Sentence examples for approximation of concepts from inspiring English sources

For the approximation of concepts, we will have: ((overline {C})^{I} = left { a in Delta ^{I} mid exists b left ((a,b) in R^{sim } wedge b in C^{I}right) right }), ((underline {C})^{I} = left { a in Delta ^{I} mid forall b left ((a,b) in R^{sim } rightarrow b in C^{I}right)right }).

Dominance-based Rough Set Approach (DRSA) is an effective mathematical tool to obtain approximations of concepts and discovery knowledge from ordered data.

The approximation synthesis of concepts from the acquired data is the main objective of the rough set analysis [33].

Loose upper approximations can be applied when there are no contexts which satisfy the upper approximation of a concept.

We can define the upper approximation of a concept C in (mathcal {ALC}) as the set of individuals in C that are indiscernible from at least an individual known to belong to C [6].

Similarly, we can define the lower approximation of a concept C as the set of all indiscernible individuals in C. In the sequel, we will introduce some basic characteristics of the rough (mathcal {ALC}), beginning with the syntax, semantics, and, lastly, alternative approaches to represent approximations, which will be used later in the query refinements.

Therefore, in order to find a context to satisfy the lower approximation of a concept C, only those minimal satisfying C are needed, since all their supersets will also satisfy C. Analogously, in order to find contexts satisfying the upper approximation of C, only the maximal ones satisfying C will suffice.

The individual behavior is modeled as a first-order approximation of the concept proposed by Song [102], building a Markov chain where states are locations visited by the user and the probability of moving from state i to state j is proportional to the number of times it has been observed in the data.

Approximations of a concept are fundamental concepts of multigranulation rough sets, which need to be updated incrementally while refining or coarsening attribute values.

The rough (mathcal {ALC}) is based on (mathcal {ALC}) with the addition of the upper and lower approximation as unary constructors of concepts, i.e., if C is a concept then (overline {C}) (possibly C) and (underline {C}) (necessarily C) are also concepts.

Two-state or linear approximation of the SH concept are typically used.