We define fuzzy neuroidal nets in a way that enables to relate their
computations to computations of fuzzy Turing machines. Namely, we show that the polynomially space-bounded computations of fuzzy Turing machines with a polynomial advice function are equivalent to the computations of a polynomially-sized family of fuzzy neuroidal nets. The same holds for fuzzy neural nets which are a special case of fuzzy neuroidal nets. This result ranks discrete fuzzy neural nets among the most powerful computational devices known in the computational complexity theory.
We have modified the axiomatic system of orness measures, originally introduced by Kishor in 2014, keeping altogether four axioms. By proposing a fuzzy orness measure based on the inner product of lattice operations, we compare our orness measure with Yager's one which is based on the inner product of arithmetic operations. We prove that fuzzy orness measure satisfies the newly proposed four axioms and propose a method to determine OWA operator with given fuzzy orness degree.
Noisy time series are typical results of observations or technical measurements. Noise reduction and signál structure saving are contradictory but useful aims. Non-linear time series processing is a way for non-gaussian noise suppression. Many valued algebras enriched by square root are able to realize the operators close to the weighted averages. Fuzzy data processing based on Łukasiewicz algebra [3] with square root satisfies the Lipschitz condition and causes constrained sensitivity of the mapping. The paper presents a fuzzy neural network based on Modus Ponens [1] with fuzzy logic function [6] preprocessing in the hidden layer. AU the fuzzy algorithms were realized in the Matlab systém and in C++. The fuzzy processing is applied to prediction of sunspot numbers. The systematic approach based on filter selection is combined with weight optimization.
In multimedia consuming, Digital Rights Management (DRM) is the important means to confirm the benefits of both digital contents/services providers and consumers. To keep the DRM system running in order, risk management should be adopted, which identifies and assesses the DRM system's security level. Now, the legitimate sharing of copyrighted digital content is still an open issue, which faces severe risks of propertied assets circumvention and copyright infringements. In this paper, we try to highlight a multi-disciplinary method for all-around examinations on risks to digital assets in the contents sharing scenario. The method is a qualitative and quantitative fuzzy risk assessment, which is used for estimating a novel concept called Risk-Controlled Utility (RCU) in DRM. Then, we emphasize an application case of the emerging trusted computing policy, and analyze the influences of different content sharing modes. Finally, we address a business model with some simulation results. Comparison with other methods shows that the fusion of qualitative and quantitative styles cannot only evaluate the RCU with uncertain risk events effectively, but also provide accurate assessment data for the security policies of DRM.
A new class of functions called fuzzy semi α-irresolute functions in fuzzy topological spaces are introduced in this paper. Some characterizations of this class and its properties and the relationship with other classes of functions between fuzzy topological spaces are also obtained.
The paper applies some properties of the monotonous operators on the complete lattices to problems of the existence and the construction of the solutions to some fuzzy relational equations, inequations, and their systems, taking a complete lattice for the codomain lattice. The existing solutions are extremal - the least or the greatest, thus we prove some extremal problems related to fuzzy sets (in)equations. Also, some properties of upper-continuous lattices are proved and applied to systems of fuzzy sets (in)equations, in a special case of a meet-continuous complete codomain lattice.
In this study, a new approach based on the computation of fuzzy similarity index was presented for discrimination of electroencephalogram (EEG) signals. The EEG, a highly complex signal, is one of the most common sources of information used to study the brain function and neurological disorders. The analyzed EEG signals were consisted of five sets (set A - healthy volunteer, eyes open; set B - healthy volunteer, eyes closed; set C - seizure-free intervals of five patients from the hippocampal formation of the opposite hemisphere; set D - seizure-free intervals of five patients from the epileptogenic zone; set E - epileptic seizure segments). The EEG signals were considered as chaotic signals and this consideration was tested successfully by the computation of Lyapunov exponents. The computed Lyapunov exponents were used to represent the EEG signals. The aim of the study is discriminating the EEG signals by the combination of Lyapunov exponents and fuzzy similarity index. Toward achieving this aim, fuzzy sets were obtained from the feature sets (Lyapunov exponents) of the signals under study. The results demonstrated that the similarity between the fuzzy sets of the studied signals indicated the variabilities in the EEG signals. Thus, the fuzzy similarity index could discriminate the healthy EEG segments (sets A and B) and the other three types of segments (sets C, D, and E) recorded from epileptic patients.
The weighted average is a well-known aggregation operator that is widely applied in various mathematical models. It possesses some important properties defined for aggregation operators, like monotonicity, continuity, idempotency, etc., that play an important role in practical applications. In the paper, we reveal whether and in which way such properties can be observed also for the fuzzy weighted average operator where the weights as well as the weighted values are expressed by noninteractive fuzzy numbers. The usefulness of the obtained results is discussed and illustrated by several numerical examples.
FYKOS [1] je zkratkou pro Fyzikální korespondenční seminář pořádaný převážně studenty MFF UK. Je to celoroční soutěž určená pro středoškoláky, kteří se zajímají o fyziku a příbuzné obory. Během roku řeší několik sérií úloh různého druhu, které v článku představujeme na konkrétních ukázkách příkladů., Dominika Kalasová, Karel Kolář., and Obsahuje seznam literatury