A rough set is a formal approximation of a crisp set which gives lower and upper approximation of original set to deal with uncertainties. The concept of neutrosophic set is a mathematical tool for handling imprecise, indeterministic and inconsistent data. In this paper, we defne concepts of Rough Neutrosophic algebra and investigate some of their properties.

We discuss the rough set approach to approximation of vague concepts. There are already published several papers on rough sets and vague concepts staring from the seminal papers by Zdzis law Pawlak. However, only a few of them are discussing the relationships of rough sets with the sorites paradox. This paper contains a continuation of discussion on this issue.

This paper is an attempt to both expound and expand upon, from an approximation theorist’s point of view, some of the theoretical results that have been obtained in the sparse representation (compressed sensing) literature. In particular, we consider in detail l1 -approximation, which is fundamental in the theory of sparse representations, and the connection between the theory of sparse represe...

This paper considers the problem of how to establish calculi of approximation spaces. Approximation spaces considered in the context of rough sets were introduced by Zdzisław Pawlak more than two decades ago. In general, a calculus of approximation spaces is a system for combining, describing, measuring, reasoning about, and performing operations on approximation spaces. An approach to achievin...

Some examples from the mathematics of shape are presented that question some of the almost hidden assumptions behind results on limiting behaviour of finitary approximations to space-time. These are presented so as to focus attention on the observational problem of refinement and suggest the necessity for an alternative theory of 'fractafolds' against which the limiting theory of C ∞-differenti...

This paper considers the challenge of designing a framework that supports the integration of multiple existing simulation models into an integrated simulation environment (multisimulation). We aim to facilitate the process of fusing together the independently created simulators into an integrated simulation environment wherein we can model and execute complex scenarios involving multiple simula...

the solutions of mathematical models for the estimation of the kinetic, and biokinetic parameters of naphthalene, anthracene and pyrene during degradation in surface and subsurface soils are presented in this work. the models were developed using the twin concepts of rate-determining step and steady-state approximation method. they described the biodegradation of single and a mixture of polycyc...

Linear Relational Embedding is a method of learning a distributed representation of concepts from data consisting of binary relations between concepts. Concepts are represented as vectors, binary relations as matrices, and the operation of applying a relation to a concept as a matrix-vector multiplication that produces an approximation to the related concept. A representation for concepts and r...

Observations of apparently random phenomena are commonplace in science. However, randomness and Christian belief are often seen as incompatible, both by naturalists and by theists. This article argues that the scientific concept of randomness and the historic Christian understanding of God’s nature are compatible. It argues that the existence of randomness cannot be settled scientifically; neve...