Many research on primary school children in Malaysia indicate an over reliance on the written symbols representation (Munirah, 2001; Parmjit, 2005; Munirah& Noor Azlan, 2002; Chinappan & Ambigapathy, 2009; Mohini & Jacinta, 2010). This is a cause for concern as researchers draw strong connections between the representations children use and their understanding (Lamon, 2001). Janvier (1987) desc...

In this chapter we introduce the fundamental concepts behind the Green Function Theory. We start from a description of the second quantization method and then, after introducing the ensemble average of an operator, we define the main object of the theory, the Green function. Further on, after obtaining the equation of motion for the Green function, we introduce the self-energy operator and we d...

Abstract. 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 introduce the concepts of neutrosophic rough Sets and investigate some of its properties. Further as the charact...

This paper extends the l-complete approximation method developed for time invariant systems to a larger system class, ensuring that the resulting approximation can be realized by a finite state machine. To derive the new abstraction method, called asynchronous l-complete approximation, an asynchronous version of the well-known concepts of state property, memory span and l-completeness is introd...

Attribute reduction is one of the challenging problems facing the effective application of computational intelligence technology for artificial intelligence. Its task is to eliminate dispensable attributes and search for a feature subset that possesses the same classification capacity as that of the original attribute set. To accomplish efficient attribute reduction, many heuristic search algor...

We study concept extents by rough operations, define respectively the upper approximation and lower approximate of the extents of formal context, and discuss their properties, study the classifications and properties of concept extents by means of the lower (upper) approximation, and investigate the dependent relationship of the extents of formal concepts, such that we get a new method to class...

Topological approximation of self-formation of artificial objects in micro-scale is well established. However expansion of the topological approximation into nanoand molecular scales requires new and more generalized concepts of self-formation. This paper represents a preliminary effort to define self-formation as an evolution of 4-D parametric space in 8-D topological space, as universal conce...

Motivated by the problem to approximate all feasible schedules by one schedule in a given scheduling environment, we introduce in this paper the concepts of strong simultaneous approximation ratio (SAR) and weak simultaneous approximation ratio (WAR). Then we study the two parameters under various scheduling environments, such as, nonpreemptive, preemptive or fractional scheduling on identical,...

In this paper we introduce Linear Relational Embedding as a means of learning a distributed representation of concepts from data consisting of binary relations between concepts. The key idea is to represent concepts 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 conce...