In a given graph G, a set S of vertices with an assignment of colors is a defining set of the vertex coloring of G, if there exists a unique extension of the colors of S to a χ(G)-coloring of the vertices of G. A defining set with minimum cardinality is called a smallest defining set (of vertex coloring) and its cardinality, the defining number, is denoted by d(G, χ). Let d(n, r, χ = k) be the ...

Similarity concept, finding the resemblance or classifying some groups of objects and study their common properties has been the interest of many researchers. Basically, in the studies the similarity between two objects or phenomena, 2-similarity in our words, has been discussed. In this paper, we consider the case when the resemblance or similarity among three objects or phenomena of a set, 3-...

Recent years have brought a significant growth in the volume of research in sentiment analysis, mostly on highly subjective text types (movie or product reviews). The main difference these texts have with news articles is that their target is clearly defined and unique across the text. Following different annotation efforts and the analysis of the issues encountered, we realised that news opini...

Probabilistic polysemantic distribution is peculiar to a word with a concrete frequency in the frequency list. Let's introduce dependence "usage polysemanticism" proceeding from the following theoretical assumptions: 1. The lexicon of a concrete language (sublanguage) is reflected in the appropriate explanatory dictionary. A certain constitutive text corpus lays in the basis of the language. 2....

This paper describes the development of a fuzzy decision support system (FDSS) for the assessment of risk in E-commerce (EC) development. A Web-based prototype FDSS is suggested to assist EC project managers in identifying potential EC risk factors and the corresponding project risks. A risk analysis model for EC development using a fuzzy set approach is proposed and incorporated into the FDSS....

A set of blocks which is a subset of blocks of only one design is called a defining set of that design. In this paper we determine smallest defining sets of the 21 nonisomorphic 2-(10,5,4) designs.

We deal with developing a Decision Support System (DSS) to promote the ridesharing among both students and staff of a big organization. The DSS includes a set of functions that allow the management of the riders’ requests and drivers’ availability and embeds a novel two-phase optimization approach that helps in defining the optimal riders-drivers matching. The first phase consists o...

A Greedy Defining Set is a set of entries in a Latin Square with the property that when the square is systematically filled in with a greedy algorithm, the greedy algorithm succeeds. Let g(n) be the smallest defining set for any Latin Square of order n. We give theorems on the upper bounds of gn and a table listing upper bounds of gn for small values of n. For a circulant Latin square, we find ...

A directed triple system of order v, DTS(v), is a pair (V,B) where V is a set of v elements and B is a collection of ordered triples of distinct elements of V with the property that every ordered pair of distinct elements of V occurs in exactly one triple as a subsequence. A set of triples in a DTS(v) D is a defining set for D if it occurs in no other DTS(v) on the same set of points. A definin...

The monoid $Cb$ of name substitutions and the notion of finitely supported $Cb$-sets introduced by Pitts as a generalization of nominal sets. A simple finitely supported $Cb$-set is a one point extension of a cyclic nominal set. The support map of a simple finitely supported $Cb$-set is an injective map. Also, for every two distinct elements of a simple finitely supported $Cb$-set, there exists...