Roughness of Filters in Equality Algebras

Rough set theory is an excellent mathematical tool for the analysis of a vague description of actions in decision problems. Now, in this paper by considering the notion of an equality algebra, the notion of the lower and the upper approximations are introduced and some properties of them are given. Moreover, it is proved that the lower and the upper approximations define an interior operator and a closure operator, respectively. Also, using D-lower and D-upper approximation, conditions for a nonempty subset to be definable are provided and investigated that under which condition D-lower and D-upper approximation can be filter

Grey sets and greyness

This paper discusses the application of grey numbers for uncertainty representation. It highlights the difference between grey sets and interval-valued fuzzy sets, and investigates the degree of greyness for grey sets. It facilitates the representation of uncertainty not only for elements of a set, but also the set itself as a whole. Our results show that a grey set could be specified for interval-valued fuzzy sets or rough sets under special conditions. With the notion of grey sets and their associated degrees of greyness, various set operations between grey sets are discussed

f-DERIVATIONS AND (f; g)-DERIVATIONS OF MV -ALGEBRAS

Recently, the algebraic theory of MV -algebras is intensively studied. In this paper, we extend the concept of derivation of $MV$-algebras and we give someillustrative examples. Moreover, as a generalization of derivations of $MV$ -algebraswe introduce the notion of $f$-derivations and $(f; g)$-derivations of $MV$-algebras.Also, we investigate some properties of them

Operasi closure pada mv-aljabar

MV-aljabar M adalah struktur aljabar dengan dua operasi biner yang memenuhi aksioma-aksioma tertentu pada MV-aljabar. Dalam MV-aljabar didefinisikan suatu Ideal dan dalam suatu Ideal MV-aljabar, dibentuk suatu himpunan yang berisikan ideal-ideal dari MV-aljabar yang dinyatakan sebagai operasi closure. Sehingga muncullah gagasan mengenai operasi closure pada MV-aljabar