2,979 publications from this institution
The paper proposes a new model of Petri nets based on the use of logic based neurons. In contrast to the existing generalizations, this approach is aimed at neural-type modeling of the entire concept with a full exploitation of the learning capabilities of the processing units being used there. The places and transitions of the net are represented by OR and AND-type and DOMINANCE neurons, respectively. A correspondence between this model and the previous two-valued counterpart is also revealed. The learning aspects associated with the nets are investigated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
In this study, we pursue fundamental ideas of granular computing by concentrating on further conceptual developments of metastructures which are inherently associated with computing involving a large number of distributed datasets. We show that such processing leads to the representatives of information granules and granular models in the form of metastructures and metamodels. The formulation of the concept is provided and presented along with some essential algorithmic developments and pertinent optimisation strategies.
In spite of their striking diversity, numerous tasks and architectures of intelligent systems such as those permeating multivariable data analysis, decision-making processes along with their underlying models, recommender systems and others exhibit two evident commonalities. They promote (a) human centricity and (b) vigorously engage perceptions (rather than plain numeric entities) in the realization of the systems and their further usage. Information granules play a pivotal role in such settings. Granular Computing delivers a cohesive framework supporting a formation of information granules and facilitating their processing. The author exploits two essential concepts of Granular Computing. The first one deals with the construction of information granules. The second one helps endow constructs of intelligent systems with a much needed conceptual and modeling flexibility. The study elaborates in detail on the three representative studies. In the first study being focused on the Analytic Hierarchy Process (AHP) used in decision-making, the author shows how an optimal allocation of granularity helps improve the quality of the solution and facilitate collaborative activities in models of group decision-making. The second study is concerned with a granular interpretation of temporal data where the role of information granularity is profoundly visible when effectively supporting human centric description of relationships existing in data. The third study concerns a formation of granular logic descriptors on a basis of a family of logic descriptors.
In this paper, we propose a gradient-based method to approximate a fuzzy set through a trapezoidal fuzzy set (TFS). By adding some constraints in the formulated optimization problem, the major characteristics of the fuzzy set such as the core, the major part of the support, and the shape of the membership function could be preserved; also the form of the optimized result as a TFS is guaranteed. We regard the optimized TFS as the "skeleton" (blueprint) of the original fuzzy set. Based on this skeleton, we further extend the TFS to a higher type, that is, an interval type-2 TFS (IT2 TFS), so that more information about the original fuzzy set could be captured but the number of the parameters used to describe the original fuzzy set is still maintained low (nine parameters are required for an IT2 TFS). The principle of justifiable granularity is used to ensure that the formed type-2 information granule exhibits a sound interpretation. Both synthetic fuzzy sets and those constructed by the fuzzy C -means algorithm applied to the publicly available data have been used to demonstrate the usefulness of the proposed approximation methods.
2 Abstract—A new method of time series segmentation is developed using differential evolution. Traditional methods of time series segmentation focus on single variable segmentation and as such often determine sections of the time series with constant slope (i.e. linear). The problem of segmenting multivariate time series is significantly more involved since several time series have to be jointly segmented. Thus the concept of boundary becomes ill-defined since each time series may not be exactly synchronized and change identically in time. The problem is rectified by minimizing the mean of the variance of the slopes determined in each segment. Performance of the method is measured in terms of the classification rate and the accuracy of determination of boundaries. Experimental evidence shows the effectiveness of the method when applied to synthetic and real-world data compared with multivariate time series clustering approaches. Keywords—Multivariate segmentation, differential evolution, time series, fuzzy clustering.
The theory of shadowed sets is one among several key contributors to the area of granular computing. As the name stipulates, granular computing embraces processing of information granules. By information granules we mean collections of entities being assembled together in order to achieve a certain conceptual and/or computational feasibility of processing carried out in any complex system, no matter whether natural or artificial. Granular computing, as being exclusively geared toward processing of information granules, subsumes the commonly encountered numeric style of processing. The intent of shadowed sets is to capture ("isolate" or "localize") and quantify the factor of uncertainty inherently existing in any real-world system. We first discuss the underlying theoretical underpinnings of shadowed sets that primarily dwell on the pillar of three-valued logic. We also come up with a number of illustrative examples that help grasp the essence of the concept. The study embarks on a variety of the applications of shadowed sets to fuzzy mappings along with an analysis of their relevance as well as data quantization. In the case of fuzzy mappings, it is revealed that shadowed sets provide an interesting three-valued quantification of the property of relevancy (such as acceptable mapping, marginal mapping, and a lack of mapping). This article includes a number of detailed calculations concerning two commonly exploited classes of triangular and Gaussian fuzzy sets. Moreover, we elaborate on the exploration of shadowed sets as an algorithmic realization of the least commitment principle advocated by Marr. © 2002 John Wiley & Sons, Inc.
Purpose The purpose is to formulate and present algorithms of reconciliation of perception of information granules regarded as fuzzy sets. It also discussed a problem of a multi‐view reconciliation of perception of granular mappings and their reconciliation. Design/methodology/approach It is realized in the framework of logically‐oriented transformation of the membership functions and mappings. Findings A suite of optimization techniques is presented and their performance illustrated with the aid of numeric experiments. Practical implications An important step enhancing the development of fuzzy rule‐based systems. Originality/value The concept of reconciliation of information granules has been formulated for the first time. The algorithmic setting offers additional practical value.
Relational data has become increasingly important in decision analysis in recent years, and so mining knowledge which preserves relationships between objects is an important topic. Graphs can represent the knowledge which contains objects and relationships between objects. Rough set theory provides an effective tool for extracting knowledge, but it is not sufficient to extract the knowledge containing the data on relationships between objects. In order to extend the application scope and enrich the rough set theory, it is essential to develop a rough set analysis of graphs. This extension is important because graphs play a crucial role in social network analysis. In this paper, the rough set analysis of graphs based on general binary relations is investigated. We introduce three types of approximation operators of graphs: vertex graph approximation operators, edge graph approximation operators, and graph approximation operators. Relationships between approximation operators of graphs and approximation operators of sets are presented. Then we investigate the approximation operators of graphs within constructive and axiomatic approaches.
An evaluation and comparative study of kernel-based fuzzy clustering algorithms is presented. The main objective is to evaluate the performance gains provided by kernelised FCM (fuzzy C-means). It is shown that kernelised FCM provides marginal improvements in the classification rate for several popular Machine Learning data sets. It is observed that the performance of kernelised FCM depends greatly on the selection of the kernel parameters.
