Fuzzy Sets and Information

Fuzzy set theory has capability to describe the uncertain situations, containing ambiguity and vagueness. Fuzziness is found in our decision, in our thinking, in the way we process information, and particularly in our language.The objective of the book is to study fuzzy mathematics with applications and to characterize new measures of fuzzy information with their various generalizations. The fuzzy information measure deals with vague and ambiguous uncertainties. Large number of measures of entropy, directed divergence and symmetric divergence for probability distributions are known. Analogously, there is a set of variety of measures for fuzzy sets available. Cross-entropy measure is also known as the information discrepancy between two probability distributions. Derived from cross-entropy, fuzzy directed divergence measures the dissimilarity between two fuzzy sets. Various generalized measures of fuzzy information have been introduced. The concept of `useful' fuzzy information by attaching utility to the uncertainties of fuzziness and probabilities of randomness has been introduced.

Autorentext

Rakesh Kr Bajaj received M.Sc. from IIT, Kanpur in 2003 and Ph.D.(Maths) from Jaypee University of Information Technology, Waknaghat in 2009. He is a faculty in Deptt. of Mathematics, JUIT, Waknaghat. Prof. D.S. Hooda is Head, Deptt. of Maths and Dean (Research) in JIET, Guna. Prof. Harinder Singh is Head, Deptt. of Mathematics, JUIT, Waknaghat.