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 α and type β 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.
Inhaltsverzeichnis (Table of Contents)
- Abstract
- Chapter 1: Introduction
- 1.1 Concept of Information Theory
- 1.2 Concept of Fuzzy Sets
- 1.3 Measures of Entropy
- 1.4 Measures of Directed Divergence
- 1.5 Measure of Fuzzy Information
- 1.6 Concept of Fuzzy Entropy
- 1.7 Concept of Fuzzy Divergence
- 1.8 Concept of Decision Making
- 1.9 Concept of Noiseless Coding Theorem
- Chapter 2: New Parametric Measure of Fuzzy Information Measure
- 2.1 Introduction
- 2.2 A New Parametric Measure of Fuzzy Information Measure Involving Two Parameters a And B
- 2.3 A New Parametric Measure of Fuzzy Information Measure Involving Three Parametersa, ẞ and y.
- Chapter 3: On Some New Divergence Measure between Fuzzy Sets
- 3.1 Introduction
- 3.2 Generalized Measure of Fuzzy Directed Divergence
- Chapter 4: Application in Decision Making
- 4.1 Introduction
- 4.2 Numerical Example Based on Fuzzy Information Measure
- 4.3 Numerical Example Based On Fuzzy Directed Divergence
- Chapter 5: Fuzzy Noiseless Coding Theorem
- 5.1 Introduction
- 5.2. Fuzzy Noiseless Coding Theorem
- Chapter 6: Fuzzy Noiseless Coding Theorem for Binary 1:1 Codes
- 6.1 Introduction
- 6.2 Fuzzy Noiseless Coding Theorem for 1:1 Codes
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
This book aims to explore the concept of information coding using fuzzy set theory, investigating new parametric measures of fuzzy information and divergence, and their applications in decision making.
- Information theory and its application to fuzzy sets
- New parametric measures of fuzzy information and divergence
- Decision making based on fuzzy information measures
- Fuzzy noiseless coding theorem and its implications
- Applications of fuzzy information theory in various fields
Zusammenfassung der Kapitel (Chapter Summaries)
Chapter 1 introduces the fundamental concepts of information theory and fuzzy sets, including measures of entropy, directed divergence, and fuzzy information. The chapter also discusses the concept of decision making and the noiseless coding theorem.
Chapter 2 delves into the development of new parametric measures of fuzzy information involving two and three parameters. The chapter explores the properties and significance of these new measures.
Chapter 3 focuses on generalized measures of fuzzy directed divergence, examining their properties and potential applications.
Chapter 4 presents numerical examples based on fuzzy information measures and directed divergence, illustrating their practical applications in decision-making processes.
Chapter 5 discusses the fuzzy noiseless coding theorem and its role in coding information using fuzzy sets.
Schlüsselwörter (Keywords)
Information coding, fuzzy set theory, fuzzy information, fuzzy entropy, fuzzy divergence, decision making, noiseless coding theorem, parametric measures, directed divergence, applications of fuzzy information theory.
- Quote paper
- Manu Banga (Author), Information Coding Using Fuzzy Set Theory, Munich, GRIN Verlag, https://www.grin.com/document/1281742
