Fuzzy Modeli G Framework

International Journal of Computers Communications & Control

In 1965 Lotfi A. Zadeh published "Fuzzy Sets", his pioneering and controversialpaper, that now reaches almost 100,000 citations. All Zadeh’s papers were citedover 185,000 times. Starting from the ideas presented in that paper, Zadeh foundedlater the Fuzzy Logic theory, that proved to have useful applications, from consumerto industrial intelligent products. We are presenting general aspects of Zadeh’s contributionsto the development of Soft Computing(SC) and Artificial Intelligence(AI),and also his important and early influence in the world and in Romania. Severalearly contributions in fuzzy sets theory were published by Romanian scientists, suchas: Grigore C. Moisil (1968), Constantin V. Negoita & Dan A. Ralescu (1974), DanButnariu (1978). In this review we refer the papers published in "From Natural Languageto Soft Computing: New Paradigms in Artificial Intelligence" (2008, Eds.: L.A.Zadeh, D. Tufis, F.G. Filip, I. Dzitac), and also from the two special issues ...

International Journal of Advanced Research in Computer Science, 2018

The term 'Fuzzy' means vague, unclear, or imprecise. Fuzzy Logic is a many-valued logic that is based on the theory of Fuzzy Sets and it facilitates the representation of approximate reasoning. It finds its use in various areas where binary representations do not suffice. In this paper, we have confined our discussions on the theoretical foundations and advancements of modern Fuzzy Logic. We start with a brief account of Fuzzy Sets followed by the operations they support. Then we discuss how the Linguistic Variables allow more realistic reasoning as opposed to traditional binary reasoning. Then we introduce the theoretical aspects of the calculus of Fuzzy Restrictions. Finally, we discuss the theory of possibility as an alternative to the theory of probability. For the sake of simplicity and intelligibility, we have tried to avoid incommodious mathematical equations throughout this paper.

2016

Building abstract concepts is essential to humans when acquiring knowledge, realizing processing (reasoning), and communicating findings. Abstraction comes hand in hand with information granules and information granulation. When analyzing digital images, we form groups (clusters) of pixels, colors, and textures that constitute familiar objects. This paramount ability of forming groups of objects (information granules), manipulating them, and producing sound conclusions, is realized in an almost subconscious manner. Information granules are critical when representing and processing knowledge. They become instrumental when solving Preface The research conducted in this thesis was performed under the supervision of Dr. Witold Pedrycz, and it was supported by the National Council of Science and Technology (CONACYT) Mexico under grant no. 213501/308562 and by the Autonomous University of Tlaxcala (UAT) Mexico. Most of the experiments presented in this thesis were completed by using the general Linux cluster for research use, provided and maintained by the Academic Information and Communication Technologies (AICT) department at the University of Alberta. Chapter 4 of this thesis has been published as O. F. Reyes-Galaviz, and W. Pedrycz, "Fuzzy relational structures: Learning alternatives for fuzzy modeling," Joint IFSA World Congress and

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1998

 Abstract— The problems of uncertainty, imprecision and vagueness have been discussed for many years. These problems have been major topics in philosophical arenas with series of debate, in particular, about the nature of vagueness and the ability of traditional Boolean logic to cope with concepts and perceptions that are imprecise or vague. These sometimes make experts to rely on common sense when they solve problems. Interestingly, a lot of experts such as scientists, philosophers, psychologists, great mathematicians and others, researched vehemently on fuzzy logic, putting each other under constant scrutiny in response to their individual propositions coupled with fuzzy logic not until Zadeh Lotfi, eventually conceived fuzzy logic in 1971. Fuzzy logic is not logic that is fuzzy, but logic that is used to describe fuzziness. Fuzzy logic is the theory of fuzzy sets, sets that calibrate vagueness. Fuzzy logic is based on the idea that all things admit of degrees. Temperature, height, speed, distance, beauty, handsome, ugly, walk, stand all comes on a sliding scale. My car is running really hot. Elvis is a very tall guy. Fuzzy logic reflects how people think. It attempts to model our sense of words, our decision making and our common sense. As a result, it is leading to new, more human, intelligent systems.

Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics, 2008

This paper introduces a fuzzy inference system, based on the Takagi-Sugeno-Kang model, to achieve efficient and reliable classification in the domain of ubiquitous computing, and in particular for smart or context-aware, sensor-augmented devices. As these are typically deployed in unpredictable environments and have a large amount of correlated sensor data, we propose to use a Gath-Geva clustering specification as well as a genetic algorithm approach to improve the model's robustness. Experiments on data from such a sensor-augmented device show that accuracy is boosted from 83% to 97% with these optimizations under normal conditions, and for more challenging data from 54% to 79%.

Studies in Fuzziness and Soft Computing, 2000

In Chapter 1 we adopted Definition 1 stating that a fuzzy classifier is any classifier which uses fuzzy sets either during its training or during its operation. So, fuzzy classifier modeling stretches beyond fuzzy if-then designs discussed in the previous two chapters. This chapter presents nonif-then fuzzy models. These models can be grouped in different ways (see [39,81, 115, 118, 273, 320]). However, the boundaries between these groups are not sharp because many of the classification schemes can be assigned to more than one group (see, e.g., [232] where the authors use multiple rulebased prototypes and call their method a knowledge-oriented fuzzy k-nearest neighbor classifier). 7.1 Early ideas The first ideas about using fuzzy sets in classification emerged soon after fuzzy sets were introduced by Zadeh in 1965. The seminal paper by Bellman, Kalaba and Zadeh [26] defines a fuzzy classification environment where the problem is to design a classifier producing soft labels. They call abstraction the process of finding a set of discriminant functions gi : !Rn-+ [0,1], i = 1, ... ,e, from the labeled data set Z. This corresponds to training the classifier. Calculating a soft labeI for a given x E !R n , not in Z, is called generalization. 7.1.1 Fuzzy and probabilistic models Various relationships between fuzziness and probability have been explored. Combinations of fuzzy and probabilistic types of uncertainty have been sought at a rather theoretical level. Examples of this are fuzzy probability spaces [160], fuzzy Bayes classification (fuzzy-statistical and statistical-fuzzy models) [86, 236], fuzzy-Bayes decision making [320], etc. Replacing the probability density functions (p.dJ's) in the classical statistical pattern recognition model (Chapter 2) by membership functions has appealed to many authors as a logical substitute. This choice has been continuously disputed ever since it emerged. The idea of substitution has given rise to the possibilistic models for classification where possibilistic distributions are constructed