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2011 | Buch

From Interval (Set) and Probabilistic Granules to Set-and-Probabilistic Granules of Higher Order Kapitel lesen Erstes Kapitel lesen

Granular Computing and Intelligent Systems

Design with Information Granules of Higher Order and Higher Type

herausgegeben von: Witold Pedrycz, Shyi-Ming Chen

Verlag: Springer Berlin Heidelberg

Buchreihe : Intelligent Systems Reference Library

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Information granules are fundamental conceptual entities facilitating perception of complex phenomena and contributing to the enhancement of human centricity in intelligent systems. The formal frameworks of information granules and information granulation comprise fuzzy sets, interval analysis, probability, rough sets, and shadowed sets, to name only a few representatives. Among current developments of Granular Computing, interesting options concern information granules of higher order and of higher type. The higher order information granularity is concerned with an effective formation of information granules over the space being originally constructed by information granules of lower order. This construct is directly associated with the concept of hierarchy of systems composed of successive processing layers characterized by the increasing levels of abstraction. This idea of layered, hierarchical realization of models of complex systems has gained a significant level of visibility in fuzzy modeling with the well-established concept of hierarchical fuzzy models where one strives to achieve a sound tradeoff between accuracy and a level of detail captured by the model and its level of interpretability. Higher type information granules emerge when the information granules themselves cannot be fully characterized in a purely numerical fashion but instead it becomes convenient to exploit their realization in the form of other types of information granules such as type-2 fuzzy sets, interval-valued fuzzy sets, or probabilistic fuzzy sets. Higher order and higher type of information granules constitute the focus of the studies on Granular Computing presented in this study. The book elaborates on sound methodologies of Granular Computing, algorithmic pursuits and an array of diverse applications and case studies in environmental studies, option price forecasting, and power engineering.

Inhaltsverzeichnis

Frontmatter
From Interval (Set) and Probabilistic Granules to Set-and-Probabilistic Granules of Higher Order
Abstract
In this chapter, we provide a natural motivation for granules of higher order, and we show that these granules provide a unified description of different uncertainty formalisms such as random sets, Dempster-Shafer approach, fuzzy sets, imprecise probabilities, and Bayesian statistics. We also prove that for fuzzy uncertainty, granules of second order are sufficient.
Vladik Kreinovich
Artificial Intelligence Perspectives on Granular Computing
Abstract
Granular computing concerns a particular human-centric paradigm of problem solving by means of multiple levels of granularity and its applications in machines. It is closely related to Artificial Intelligence (AI) that aims at understanding human intelligence and its implementations in machines. Basic ideas of granular computing have appeared in AI under various names, including abstraction and reformulation, granularity, rough set theory, quotient space theory of problem solving, hierarchical problem solving, hierarchical planning, learning, etc. However, artificial intelligence perspectives on granular computing have not been fully explored. This chapter will serve the purpose of filling in such a gap. The results will have bidirectional benefits. A synthesis of results from artificial intelligence will enrich granular computing; granular computing philosophy, methodology, and tools may help in facing the grand challenge of reverse-engineering the brain, which has significant implications to artificial machine intelligence.
Yiyu Yao
Calculi of Approximation Spaces in Intelligent Systems
Abstract
Solving complex real-life problems requires new approximate reasoning methods based on new computing paradigms. One such recently emerging computing paradigm is Rough-Granular Computing (Pedrycz et al. 2008, Stepaniuk 2008) (RGC, in short). The RGC methods have been successfully applied for solving complex problems in areas such as identification of behavioral patterns by autonomous systems, web mining, and sensor fusion. In RGC, an important role play special information granules (Zadeh 1979, Zadeh 2006) called as approximation spaces. These higher order granules are used for approximation of concepts or, in a more general sense, complex granules. We discuss some generalizations of the approximation space definition introduced in 1994 (Skowron and Stepaniuk 1994, Skowron and Stepaniuk 1996, Stepaniuk 2008). The generalizations are motivated by reallife applications of intelligent systems and are related to inductive extensions of approximation spaces.
Andrzej Skowron, Jarosław Stepaniuk, Roman Swiniarski
Feature Discovery through Hierarchies of Rough Fuzzy Sets
Abstract
Rough set theory and fuzzy logic are mathematical frameworks for granular computing forming a theoretical basis for the treatment of uncertainty in many real-world problems, including image and video analysis. The focus of rough set theory is on the ambiguity caused by limited discernibility of objects in the domain of discourse; granules are formed as objects and are drawn together by the limited discernibility among them. On the other hand, membership functions of fuzzy sets enables efficient handling of overlapping classes. The hybrid notion of rough fuzzy sets comes from the combination of these two models of uncertainty and helps to exploit, at the same time, properties like coarseness, by invoking rough sets, and vagueness, by considering fuzzy sets. We describe a model of the hybridization of rough and fuzzy sets, that allows for further refinements of rough fuzzy sets. This model offers viable and effective solutions to some problems in image analysis, e.g. image compression.
Alfredo Petrosino, Alessio Ferone
Comparative Study of Fuzzy Information Processing in Type-2 Fuzzy Systems
Abstract
Fuzzy information processing in type-2 fuzzy systems has been implemented in most cases based on the Karnik and Mendel (KM) and Wu-Mendel (WM) approaches. However, both of these approaches are time consuming for most real-world applications, in particular for control problems. For this reason, a more efficient method based on evolutionary algorithms has been proposed by Castillo and Melin (CM). This method is based on directly obtaining the type reduced results by using an evolutionnary algorithm (EA). The basic idea is that with an EA the upper and lower membership functions in the output can be obtained directly based on experimental data available for a particular problem. A comparative study (in control applications) of the three methods, based on accuracy and efficiency is presented, and the CM method is shown to outperform both the KM and WM methods in efficiency while accuracy produced by this method is comparable.
Oscar Castillo, Patricia Melin
Type-2 Fuzzy Similarity in Partial Truth and Intuitionistic Reasoning
Abstract
Representing and manipulating the vague concepts of partially true knowledge pose a major challenge to the development of machine intelligence. In particular, the issue of how to extract approximate facts from vague and partially true statements has received considerable attention in the field of fuzzy information processing. However, vagueness is often due to a lack of available information, making it impossible to satisfactorily evaluate membership. Atanassov (1996) demonstrated the feasibility of mapping intuitionistic fuzzy sets to historical fuzzy sets. Intuitionistic fuzzy sets are isomorphic to interval valued fuzzy sets, while interval valued fuzzy sets have been regarded as unique value among type-2 fuzzy sets. This study presents a theoretical method to represent and manipulate partially true knowledge. The proposed method is based on the measurement of similarity among type-2 fuzzy sets, which are used directly to handle rule uncertainty that type-1 fuzzy sets are unable to deal with. Moreover, the switching relationship between type-2 fuzzy sets and intuitionist fuzzy sets is defined axiomatically. Results of this study demonstrate the effectiveness of the proposed theoretical method in pattern recognition and reasoning with regard to medical diagnosis.
Chung-Ming Own
Decision Making with Second Order Information Granules
Abstract
Decision-making under uncertainty has evolved into a mature field. However, in most parts of the existing decision theory, one assumes decision makers have complete decision-relevant information. The standard framework is not capable to deal with partial or fuzzy information, whereas, in reality, decision-relevant information about outcomes, probabilities, preferences etc is inherently imprecise and as such described in natural language (NL). Nowadays, there is no decision theory with second-order uncertainty in existence albeit real-world uncertainties fall into this category. This applies, in particular, to imprecise probabilities expressed by terms such as likely, unlikely, probable, usually etc. We call such imprecise evaluations second-order information granules.
In this study, we develop a decision theory with second-order information granules. The first direction we consider is decision making with fuzzy probabilities. The proposed theory differs from the existing ones as one that accumulates non-expected utility paradigm with NL-described decision-relevant information. Linguistic preference relations and fuzzy utility functions are used instead of their classical counterparts as forming a more adequate description of human preferences expressed under fuzzy probabilities. Fuzzy probability distribution is incorporated into the suggested fuzzy utility model by means of a fuzzy number-valued fuzzy measure instead of a real-valued non-additive probability. We provide representation theorems for a fuzzy utility function described by a fuzzy number-valued Choquet integral with a fuzzy number-valued integrand and a fuzzy number-valued fuzzy measure. The proposed theory is intended to solve decision problems when the environment of fuzzy states and fuzzy outcomes are characterized by fuzzy probabilities. As the second direction in this realm we consider hierarchical imprecise probability models. Such models allow us to take into account imprecision and imperfection of our knowledge, expressed by interval values of probabilities of states of nature and degrees of confidence associated with such values. A decision-making process analysis and a choice of the most preferable alternative subject to variation of intervals at the lower and upper levels of models and the types of distribution on the sets of random values of probabilities of states of nature is also of significant interest.
We apply the developed theories and methodologies to solving real-world economic decision-making problems. The obtained results show validity of the proposed approaches.
R. A. Aliev, W. Pedrycz, O. H. Huseynov, L. M. Zeinalova
On the Usefulness of Fuzzy Rule Based Systems Based on Hierarchical Linguistic Fuzzy Partitions
Summary
In the recent years, a high number of fuzzy rule learning algorithms have been developed with the aim of building the Knowledge Base of Linguistic Fuzzy Rule Based Systems. In this context, it emerges the necessity of managing a flexible structure of the Knowledge Base with the aim of modeling the problems with a higher precision. In this work, we present a short overview on the Hierarchical Fuzzy Rule Based Systems, which consists in a hierarchical extension of the Knowledge Base, preserving its structure and descriptive power and reinforcing the modeling of those problem subspaces with more difficulties by means of a hierarchical treatment (higher granularity) of the rules generated in these areas. Finally, this methodology includes a summarisation step by means of a genetic rule selection process in order to obtain a compact and accurate model. We will show the goodness of this methodology by means of a case of study in the framework of imbalanced data-sets in which we compare this learning scheme with some basic Fuzzy Rule Based Classification Systems and with the well-known C4.5 decision tree, using the proper statistical analysis as suggested in the specialised literature. Finally, we will develop a discussion on the usefulness of this methodology, analysing its advantages and proposing some new trends for future work on the topic in order to extract the highest potential of this technique for Fuzzy Rule Based Systems.
Alberto Fernández, Victoria López, María José del Jesus, Francisco Herrera
Fuzzy Information Granulation with Multiple Levels of Granularity
Abstract
Granular computing is a problem solving paradigm based on information granules, which are conceptual entities derived through a granulation process. Solving a complex problem, via a granular computing approach, means splitting the problem into information granules and handling each granule as a whole. This leads to a multi-level view of information granulation, which permeates human reasoning and has a significant impact in any field involving both human-oriented and machine-oriented problem solving. In this chapter we examine a view of granular computing as a paradigm of human-inspired problem solving and information processing with multiple levels of granularity, with special focus on fuzzy information granulation. To support the importance of granulation with multiple levels, we present a multi-level approach for extracting well-defined and semantically sound fuzzy information granules from numerical data.
Giovanna Castellano, Anna Maria Fanelli, Corrado Mencar
A Rough Set Approach to Building Association Rules and Its Applications
Abstract
Data mining is a process or method of finding information, evidence, insight, knowledge and hypotheses in a huge database, such as marketing data.
Recently, the association rule presented by R. Agrawal in 1983 has been used to rapidly expand a data mining method. This method is general and flexible and can be applied to both general data analysis and very wide surveys. In addition, the rules for this method are complicated. On the other hand, when the support value is minimal and the confidence value is high, the obtained value is already known and trivial. A breakthrough method is needed.
The objective of this paper is to present a rough set model to overcome such issues. Employing the rough set model, we analyzed three different scales of databases and compared the results of simulation experiments using proposed and conventional models. The rough set model obtained an efficient number of association rules and usually took less computation time.
Junzo Watada, Takayuki Kawaura, Hao Li
Fuzzy Modeling with Grey Prediction for Designing Power System Stabilizers
Abstract
This work presents a novel method for designing power system stabilizers (PSS) by using a fuzzy PID controller tuned with grey prediction. The PSS design can be formulated as an optimal linear regulator control problem; however, implementing the PSS requires designing estimators, increasing implementation complexity and reducing control system reliability. Therefore, this work seeks a control scheme that adopts only the desired state variable, for example speed. The grey fuzzy PID control is integrated with grey prediction to determine the control signal of each generator thus simplifying the design and increasing system performance. The grey prediction uses forecast information regarding the output state variables of the generators to the fuzzy tuning PID controller to control power system behaviorand thus achieve good performance, enabling the presented method to reduce power system oscillation and increase dynamic stability. Finally, the advantages of the proposed method are highlighted by simulating the detailed behavior of a multimachine power system.
Y. T. Hsiao, T. L. Huang, S. Y. Chang
A Weighted Fuzzy Time Series Based Neural Network Approach to Option Price Forecasting
Abstract
Option price forecasting has become an important financial issue in recent years. However, it remains a challenging problem due to the fact that the option price is determined by many factors. This paper proposes a new method to forecast the option price. The proposed approach, a weighted fuzzy time series based neural network (WFTSNN) model, is a hybrid method composed of a fuzzy time series model and a neural network model. In the WFTSNN, a fuzzy time series model is used to select the training data set from the historical data set to train a neural network for option price forecasting. The experimental results show that the WFTSNN outperforms several existing hybrid methods in terms of the mean absolute error and the root mean squared error.
Yungho Leu, Chien-Pang Lee, Chen-Chia Hung
A Rough Sets Approach to Human Resource Development in IT Corporations
Abstract
In IT corporations, it is essential to increase competitive advantages and organizational performance. Employees are critical to a company’s success. A new research method is needed to quantify employees’ influence on building relationships with customers and to facilitate human resource and customer relationship management. Rough sets theory is a mathematical approach to dealing with vagueness and uncertainty. It can change a qualitative problem into a quantitative one and produce a possible solution by providing useful and valuable information and guidelines for decision making. The objective of this study is to determine through the use of analysis analyzed with rough employee characteristics and behaviors that yield positive or negative relationships with customers. The rough set approach distinguishes between these two groups and leads us to suggest policies to improve human resource and customer relationship management and development. The proper management of employees and customers will ensure project success and good corporate performance.
Quality is an attribute that is important for products as well as for management and the company itself. The development and promotion of personnel resources is indispensable for improving the quality of a company’s management. Management quality is closely related to corporate culture and a sense of social responsibility. Therefore, personnel resource development and personnel training for employees should be emphasized. In the main discussion of this paper, information was gathered from engineers at a regional IT company through questionnaires and their observable talents were analyzed. The research addressed questions such as what kinds of values should be promoted. An attempt was made to clarify the relation between QWL (Quality of Working Life) and personnel training. This paper suggests that the management quality and CSR (Corporate Social Responsibility) of regional companies is closely related with the quality and improvement of their growth.
Shinya Imai, Junzo Watada
Environmental Applications of Granular Computing and Intelligent Systems
Abstract
This paper presents the environmental applications of granular computing. First, the relevance of information granulation in the description of environmental phenomena is discussed. A granular prediction model of time series of a dust storm concentration is described. This example is used to explain the technique of information granulation of an environmental phenomenon. Then the issue of environmental management is discussed. Granular computing helps us establish the pattern recognition technique which is also very helpful in environmental management. In addition, this study presents an approach to extract interpretable rules of natural hazards from available data. Finally, the multi-objective design of a granular hierarchy model is presented to determine the optimal management strategy of air quality. The environmental application experiments show that granular computing comes as a promising vehicle for solving social problems related to protection of the environment.
Wang-Kun Chen
Backmatter
Metadaten
Titel
Granular Computing and Intelligent Systems
herausgegeben von
Witold Pedrycz
Shyi-Ming Chen
Copyright-Jahr
2011
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-19820-5
Print ISBN
978-3-642-19819-9
DOI
https://doi.org/10.1007/978-3-642-19820-5

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