Unique Factorization Theorem and Formal Concept Analysis
نویسندگان
چکیده
In the theory of generalised colourings of graphs, the Unique Factorization Theorem (UFT) for additive induced-hereditary properties of graphs provides an analogy of the well-known Fundamental Theorem of Arithmetics. The purpose of this paper is to present a new, less complicated, proof of this theorem that is based on Formal Concept Analysis. The method of the proof can be successfully applied even for more general mathematical structures known as relational structures.
منابع مشابه
Unique factorization theorem for object-systems
The concept of an object-system is a common generalization of simple graph, digraph and hypergraph. In the theory of generalised colourings of graphs, the Unique Factorization Theorem (UFT) for additive induced-hereditary properties of graphs provides an analogy of the well-known Fundamental Theorem of Arithmetics. The purpose of this paper is to present UFT for object-systems. This result gene...
متن کامل$n$-factorization Property of Bilinear Mappings
In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity...
متن کاملA prime factor theorem for a generalized direct product
We introduce the concept of neighborhood systems as a generalization of directed, reflexive graphs and show that the prime factorization of neighborhood systems with respect to the the direct product is unique under the condition that they satisfy an appropriate notion of thinness.
متن کاملA unique common fixed point theorem for six maps in g-metric spaces
In this paper we obtain a unique common xed point theorem for sixweakly compatible mappings in G-metric spaces.
متن کاملFactorization Methods of Binary, Triadic, Real and Fuzzy Data
We compare two methods regarding the factorization problem of binary, triadic, real and fuzzy data, namely Hierarchical Classes Analysis and the formal concept analytical approach to Factor Analysis. Both methods search for the smallest set of hidden variables, called factors, to reduce the dimensionality of the attribute space which describes the objects without losing any information. First, ...
متن کامل