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Abstract
Mathematical decision-making is an important criterion to take the appropriate decision regarding the representation of an imprecise parameter under uncertain situations. In the existing literature, it is observed that one such representation is interval representation. The goal of this paper is to introduce a new concept of Type-2 interval which might be used to represent the impreciseness appropriately. The definitions of arithmatical operations, interval functions and algebraic properties of Type-2 interval are proposed here. Then, the order relations between two Type-2 interval numbers are introduced and all the definitions are illustrated using some numerical examples. Finally, an application of Type-2 interval mathematics and order relation is made in the area of inventory control.
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Notes on contributors
Md Sadikur Rahman
Md Sadikur Rahman is a full time research scholar under UGC Moulana Azad fellowship. He obtained his M.Sc. degree in Mathematics in the year 2017 from the University of Kalyani, West Bengal, India. He has published three more research articles in reputed journals and three accepted articles in various international journals of repute. Also, three research articles are accepted and more than ten articles are communicated in different international journals. His research interests include theory of optimization, interval analysis, optimal control, numerical analysis, interval differential equation etc.
Ali Akbar Shaikh
Ali Akbar Shaikh is currently working as an Assistant Professor in Mathematics at The University of Burdwan, Burdwan, West Bengal, India. He was a postdoctoral fellow at School of Engineering and Sciences of Tecnológico de Monterrey, México. He has obtained the award SNI of level 1 (out of 0-3) given by National System of Researchers of México from government of México in the year 2017. He obtained MSc in Applied Mathematics from University of Kalyani, India, MPhil and PhD in Mathematics from University of Burdwan, India. Dr. Shaikh has published more than 55 research papers in different peer reviewed and JCR international journals. He is an author of four book chapters and a book published by Springer Nature. His research interests include inventory control theory, interval optimization and Particle Swarm Optimization.
Asoke Kumar Bhunia
Asoke Kumar Bhunia is a Professor at the Department of Mathematics, The University of Burdwan, West Bengal, India. He obtained his PhD in Mathematics and MSc in Applied Mathematics from Vidyasagar University, India. His research interests include computational optimisation, soft computing, interval mathematics and interval ranking. He has published 125 research more research papers in various national and international journals of repute. He is a reviewer of several SCI journals. He has guided 13 PhD and two MPhil students. He is an author of four research monographs, six book chapters and a book published by Springer Nature. He is an INSA Visiting Fellow and former Associate Editor of the Springer's journal, OPSEARCH.