http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Families of fuzzy and crisp languages defined by identities
Magnus Steinby 원광대학교 기초자연과학연구소 2020 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.19 No.3
We present a general scheme for defining families of fuzzy languages and the related families of crisp languages. In particular, all the varieties of regular fuzzy languages of T.~Petkovi\'c (2005) together with their associated $\star$-varieties of S.~Eilenberg (1976) and varieties of finite monoids are obtained this way, but also pairs of more general families of regular fuzzy and crisp languages can be defined. For the families that are not varieties, we show how to get the greatest varieties contained in them. As examples we consider the varieties of commutative fuzzy and crisp languages, the families of rotation invariant fuzzy and crisp regular languages, which are not varieties, and the varieties of aperiodic fuzzy and crisp languages, which are ultimately defined by a sequence of identities.