Constructions of quotient algebras via triangular norms

Rok, strany: 2010, 279 - 288

In this paper, properties of certain real-valued mappings $\vartriangle$ on binary systems $X$ which satisfy versions of the triangle inequality are investigated. For example, via a quotient construction using $Ker{\vartriangle} =\{x: \vartriangle(x)=0\}$ it is shown that $X/Ker{\vartriangle}$ is a $d$-algebra if $X$ is a $d$-algebra. In addition fuzzy versions of these triangular norms and their properties are considered as well. Finally boundedness conditions on $\vartriangle$ and a concept of magnitude are both introduced and some consequences are derived.

ISO 690:

Han, J., Kim, H., Neggers, J. 2010. Constructions of quotient algebras via triangular norms. In Mathematica Slovaca, vol. 60, no.3, pp. 279-288. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0012-z

APA:

Han, J., Kim, H., Neggers, J. (2010). Constructions of quotient algebras via triangular norms. Mathematica Slovaca, 60(3), 279-288. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0012-z