principles of minimum distance and least cost are revisited. Subsequently, we give a modified generalized model of decision-theoretic three-way approximation, called system, which does not impose values for and as against the trend in literature where and are chosen to be and respectively. A suitable formula for computing viable threshold from cost-sensitive and minimum distance-based models is derived.
Chapter 4 This chapter depicts a wide survey on Intuitionistic Fuzzy Rough Set theory. Several extensions of intuitionistic fuzzy rough sets and hybridization of intuitionistic fuzzy rough sets with other theories dealing with uncertainties are thoroughly looked over. A detailed discussion on intuitionistic fuzzy rough set theory in various real-world application fields is also presented.
Chapter 5 Air quality of different metropolitan cities of India has worsened over the last decade. Kolkata is among the most polluted urban areas of the country. Particulate matter smaller than 2.5μm (PM2.5) is considered as one of the significant parameters for indicating the air quality. Ground based monitoring stations for PM 2.5 are limited over Kolkata. So, Aerosol optical depth (AOD) obtained by Aqua satellites and Moderate Resolution Imaging Spectroradiometer (MODIS) onboard EOS Terra are used to evaluate the local PM2.5 concentration over Kolkata. This work attempts to develop a statistical model to estimate PM2.5 concentration using AODMODIS and meteorological parameters (Temperature, Relative Humidity, Planetary Boundary Layer Height, Total Cloud Cover, Wind speed). The concentration of PM2.5 is found to be influenced by various meteorological parameters. It is found that 52% of the variability of the dependent variable PM2.5 is explained by the 6 explanatory variables (i.e., AODMODIS, temperature, relative humidity, average total cloud, planetary boundary layer height and wind speed) whereas only 3.9% of the variability of the dependent variable PM2.5 is explained by AOD alone as explanatory variable.
Chapter 6 In this chapter we would see inventory systems and learn to manage it with simulation technique. We would study simulation which is performed manually for better understanding of the topic. Then some merits and demerits of it, Monte Carlo simulation technique and its application in a real life problem would be delved in. We would use Excel software to generate random numbers and perform simulation with it. Inventory sales for a confectionary bakery shop would be predicted for next few days. At the end we would compare and plot a graph so as to see and understand simulation better.
Chapter 7 The chapter gives an idea about change in characteristics of cement mortar while adding some nano admixtures and polymer PVA. Workability of mortar is measured in terms of flow value that is necessary to know how the mortar will behave with these additives. Final strength is dependent on various factors out of which workability is one factor. Also the handling with mortar in the field while mixing, transporting, pouring and compacting the workability plays important role hence various additives are added to achieve proper workability. In this article various nano materials like nano alumina, nano silica, nano zinc oxide, and polyvinyl alcohol has been tried for changing the workability.
Chapter 8 This chapter explores various properties of half-Heusler alloys; LiZnP and LiCdP. All the calculations are carried out based on the density functional theory using pseudopotential plane-wave method as implemented in the Quantum espresso package. The structural and electronic features are well described in result and discussion part along with thermodynamic properties. This chapter exposes the semiconductor and brittle behavior of LiZnP and LiCdP alloys.
Chapter 9 In this chapter, we establish a new common fixed point theorem satisfying the digital topology with Contractive mappings in fuzzy sets. Rather than focussing on mathematical details, we will concentrate on making the concepts as clear as possible. There are several useful technical introductions in fuzzy sets and fuzzy logic with digital space. fuzzy set theory is an analytic framework for handling concepts that are simultaneously categorical and dimensional. starting with a rational for fuzzy sets. in this chapter we provide some basic definitions and results for fuzzy sets. In this chapter we shall discuss two important categories of fuzzy logic with linear applications “digital” and “contractions “ with respect to fuzzy digital applications.
Chapter 10 This chapter discusses the bond between mathematics & Artificial intelligence. Mathematics helps to solve the challenging task of hypothetical problems in artificial intelligence using traditional methods and techniques. In the first part the main concern is to demonstrate the mathematical concepts like Linear Algebra in dimensionality reduction of large datasets, Eigen Vectors in ranking of features of dataset, Calculus in optimization task, Statistics for data visualization and so on. The later part discusses the work flow of artificial intelligence and the application areas where Artificial Intelligence is using now a days.
Chapter 11 In this chapter three mathematical models have been used. One is model based on Geometric Progression (G.P.). The second is SIR model and the third one is constructed using differential equations. The model based on G.P. shows how coronavirus is spread using tree chart, assuming that an infected person is capable of infecting two persons who come in contact with the former. It can also be observed that there is a significant difference between the number of covid patients with and without the lockdown.
Chapter 12 This chapter describes about the application of Fuzzy Logic in Mathematical modelling. The chapter is started with explanation about Mathematical modelling with definition and examples. With the help of principles of Mathematical Models, how real world problems can be solved by it, is described. Fuzzy logic is widely accepted and used term in the light of development for application, tools, techniques as Fuzzy Cognitive Maps, Fuzzy Cluster Means, etc. Here Fuzzy Logic Concept has been studied and tried to explain applications of the concept in various fields as Mathematics, Science, Business, Finance, Controller of Temperature, Home appliances, Aeronautics, Defence, Medical Science and Bioinformatics, Engineering Fields such as Mechanical, Industrial, Production, Electronics, Chemical, Automotives, Signal Processing and Communication, Robotics.
Chapter 13 This chapter explores the different types of recommender techniques with its mathematical foundation and also discusses some of the problems in the prevailing system. It discusses use of sequential patterns of web navigation along with the content information and is based on set and sequence similarity measure (S3M), principle of upper approximation and singular value decomposition for generating recommendations on web data. This chapter makes use of mathematics involved in finding the set and sequence similarity for recommendation to user on CTI news dataset.
Chapter 14 The adhesive anchors are usually installed into un-cracked hardened concrete. The Artificial Intelligence methodology of Neural Network (NN) and Genetic Expression Programming (GEP) are used to develop an explicit equation for estimating and predicting the shear capacity of a single adhesive anchor post. The main objective in this chapter is to provide a mathematical tool to predict shear capacity or shear strength of an anchor without any expansive laboratory testing. The Artificial Intelligence (AI) techniques are well-suited for assessment and prediction purposes.
Chapter 15 Genetic Algorithms is an easy form of learning and improvising design of Algorithm. The foundation of the principle is Darwin’s Natural selection, which states survival of the fittest. It offers solutions to various problems and helps to evaluate the
