Normalization of Multidimensional Data for Multi-Criteria Decision Making Problems: Inversion, Displacement, Asymmetry

This book presents a systematic review of multidimensional  normalization methods and addresses problems frequently encountered when  using various methods and ways to eliminate them.The invariant  properties of the linear normalization methods presented here can be  used to eliminate simple problems and avoid obvious errors when choosing  a normalization method. The book introduces valuable, novel techniques  for the multistep normalization of multidimensional data. One of these  methods involves inverting the normalized values of cost attributes into  profit attributes based on the reverse sorting algorithm (ReS  algorithm). Another approach presented is the IZ method, which addresses  the issue of shift in normalized attribute values. Additionally, a new  method for normalizing the decision matrix is proposed, called the MS  method, which ensures the equalization of average values and variances  of attributes.Featuring numerous illustrative examples throughout, the  book helps readers to understand what difficulties can arise in  multidimensional normalization, what to expect from such problems, and  how to solve them. It is intended for academics and professionals in  various areas of data science, computing in mathematics, and statistics,  as well as decision-making and operations.