The investigation of the Bayesian rough set model

AbstractThe original Rough Set model is concerned primarily with algebraic properties of approximately defined sets. The Variable Precision Rough Set (VPRS) model extends the basic rough set theory to incorporate probabilistic information. The article presents a non-parametric modification of the VPRS model called the Bayesian Rough Set (BRS) model, where the set approximations are defined by using the prior probability as a reference. Mathematical properties of BRS are investigated. It is shown that the quality of BRS models can be evaluated using probabilistic gain function, which is suitable for identification and elimination of redundant attributes

The investigation of the Bayesian rough set model

AbstractThe original Rough Set model is concerned primarily with algebraic properties of approximately defined sets. The Variable Precision Rough Set (VPRS) model extends the basic rough set theory to incorporate probabilistic information. The article presents a non-parametric modification of the VPRS model called the Bayesian Rough Set (BRS) model, where the set approximations are defined by using the prior probability as a reference. Mathematical properties of BRS are investigated. It is shown that the quality of BRS models can be evaluated using probabilistic gain function, which is suitable for identification and elimination of redundant attributes

Variable Precision Rough Set Approximations in Concept Lattice

The notions of variable precision rough set and concept lattice are can be shared by a basic notion, which is the definability of a set of objects based on a set of properties. The two theories of rough set and concept lattice can be compared, combined and applied to each other based on definability. Based on introducing the definitions of variable precision rough set and concept lattice, this paper shows that any extension of a concept in concept lattice is an equivalence class of variable precision rough set. After that, we present a definition of lower and upper approximations in concept lattice and generate the lower and upper approximations concept of concept lattice. Afterwards, we discuss the properties of the new lower and upper approximations. Finally, an example is given to show the validity of the properties that the lower and upper approximations have

Extended Tolerance Relation to Define a New Rough Set Model in Incomplete Information Systems

This paper discusses and proposes a rough set model for an incomplete information system, which defines an extended tolerance relation using frequency of attribute values in such a system. It first discusses some rough set extensions in incomplete information systems. Next, “probability of matching” is defined from data in information systems and then measures the degree of tolerance. Consequently, a rough set model is developed using a tolerance relation defined with a threshold. The paper discusses the mathematical properties of the newly developed rough set model and also introduces a method to derive reducts and the core

A novel imputation based predictive algorithm for reducing common cause variation from small and mixed datasets with missing values

Most process control algorithms need a predetermined target value as an input for a process variable so that the deviation is observed and minimized. In this paper, a novel machine learning algorithm is proposed that has an ability to not only suggest new target values for both categorical and continuous variables to minimize process output variation but also predict the extent to which the variation can be minimized.In foundry processes, an average rejection rate of 3%–5% within batches of castings produced is considered as acceptable and is considered as an effect of the common cause variation. As a result, the operating range for process input values is often not changed during the root cause analysis. The relevant available historical process data is normally limited with missing values and it combines both categorical and continuous variables (mixed dataset). However, technological advancements manufacturing processes provide opportunities to further refine process inputs in order to minimize undesired variation in process outputs.A new linear regression based algorithm is proposed to achieve lower prediction error in comparison to the commonly used linear factor analysis for mixed data (FAMD) method. This algorithm is further coupled with a novel missing data algorithm to predict the process response values corresponding to a given set of values for process inputs. This enabled the novel imputation based predictive algorithm to quantify the effect of a confirmation trial based on the proposed changes in the operating ranges of one or more process inputs. A set of values for optimal process inputs is generated from operating ranges discovered by a recently proposed quality correlation algorithm (QCA) using a Bootstrap sampling method. The odds ratio, which represents a ratio between the probability of occurrence of desired and undesired process output values, is used to quantify the effect of a confirmation trial.The limitations of the underlying PCA based linear model have been discussed and the future research areas have been identified

On Probability of Matching in Probability Based Rough Set Definitions

Abstract-The original rough set theory deals with precise and complete data, while real applications frequently contain imperfect information. A typical imperfect data studied in rough set research is the missing values. Though there are many ideas proposed to solve the issue in the literature, the paper adopts a probabilistic approach, because it can incorporate other types of imperfect data including imprecise and uncertain values in a single approach. The paper first discusses probabilities of attribute values assuming different type of attributes in real applications, and proposes a generalized method of probability of matching. It also discusses the case of continuous data as well as discrete one. The proposed probability of matching could be used for defining valued tolerance/similarity relations in rough set approaches

Detection of heat flux failures in building using a soft computing diagnostic system

The detection of insulation failures in buildings could potentially conserve energy supplies and improve future designs. Improvements to thermal insulation in buildings include the development of models to assess fabric gain - heat flux through exterior walls in the building- and heating processes. Thermal insulation standards are now contractual obligations in new buildings, and the energy efficiency of buildings constructed prior to these regulations has yet to be determined. The main assumption is that it will be based on heat flux and conductivity measurement. Diagnostic systems to detect thermal insulation failures should recognize anomalous situations in a building that relate to insulation, heating and ventilation. This highly relevant issue in the construction sector today is approached through a novel intelligent procedure that can be programmed according to local building and heating system regulations and the specific features of a given climate zone. It is based on the following phases. Firstly, the dynamic thermal performance of different variables is specifically modeled. Secondly, an exploratory projection pursuit method called Cooperative Maximum-Likelihood Hebbian Learning extracts the relevant features. Finally, a supervised neural model and identification techniques constitute the model for the diagnosis of thermal insulation failures in building due to the heat flux through exterior walls, using relevant features of the data set. The reliability of the proposed method is validated with real data sets from several Spanish cities in winter time