Development Of Information Granules And Their Applications To System Modeling

With the rapid growth of information technology,a large amount of data are generated and collected in the industry as well as our daily life.A genuine challenge is how to make sense of these data to help users understand their meaning and support decision-making.Due to the limitations of numerical solutions,information granules are introduced for describing and representing data more efficiently and effectively.Information granules are abstract and carefully structured collections of data built based on their closeness,similarity,and relationship.Through information granulation,complex problems are divided into a series of sub-problems that are easier to handle,and the overall cost of problem-solving can be reduced.This dissertation aims to develop a generic way of constructing information granules,many fields are investigated from both conceptually and algorithmically perspectives,such as the development of hierarchically structured information granules,granular data aggregation,and applications of information granules to fuzzy rule-based models.Previous studies majorly focus on the construction of type-1 information granules using the principle of justifiable granularity,especially intervals and fuzzy sets.To deal with complex problems,it is usually incapable for type-1 information granules of meeting the requirements of describing data with a high level of accuracy and completeness.Information granules of higher type are thus proposed.In this dissertation,the principle of justifiable granularity is engaged as a way of forming type-2 information granules – granular interval-valued information granules,whose descriptors are intervals themselves rather than numeric entities.A two-phase design process is presented: first,intervals(viz.information granules of type-1)are constructed based on available experimental evidence.Second,based on the data that have not been “covered” by the interval(the data one can refer to as residual granular data),their bounds are constructed in the form of information granules(instead of numeric values)thereby giving rise to the concept of granular intervals,namely information granules of type-2.This two-phase design process provides a generic way that can be applied to several types of information granules and information granules of higher type.The information granules obtained with the use of the principle of justifiable granularity are strongly influenced by the distribution of data.Usually one can not obtain an optimal information granule without considering the particularity of different data.A worthy investigating problem is to design a model of granular data aggregation based on different data.This dissertation proposes an adaptive principle of justifiable granularity.It builds upon the existing principle – the principle of justifiable granularity,which offers a conceptually and algorithmically attractive way of designing information granules on the basis of some experimental evidence(especially present in the form of numeric data).The method supports a granular data aggregation by producing an optimal information granule(with the optimality expressed in terms of the criteria of coverage and specificity commonly used for characterizing quality of information granules).The flexibility of the method stems from the introduction of an adaptive weighting scheme of the data leading to a vector of weights used in the construction of the optimal information granules.A detailed design procedure is provided along with the required optimization vehicle(realized with the aid of the population-based optimization techniques such as Particle Swarm Optimization(PSO)and Differential Evolution(DE)).Two direct application areas in which the principle becomes of direct usage include prediction of time series and prediction in spatial distributed data.In both cases,it is advocated that the results formed by the principle(information granules)are reflective of the precision(quality)of the prediction process.Two main problems in fuzzy rule-based models are the acquisition and optimization of fuzzy rules.Information granules can be applied to fuzzy rule-based model and consist of the condition and conclusion parts of the fuzzy rules,which leads to an great improvement on the performance of the model.This dissertation contributes to this area by bringing forward a two-phase design of fuzzy rules completed on the basis of experimental data.This design directly reflects upon the nature of the rules regarding the data used in their construction.First,information granules(fuzzy sets)standing in the condition and conclusion parts of individual rules are formed following a commonly used clustering technique of Fuzzy CMeans(FCM).The obtained results of fuzzy clustering are directly used to form a collection of fuzzy sets of conditions and conclusions forming the individual rules.Some optimization aspects are raised in this context by expressing the performance of the condition and conclusion fuzzy sets in terms of the reconstruction abilities of the data captured by the rules.Second,fuzzy sets present in the rules(which are typically described by membership functions having infinite support)are transformed into interval-valued information granules of finite support that capture the essential(core)relationships between the regions in the input and output spaces strongly supported by the experimental data.In this way,the proposed rule-based model exhibits a two-tier architecture built in two successive phases.Subsequently,the proposed architecture of the rules invokes two fundamentally different modes of reasoning:(a)a recall mode in the case where a new datum is positioned within the interval-valued information granules and(b)an approximation mode in the case where a new datum does not belong to the core structure of the rules.These two modes produce granular results(represented by intervals).A way of assessing the quality of the obtained results is provided.Along with these two modes,a characterization of the quality of results as well as the quality of the rules(expressed in terms of coverage,specificity of condition and conclusion)is offered.This dissertation bring forth a new research field in Granular Computing by discussing the ways of constructing information granules and their applications to system modeling.First,the development of information granules of higher type(especially granular interval-valued information granules)offers a new path for designing hierarchically structured information granules.In the meantime,it is interesting to design of granular fuzzy model of higher type.By flexibly forming different formalisms of information granules,complex problems can be solved effectively and the efficiency can be improved while ensuring the functionality of the system.Second,the proposed adaptive principle of justifiable granularity provides a new method of solving practical problems.For example,it can be used to reveal the development of certain industries by predicting the rules of data.Furthermore,information granules are applied to the design of fuzzy rule-based models,which helps to reduce the instability of numerical model and improve its quality.In future studies,some application areas can be discussed in detail,such as granular data imputation,optimization of fuzzy relation equations and granular time series segmentation.