The basic aim of our study is to give a possible model for handling uncertain information. This model is worked out in the framework of DATALOG. The concept of multivalued knowledgebase will be defined as a quadruple of any background knowledge; a deduction mechanism; a connecting algorithm, and a function set of the program, which help us to determine the uncertainty levels of the results. At ...

Kaneko and Sessa defined the concept of compatibility for multivalued mappings with Hausdorff metric and proved a coincidence point theorem. After then, Pathak defined the concept of weak compatibility and proved a coincidence theorem. In the present work, we define a new type compatibility for multivalued mappings with Hausdorff metric. This new type compatibility is different from compatibili...

Multivalued projections are applied to the study of weighted least squares solutions linear relations equations (or inclusions) and some its applications. To this end a matrix representation multivalued with respect closure their ranges is described.

The study of fixed points of single-valued self-mappings or multivalued self-mappings satisfying certain contraction conditions has a great majority of results inmetric fixed point theory. All these results are mainly generalizations of Banach contraction principle. The Banach contraction principle guarantees the existence and uniqueness of fixed points of certain self-maps in complete metric s...

We consider the modeling approach introduced by R. Thomas for the qualitative study of gene regulatory networks. Tools and results on regulatory networks are often concerned only with the Boolean case of this formalism. However, multivalued approaches are sometimes more suited to model biological situations. Multivalued networks can be converted to partial Boolean maps, in a way that preserves ...

Nesting of relations is very much essential for many database representations in reality. Nesting of relations tends to reduce the data redundancy in the relations. It helps in dropping certain constraints in normalization which tend to omit certain sensitive data when tried to be normalized. Query processing or conversion of data repositories, as required, can be easily being tackled by the ai...

We establish a general fixed point theorem for multivalued maps defined on cones in Banach spaces. Applications to single and multivalued equations are presented. 2000 Mathematics Subject Classification: 47H10, 45M20.

This paper is a survey devoted to the transformations $$\begin{aligned} C&\mapsto \frac{1}{(2\pi i)^2}\int _{\Gamma _1}\int _2}f(\lambda ,\mu )\,R_{1,\,\lambda }\,C\, R_{2,\,\mu }\,{\mathrm{d}}\mu \,{\mathrm{d}}\lambda ,\\ \frac{1}{2\pi i}\int }g(\lambda )R_{1,\,\lambda R_{2,\,\lambda }\,{\mathrm{d}}\lambda , \end{aligned}$$ where $$R_{1,\,(\cdot )}$$ and $$R_{2,\,(\cdot are pseudo-resolvents a...

Functional dependencies, a notion originated in Relational Database Theory, are known to admit interesting characterizations in terms of Formal Concept Analysis. In database terms, two successive, natural extensions of the notion of functional dependency are the socalled degenerate multivalued dependencies, and multivalued dependencies proper. We propose here a new Galois connection, based on a...