Information Coding Using Fuzzy Set Theory

Document in the subject Mathematics - General, Basics, , language: English, abstract: Chapter 1: In this chapter a brief literature survey on measures of entropy and divergence measures is presented. It also outlines the basic concepts of fuzzy sets. A brief review on fuzzy information measures and fuzzy directed divergence are given here. The concept of multiple criteria decision making problem is also presented. In addition, a general overview of coding theory is given and summarizes the objectives with an overview of the work reported in later chapters. Chapter 2: In Chapter 2 after reviewing some literature on measures of information for fuzzy sets, a new generalized fuzzy information measure involving two parameters of order a and type ß has been introduced. The necessary properties of the proposed measure have been verified. Further, the monotonic nature of generalized fuzzy information measure with respect to the parameters is studied and the validity of the same is verified by constructing the computed tables and plots on taking different values of the parameters. Chapter 3: Divergence is an important measure in information theory as well as in fuzzy set theory which has widely used by researchers in many application areas. Generalized divergence measures provide flexibility to the users and enhance their applicability range. This chapter proposes a new generalized fuzzy divergence measure. It may be remarked that the strength of a measure lies in its properties. The new measure has important properties proved in this chapter to enhance the employability of this measure. Special cases are also discussed for providing particular results. Chapter 3 deals with the introduction of a new generalized measure of fuzzy directed divergence involving two real parameters. The proposed measure satisfies all the necessary properties of being a measure. Some additional properties of the proposed measure have also been studied. Further, the monotonic nature of generalized fuzzy directed divergence measure with respect to the parameters is studied and validity of the same is checked by constructing the computed tables and plots on taking different fuzzy sets and different values of the parameters. Corresponding measures of total ambiguity and fuzzy information improvement have also been defined and studied.