Fuzzy Filtering: A Mathematical Theory and Applications in Life Science (original) (raw)
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A Fuzzy System for Uncertain Data Modeling
International Journal of Scientific & Engineering Research, 2013
This text presents a fuzzy rules based system for modeling the relationships between inputs and output data in the presence of uncertainties. The fuzzy system is designed by separating the uncertainties from the data using fuzzy filtering algorithms. A stochastic modeling of the uncertainties helps in designing the fuzzy system to approximate the uncertain relationships. The proposed fuzzy model offers the followings: 1) predicts the output value for the given inputs assuming that there were no uncertainties in the input-output behavior; 2) assesses the worst effect of uncertainties on the model-predicted output value via predicting upper and lower limits on the output; 3) predicts the output value for the given inputs taking mathematically into account the underlying uncertainties (whose probabilistic-model was extracted from the data) in a sensible way. The paper illustrates through an example that the proposed fuzzy system is a useful modeling tool in presence of uncertainties.
Fuzzy Sets and Systems, 2003
This is an unusual book. Why and in which respect? It is amazing how Prof. Klir is able to explain a number of nontrivial facts using simple and succinct means. In 19 chapters of this small book he has succeeded in describing the essential theory of fuzzy set and fuzzy logic theory including their applications as well as explaining the main philosophical problems araising when dealing with uncertainty and vagueness. Thus, the book is very informative-one can ÿnd everything relevant there, mostly only outlined. However, the core of the problem is completed by enough references to be able to ÿnd missing information.
Recent advancements of fuzzy sets: Theory and practice
Information Sciences, 2006
This special issue encompasses six papers devoted to the recent advancements in the field of fuzzy sets. The seed of the current issue were some of the presentations made in three special sessions organized by the guest editors at the Nineth International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU 2002) that was held in Annecy, France, July 1-5, 2002. These six original contributions have been thoroughly revised and expanded to become the papers currently presented in this issue.
American Journal of Computational and Applied Mathematics, 2012
In the present paper we use principles of fuzzy logic to develop a general model representing several processes in a system's operation characterized by a degree of vagueness and/or uncertainty. For this, the main stages of the corresponding process are represented as fuzzy subsets of a set of linguistic labels characterizing the system's performance at each stage. We also introduce three alternative measures of a fuzzy system's effectiveness connected to our general model. These measures include the system's total possibilistic uncertainty, the Shannon's entropy properly modified for use in a fuzzy environment and the "centroid" method in which the coordinates of the center of mass of the graph of the membership function involved provide an alternative measure of the system's performance. The advantages and disadvantages of the above measures are discussed and a combined use of them is suggested for achieving a worthy of credit mathematical analysis of the corresponding situation. An application is also developed for the Mathematical Modelling process illustrating the use of our results in practice.
Fuzzy Sets and Systems, 2007
A basic problem, at the present stage of the Information society, is how to manage cognitive processes while taking into account their intrinsic features of uncertainty, including imprecision and vagueness. This has both theoretical and practical implications in Technology, Economics, Bio-Medicine, and so on. In fact, real-life situations are the prime source of motivation for this management to be considered. Traditional Statistics has developed tools and procedures for coping with this problem, assuming that uncertainty is basically due to random mechanisms appropriately handled by means of models from Probability Theory. Fuzzy Sets Theory and its generalization to what may be called "Fuzzy thinking'' has widened the scope of Statistics enabling us to deal with other sources of uncertainty, such as vagueness and imprecision, pervading both empirical data and/or models for data analysis. In this respect, for the last decades many research studies have been developed in which a coalition of Fuzzy Sets Theory and Statistics has been established with different purposes, namely,
Book Review Consequently, we do not recommend this book to beginners with fuzzy systems. Indeed, in spite of its title, we think that this book does not present an "introduction to fuzzy systems''. On the contrary, confirmed readers with well-founded knowledge can probably find some interest in some advanced ideas.