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Mathematics in Computational Science and Engineering
Edited by
Ramakant Bhardwaj
Jyoti Mishra
Satyendra Narayan
and
Gopalakrishnan Suseendran
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Library of Congress Cataloging-in-Publication Data
ISBN 978-1-119-77715-1
Cover image: Pixabay.com Cover design by Russell Richardson
Set in size of 11pt and Minion Pro by Manila Typesetting Company, Makati, Philippines
Printed in the USA
10 9 8 7 6 5 4 3 2 1
Dedication
Gopalakrishnan Suseendran, Assistant Professor, who is now deceased, as the co-author of this book. He received his PhD in Information Technology-Mathematics from Presidency College, University of Madras, Tamil Nadu, India. He worked as assistant professor in the Department of Information Technology, School of Computing Sciences, Vels Institute of Science, Technology & Advanced Studies (VISTAS). He published more than 75 research papers in various referred journals, authored 11 books and received 6 awards.
Preface
Chapter 1 The main aim of Inventory EOQ model is to reduce the Ordering Cost and Holding Cost in the Company. Based on Numerical Example, three proposed models are applied in EOQ. This leads to Brownian Path, which is based on Hausdroff Measure and Levy processes. Hence it is Fractals.
Chapter 2 This chapter gives a good description of ill-posed inverse problems encountered in the field of electrical geophysics. It begins with an overview of the present state of knowledge about electrical resistivity methods for mapping and monitoring in-situ processes that cannot be accessed directly. Based on reciprocity and perturbation analysis, an attempt has been made to introduce generalized multi-dimensional resistivity inversion methods. It may be found highly useful in environmental geophysics and geoengineering discipline to mapping and monitoring in-situ processes where electrical resistivity contrast is encountered.
Chapter 3 In this chapter, theoretical formulations of shadowed sets approximations (SSA) which hinge on ideas of uncertainty balance, average uncertainty and minimum approximation error are presented. Also, decision-theoretic three-way approximation (DTA) models which anchor on 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