0000000000588807
AUTHOR
Aleksandrs Eļkins
showing 3 related works from this author
On a Category of Extensional Fuzzy Rough Approximation L-valued Spaces
2016
We establish extensionality of some upper and lower fuzzy rough approximation operators on an L-valued set. Taking as the ground basic properties of these operators, we introduce the concept of an (extensional) fuzzy rough approximation L-valued space. We apply fuzzy functions satisfying certain continuity-type conditions, as morphisms between such spaces, and in the result obtain a category \(\mathcal{FRA}{} \mathbf{SPA}(L)\) of fuzzy rough approximation L-valued spaces. An interpretation of fuzzy rough approximation L-valued spaces as L-fuzzy (di)topological spaces is presented and applied for constructing examples in category \(\mathcal{FRA}{} \mathbf{SPA}(L)\).
Raupjas kopas un aproksimācijas operatori
2009
Darbs sastāv no trim daļām. Pirmajā daļā tiek apskatīta klasiskā Pavlaka raupju kopu teorija, kas balstās uz ekvivalences attiecībām. Otrajā daļā tiek apskatīti vispārinātās raupju kopu teorijas izklāsti divās pieejās. Konstruktīvā pieejā aproksimācijas operatori tiek definēti ar binārās attiecības palīdzību. Aksiomātiskā vai algebriskā pieejā aproksimācijas operatori tiek definēti aksiomātiski. Tiek apskatītas aproksimāciju operatoru īpašības un to saiknes ar attiecīgo bināro attiecību. Trešajā daļā apskatīti divi piemēri, kas ilustrē raupju kopu teorijas iespējamo praktisko pielietojumu.
Variable-Range Approximate Systems Induced by Many-Valued L-Relations
2014
The concept of a many-valued L-relation is introduced and studied. Many-valued L-relations are used to induce variable-range quasi-approximate systems defined on the lines of the paper (A. Sostak, Towards the theory of approximate systems: variable-range categories. Proceedings of ICTA2011, Cambridge Univ. Publ. (2012) 265–284.) Such variable-range (quasi-)approximate systems can be realized as special families of L-fuzzy rough sets indexed by elements of a complete lattice.