1647 | Page A New Generalized Fuzzy Information Measure and Its Properties Safeena Peerzada 1 , Saima Manzoor Sofi 2 , Rifat Nisa 3 P.G Department of Statistics University of Kashmir, Srinagar, (India) ABSTRACT In this paper we propose a new two parametric generalized measure of fuzzy entropy of order α and type β and study its properties. Also, we study the behaviour of the new proposed measure with the numerical illustration. Keywords- Shannon’s entropy, Fuzziness, Fuzzy measure of information, Fuzzy set and Membership function. I.INTRODUCTION Fuzziness is a feature of imperfect information that results from the lack of crisp distinction between the elements belonging and not belonging to a set that is the boundaries of the set under consideration are not sharply defined. A measure of fuzziness often used and cited in the literature is the entropy that was first conceived by Lofti A. Zadeh [1], Professor at the University of Berkley, in 1965. The name entropy was chosen due to an intrinsic similarity of equations to the ones in the Shannon entropy. However, the two functions measure fundamentally different types of uncertainty. Basically, the Shannon [2] entropy measures the average uncertainty in bits associated with the prediction of outcomes in a random experiment. The concept of fuzziness has been applied to apparently all the phenomena: engineering, medicine, computer science and decision making, fuzzy traffic control, fuzzy aircraft control, etc. Different information measures were considered and investigated by several authors. Some of them are: Aczel. J. [3], Kapur J. N. [4], Khan A. B., Autur R. and Ahmad H. [5], Van Der Lubbe J. C. A. [6], Renyi. [7], Ashiq H. B. and M. A. K. Baig [8, 9] etc. There are situations where probabilistic measures of entropy do not work. To deal with such situations, instead of taking the probability, the idea of fuzziness can be explored. 1.1 Preliminaries In this section, we introduce some well-known concepts and the notations related to fuzzy entropy measure. We will also focus on the theory of fuzzy sets. Let   n x x x X ..., , 2 , 1  be a universal set defined in the universe of discourse and it includes all possible elements related to the given problem then a fuzzy subset of universe X is defined as:           1 , 0 , : ,    i x A X i x i x A i x A   where ) ( i A x  is a membership function (characteristic function or discrimination function) and gives the degree of belongingness of the element ' ' i x to the set ‘A’. If every element of the set ‘A’ is ‘0’ or ‘1’, there is