This paper investigated the incomplete information system in which situation of the more missing or absent unknown values. Based on the original characteristic relation, we proposed a new reflective relation which was controlled by the parameter alpha, beta. By analyzing illustrative examples and comparing to the original characteristic relation, this paper indicated the validity and practicabi...

This paper introduces some notions concerning binary relations according to [9]. It is also an attempt to complement the knowledge contained in the Mizar Mathematical Library regarding binary relations. We define here an image and inverse image of element of set A under binary relation of two sets A, B as image and inverse image of singleton of the element under this relation, respectively. Nex...

This study investigates the relation between overweight/obesity and self-rated health (SRH), and whether this relation varies by social factors. Data was taken from the German Health Interview and Examination Survey for Children and Adolescents (KiGGS, baseline 2003‒2006). For the definition of overweight and obesity, body mass index was calculated based on standardized height and weight measur...

The property of transitivity is one of the most important for fuzzy binary relations, especially in the cases when they are used for the representation of real life similarity or ordering information. As far as the algorithmic part of the actual calculation of the transitive closure of such relations is concerned, works in the literature mainly focus on crisp symmetric relations, paying little ...

In this paper we say that a preference for freedom of choice is justifiable if there exists a reflexive and complete binary relation on the set of alternatives, such that one opportunity set is at least as good as a second, if and only if the there is at least one alternative from the first set which is no worse than any alternative of the two sets combined together, with respect to the binary ...

This paper introduces the concept of ordient for binary relations (preferences), a relative of the concept of gradient for functions (utilities). The main motivation for this study is to replace the binary relation at the center stage of economic analysis, rather than its representation (whenever it exists). Moreover, ordients have a natural economic interpretation as marginal rates of substitu...

Let us say that an infinite binary sequence q lies above an infinite binary sequence p if q can be obtained from p by replacing selected 0’s in p by 1’s. We show that above any infinite binary Martin-Löf random sequence p there exists an infinite binary nonrandom sequence q above which there exists an infinite binary random sequence r. This result is of interest especially in connection with th...

We perform an extensive comparison of relational consistencies along four dimensions: on binary constraints, on non-binary constraints, on encodings of non-binary constraints, and on decomposable non-binary constraints. Our results contain some surprises. For example, on binary constraints, relational path-consistency does not reduce to path-consistency. On non-binary constraints, relational ar...