# Information Diffusion

• Chongfu Huang
• Yong Shi
Chapter
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 99)

## Abstract

This chapter describes the principle of information diffusion. First we introduce the concept of incomplete-data set and study “fuzziness” of a given sample. Some mathematical proofs are given to show that the principle holds, at least, in the case of probability density distribution (PDF) estimation if we take information diffusion functions which satisfy the conditions as same as that in the kernel estimator, and use the formulae which are employed in the kernel estimator. The chapter is organized as follows: in section 5.1, we discuss the “bottle neck” problems of the information distribution. In section 5.2, we give the definition of incomplete-data set. In section 5.3, we discuss the incompleteness and fuzziness of a given sample. In section 5.4, we mathematically give the definition of information diffusion. In section 5.5, we review some properties of random sets. In section 5.6, the principle of information diffusion as an assertion is described with respect to function approximation. Section 5.7 proves that the principle of information diffusion holds, at least, in the case of estimating a PDF.

## Keywords

Membership Function Information Diffusion Diffusion Estimate Diffusion Function Kernel Estimator

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