Fuzzy L languages

In this paper we introduce some families of fuzzy L-systems and investigate their properties. We further discuss the relationship between fuzzy L languages and the fuzzy languages generated by fuzzy grammar proposed in Ref.[3,5]. A measure of fuzziness for a string, called the fuzzy entropy of a string with respect to a given fuzzy L system, will be defined. The relationship between fuzzy L languages and the ordinary L languages is also discussed.Comment: 9 pages with no figure. International J. of Fuzzy sets and Systems (Accepted for publ ication

1Institute of Theoretical Physics, Academia Sinica,

A fuzzy aspect is introduced into L systems and some of its properties are investigated. The relationship between fuzzy L languages and the fuzzy languages generated by fuzzy grammar defined by Lee and Zadeh is elucidated. The concept of fuzzy entropy of a string is proposed as a measure of fuzziness of the latter. Some relationship between fuzzy L systems and the ordinary L systems is discussed. Key words: Fuzzy set, fuzzy L system/language, fuzzy entropy of a string.