General fuzzy multiset grammar and language

Ranjeet Kaur; Alka Tripathi

Ranjeet Kaur Department of Mathematics, Jaypee Institute of Information Technology, Noida,\\ Uttar Pradesh, India.\\ ABES Engineering College, Ghaziabad, Uttar Pradesh, India.
Alka Tripathi Department of Mathematics, Jaypee Institute of Information Technology, Noida,\\ Uttar Pradesh, India.

Abstract

In the present work, the General Fuzzy Multiset Automata (GFMA) is introduced and a framework for General Fuzzy Multiset Grammar (GFMG) which recognises the General Fuzzy Multiset Language (GFML) is established. Further, the relationship between the generator GFMG and acceptor GFMA is discussed. The repetitive elements with varying degree have been considered, so elements with smaller membership values can also be taken into account. It is difficult to form production rules for fuzzy grammar of a GFMA having more than one initial state, hence a method is proposed to construct an equivalent GFMA with single initial state corresponding to GFMA with more than one initial states. Again, a simplified form of GFMA is obtained by splitting strings into alphabets, so that more combinations of input strings can be considered.