special) interest in spaces of single and double sequences, matrix transformations and matrix domains.