A Study on the Generalized Fuzzy Mean Codeword Lengths

Abstract

Information Theory has ideas which are widely applicable to the situations remote from its original inspiration. Although, the applicability of ideas is not always exact; yet these are very useful. One of the best applications of information measure is noiseless coding theorem which provides the bounds for suitable encoding of entropies and fuzzy information measures.

In present chapter, mean code word and fuzzy mean codeword lengths are defined, and some generalizations of mean codeword length are also described. A generalized fuzzy mean codeword length of degree \(\beta\) is defined and its bounds in the term of a generalized fuzzy information measure are studied. Further, the fuzzy mean codeword length of type (\(\alpha\), \(\beta\)) is introduced and its bounds are studied. Monotonic behavior of these fuzzy mean codeword lengths is illustrated graphically by taking some empirical data.