What is it about?
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 β is defined and its bounds in the term of a generalized fuzzy information measure are studied. Further, the fuzzy mean codeword length of type (α, β) is introduced and its bounds are studied. Monotonic behavior of these fuzzy mean codeword lengths is illustrated graphically by taking some empirical data.
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Why is it important?
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.
Perspectives
In this chapter, a new fuzzy mean codeword length of degree β is defined and its bounds in term of a generalized information measure are studied. Further, another generalized fuzzy mean codeword length of type (α,β) and its bounds are also studied. Monotonic behavior these code word lengths are illustrated graphically by taking some empirical data. As parametric generalized fuzzy mean codeword length represents a family of codeword lengths, so it is flexible for application point of view. The present study can further be extended to the generalized ‘useful’ mean codeword lengths and can be applied in solving the problems related to source coding and data compression.
Prof. D S Hooda
Guru Jambheshwar University of Science and Technology
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This page is a summary of: A Study on the Generalized Fuzzy Mean Codeword Lengths, July 2021, Sciencedomain International,
DOI: 10.9734/bpi/ctmcs/v6/3167f.
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