Open AccessSome fundamental properties of fuzzy linear relations between vector spaces
Author(s) -
Sorin Nădăbana
Publication year - 2016
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1601041n
Subject(s) - mathematics , fuzzy logic , fuzzy subalgebra , fuzzy number , fuzzy mathematics , algebra over a field , relation (database) , multiplication (music) , fuzzy classification , vector space , scalar multiplication , scalar (mathematics) , pure mathematics , discrete mathematics , fuzzy set , artificial intelligence , combinatorics , computer science , data mining , geometry
This paper aims at studying the fundamental properties of fuzzy linear relations between vector spaces. The sum of two fuzzy relations and the scalar multiplication are defined, in a natural way, and some properties of this operations are established. Fuzzy linear relations are investigated and among the results obtained, there should be underlined a characterization of fuzzy linear relations and the fact that the inverse of a fuzzy linear relation is also a fuzzy linear relation. Moreover, the paper shows that the composition of two fuzzy linear relations is a fuzzy linear relation as well. Finally, the article highlights that the family of all fuzzy linear relations is closed under addition and it is closed under scalar multiplication.