
WYDZIAŁ
... Fuzzy expert systems as real-time controllers (navigation system for mobile robots). Medical diagnostic systems. Learning algorithms for OCR (perceptrons, Hopfield networks). Adaptive linear networks. Efficiency of learning methods. Speech recognition. Cancer diagnosis using SVM. Laboratory: Fuzzy e ...
... Fuzzy expert systems as real-time controllers (navigation system for mobile robots). Medical diagnostic systems. Learning algorithms for OCR (perceptrons, Hopfield networks). Adaptive linear networks. Efficiency of learning methods. Speech recognition. Cancer diagnosis using SVM. Laboratory: Fuzzy e ...
i S dS i S dS Fuzzy Logic, Sets and Systems Lecture 1 Introduction
... uncertain information, and to create systems that are much closer in spirit to human thinking. thinking Fuzzy logic is a strong candidate for this purpose. purpose Fuzzy Logic, Sets and Systems ...
... uncertain information, and to create systems that are much closer in spirit to human thinking. thinking Fuzzy logic is a strong candidate for this purpose. purpose Fuzzy Logic, Sets and Systems ...
What is rule-based reasoning
... in order to reach a conclusion. Expert systems can include different types of reasoning like rulebased, case-based, fuzzy logic, neural networks, bayesian networks, etc. The most common expert system is rule-based, containing a knowledge base (rules) and an inference engine (routing mechanism) which ...
... in order to reach a conclusion. Expert systems can include different types of reasoning like rulebased, case-based, fuzzy logic, neural networks, bayesian networks, etc. The most common expert system is rule-based, containing a knowledge base (rules) and an inference engine (routing mechanism) which ...
Computational Intelligence
... Deals badly with noisy & imprecise environments Is very sensitive to representation choices It can be hard to find a usable formal representation Deals badly with quantitative measurements ...
... Deals badly with noisy & imprecise environments Is very sensitive to representation choices It can be hard to find a usable formal representation Deals badly with quantitative measurements ...
Chap 11: Artificial Intelligence II: Operational Perspective
... We must combine the recommendations of Rule 1 and Rule 2 into a single result. There are several ways to do this; one method is to generate a weighted average. The weight of each rule action is weighted by the corresponding membership of its condition and the result is then averaged. ...
... We must combine the recommendations of Rule 1 and Rule 2 into a single result. There are several ways to do this; one method is to generate a weighted average. The weight of each rule action is weighted by the corresponding membership of its condition and the result is then averaged. ...
Modeling and Experimentation Framework for Fuzzy Cognitive Maps Maikel Leon Espinosa
... Many papers describe the use of Fuzzy Cognitive Maps as a modeling/representation technique for real-life scenarios’ simulation or prediction. However, not many real software implementations are described neither found. In this proposal the authors describe a modeling and experimentation framework w ...
... Many papers describe the use of Fuzzy Cognitive Maps as a modeling/representation technique for real-life scenarios’ simulation or prediction. However, not many real software implementations are described neither found. In this proposal the authors describe a modeling and experimentation framework w ...
lesson plan
... Fuzzy Sets – Operations on Fuzzy Sets – Fuzzy Relations – Membership Functions- Fuzzy Rules and Fuzzy Reasoning – Fuzzy Inference Systems – Fuzzy Expert Systems – Fuzzy Decision Making Objective: To impart knowledge on fuzzy logic and different stages in fuzzy systems ...
... Fuzzy Sets – Operations on Fuzzy Sets – Fuzzy Relations – Membership Functions- Fuzzy Rules and Fuzzy Reasoning – Fuzzy Inference Systems – Fuzzy Expert Systems – Fuzzy Decision Making Objective: To impart knowledge on fuzzy logic and different stages in fuzzy systems ...
Computational Intelligence
... Silicon-based computational intelligence systems usually comprise hybrids of paradigms such as artificial neural networks, fuzzy systems, and evolutionary algorithms, augmented with knowledge elements, and are often designed to mimic one or more aspects of carbon-based biological intelligence. The c ...
... Silicon-based computational intelligence systems usually comprise hybrids of paradigms such as artificial neural networks, fuzzy systems, and evolutionary algorithms, augmented with knowledge elements, and are often designed to mimic one or more aspects of carbon-based biological intelligence. The c ...
CS607_Current_Subjective
... What is fuzzy logic? A type of logic that recognizes more than simple true and false values. With fuzzy logic, propositions can be represented with degrees of truthfulness and falsehood. For example, the statement, today is sunny,might be 100% true if there are no clouds, 80% true if there are a few ...
... What is fuzzy logic? A type of logic that recognizes more than simple true and false values. With fuzzy logic, propositions can be represented with degrees of truthfulness and falsehood. For example, the statement, today is sunny,might be 100% true if there are no clouds, 80% true if there are a few ...
Chapter 02 for Neuro-Fuzzy and Soft Computing
... cybernetics (the study of information and control in human and machines) ...
... cybernetics (the study of information and control in human and machines) ...
Neuro-fuzzy systems
... The weighted inputs xi o wi, where o is a t-norm and tconorm, can be general fuzzy relations too, not just simple products as in standard neurons The transfer function g can be a non-linear such as a sigmoid ...
... The weighted inputs xi o wi, where o is a t-norm and tconorm, can be general fuzzy relations too, not just simple products as in standard neurons The transfer function g can be a non-linear such as a sigmoid ...
cs621-lect19-fuzzy-logic-neural-net-based-IR-2008-10
... • Queries and docs represented by sets of index terms: matching is approximate from the start • This vagueness can be modeled using a fuzzy framework, as follows: – with each term is associated a fuzzy set – each doc has a degree of membership in this fuzzy set • This interpretation provides the fou ...
... • Queries and docs represented by sets of index terms: matching is approximate from the start • This vagueness can be modeled using a fuzzy framework, as follows: – with each term is associated a fuzzy set – each doc has a degree of membership in this fuzzy set • This interpretation provides the fou ...
Special issue: Computational intelligence models for image
... more effective than other evolutionary-based methods in terms of applicability and computational efficiency. A multi-objective image segmentation model with an interactive evolutionary computation framework is described in the fourth article [5]. The multi-objective genetic algorithm is used to simu ...
... more effective than other evolutionary-based methods in terms of applicability and computational efficiency. A multi-objective image segmentation model with an interactive evolutionary computation framework is described in the fourth article [5]. The multi-objective genetic algorithm is used to simu ...
History of AI
... Fuzzy Logic is a departure from classical two-valued logic (True or False) It is a multi-valued logic that allows intermediate values to be defined between conventional evaluations Notions like rather warm or pretty cold can be formulated mathematically and processed by computers. In this wa ...
... Fuzzy Logic is a departure from classical two-valued logic (True or False) It is a multi-valued logic that allows intermediate values to be defined between conventional evaluations Notions like rather warm or pretty cold can be formulated mathematically and processed by computers. In this wa ...
A Tutorial on Cognitive Network Process for Business Applications
... E-business and his Ph.D. in Computational Intelligence and Operations Research from the Hong Kong Polytechnic University in 2004 and 2009 respectively. His research interests include computational intelligence, decisions analysis, information systems, algorithms, social computing, and operations res ...
... E-business and his Ph.D. in Computational Intelligence and Operations Research from the Hong Kong Polytechnic University in 2004 and 2009 respectively. His research interests include computational intelligence, decisions analysis, information systems, algorithms, social computing, and operations res ...
Type-2 fuzzy sets and systems

Type-2 fuzzy sets and systems generalize Type-1 fuzzy sets and systems so that more uncertainty can be handled. From the very beginning of fuzzy sets, criticism was made about the fact that the membership function of a type-1 fuzzy set has no uncertainty associated with it, something that seems to contradict the word fuzzy, since that word has the connotation of lots of uncertainty. So, what does one do when there is uncertainty about the value of the membership function? The answer to this question was provided in 1975 by the inventor of fuzzy sets, Prof. Lotfi A. Zadeh [27], when he proposed more sophisticated kinds of fuzzy sets, the first of which he called a type-2 fuzzy set. A type-2 fuzzy set lets us incorporate uncertainty about the membership function into fuzzy set theory, and is a way to address the above criticism of type-1 fuzzy sets head-on. And, if there is no uncertainty, then a type-2 fuzzy set reduces to a type-1 fuzzy set, which is analogous to probability reducing to determinism when unpredictability vanishes,.In order to symbolically distinguish between a type-1 fuzzy set and a type-2 fuzzy set, a tilde symbol is put over the symbol for the fuzzy set; so, A denotes a type-1 fuzzy set, whereas à denotes the comparable type-2 fuzzy set. When the latter is done, the resulting type-2 fuzzy set is called a general type-2 fuzzy set (to distinguish it from the special interval type-2 fuzzy set). Prof. Zadeh didn't stop with type-2 fuzzy sets, because in that 1976 paper [27] he also generalized all of this to type-n fuzzy sets. The present article focuses only on type-2 fuzzy sets because they are the next step in the logical progression from type-1 to type-n fuzzy sets, where n = 1, 2, … . Although some researchers are beginning to explore higher than type-2 fuzzy sets, as of early 2009, this work is in its infancy.The membership function of a general type-2 fuzzy set, Ã, is three-dimensional (Fig. 1), where the third dimension is the value of the membership function at each point on its two-dimensional domain that is called its footprint of uncertainty (FOU). For an interval type-2 fuzzy set that third-dimension value is the same (e.g., 1) everywhere, which means that no new information is contained in the third dimension of an interval type-2 fuzzy set. So, for such a set, the third dimension is ignored, and only the FOU is used to describe it. It is for this reason that an interval type-2 fuzzy set is sometimes called a first-order uncertainty fuzzy set model, whereas a general type-2 fuzzy set (with its useful third-dimension) is sometimes referred to as a second-order uncertainty fuzzy set model.The FOU represents the blurring of a type-1 membership function, and is completely described by its two bounding functions (Fig. 2), a lower membership function (LMF) and an upper membership function (UMF), both of which are type-1 fuzzy sets! Consequently, it is possible to use type-1 fuzzy set mathematics to characterize and work with interval type-2 fuzzy sets. This means that engineers and scientists who already know type-1 fuzzy sets will not have to invest a lot of time learning about general type-2 fuzzy set mathematics in order to understand and use interval type-2 fuzzy sets. Work on type-2 fuzzy sets languished during the 1980s and early-to-mid 1990's, although a small number of articles were published about them. People were still trying to figure out what to do with type-1 fuzzy sets, so even though Zadeh proposed type-2 fuzzy sets in 1976, the time was not right for researchers to drop what they were doing with type-1 fuzzy sets to focus on type-2 fuzzy sets. This changed in the latter part of the 1990s as a result of Prof. Jerry Mendel and his student's works on type-2 fuzzy sets and systems (e.g., [12]). Since then, more and more researchers around the world are writing articles about type-2 fuzzy sets and systems.