Using optimisation techniques to granulise rough set partitions

Rough set theory (RST) is concerned with the formal approximation of crisp sets and is a mathematical tool which deals with vagueness and uncertainty. RST can be integrated into machine learning and can be used to forecast predictions as well as to determine the causal interpretations for a particular data set. The work performed in this research is concerned with using various optimisation techniques to granulise the rough set input partitions in order to achieve the highest forecasting accuracy produced by the rough set. The forecasting accuracy is measured by using the area under the curve (AUC) of the receiver operating characteristic (ROC) curve. The four optimisation techniques used are genetic algorithm, particle swarm optimisation, hill climbing and simulated annealing. This newly proposed method is tested on two data sets, namely, the human immunodeficiency virus (HIV) data set and the militarised interstate dispute (MID) data set. The results obtained from this granulisation method are compared to two previous static granulisation methods, namely, equal-width-bin and equal-frequency-bin partitioning. The results conclude that all of the proposed optimised methods produce higher forecasting accuracies than that of the two static methods. In the case of the HIV data set, the hill climbing approach produced the highest accuracy, an accuracy of 69.02% is achieved in a time of 12624 minutes. For the MID data, the genetic algorithm approach produced the highest accuracy. The accuracy achieved is 95.82% in a time of 420 minutes. The rules generated from the rough set are linguistic and easy-to-interpret, but this does come at the expense of the accuracy lost in the discretisation process where the granularity of the variables are decreased

A unified theory of granularity, vagueness and approximation

Abstract: We propose a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this semantic view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We provide a new formulation of these ideas in terms of a theory of granular partitions. We show that this theory provides a general framework within which we can understand the relation between vague terms and concepts and the corresponding crisp portions of reality. We also sketch how it might be possible to formulate within this framework a theory of vagueness which dispenses with the notion of truth-value gaps and other artifacts of more familiar approaches. Central to our approach is the idea that judgments about reality involve in every case (1) a separation of reality into foreground and background of attention and (2) the feature of granularity. On this basis we attempt to show that even vague judgments made in naturally occurring contexts are not marked by truth-value indeterminacy. We distinguish, in addition to crisp granular partitions, also vague partitions, and reference partitions, and we explain the role of the latter in the context of judgments that involve vagueness. We conclude by showing how reference partitions provide an effective means by which judging subjects are able to temper the vagueness of their judgments by means of approximations

Uncertainty behind the veil of ignorance

This paper argues that the decision problem in the original position should be characterized as a decision problem under uncertainty even when it is assumed that the denizens of the original position know that they have an equal chance of ending up in any given individual's place. It argues for this claim by arguing that (a) the continuity axiom of decision theory does not hold between all of the outcomes the denizens of the original position face and that (b) neither us nor the denizens of the original position can know the exact point where discontinuity sets in, because the language we employ in comparing different outcomes is ineradicably vague. It is also argued that the account underlying (b) can help proponents of superiority in value theory defend their view against arguments offered by Norcross and Griffin

On Vague Computers

Vagueness is something everyone is familiar with. In fact, most people think that vagueness is closely related to language and exists only there. However, vagueness is a property of the physical world. Quantum computers harness superposition and entanglement to perform their computational tasks. Both superposition and entanglement are vague processes. Thus quantum computers, which process exact data without "exploiting" vagueness, are actually vague computers

Intelligent computational sketching support for conceptual design

Sketches, with their flexibility and suggestiveness, are in many ways ideal for expressing emerging design concepts. This can be seen from the fact that the process of representing early designs by free-hand drawings was used as far back as in the early 15th century [1]. On the other hand, CAD systems have become widely accepted as an essential design tool in recent years, not least because they provide a base on which design analysis can be carried out. Efficient transfer of sketches into a CAD representation, therefore, is a powerful addition to the designers' armoury.It has been pointed out by many that a pen-on-paper system is the best tool for sketching. One of the crucial requirements of a computer aided sketching system is its ability to recognise and interpret the elements of sketches. 'Sketch recognition', as it has come to be known, has been widely studied by people working in such fields: as artificial intelligence to human-computer interaction and robotic vision. Despite the continuing efforts to solve the problem of appropriate conceptual design modelling, it is difficult to achieve completely accurate recognition of sketches because usually sketches implicate vague information, and the idiosyncratic expression and understanding differ from each designer