Eighteen open problems posed during FSTA 2010 (Liptovský Ján, Slovakia) are presented. These problems concern copulas, triangular norms and related aggregation functions. Some open problems concerning effect algebras are also included.
This article introduces a floppy logic – a new method of work with fuzzy sets. This theory is a nice connection between the logic, the probability theory and the fuzzy sets. The floppy logic has several advantages compared to the fuzzy logic: All propositions, which are equivalent in the bivalent logic, are equivalent in the floppy logic too. Logical operations are modeled unambiguously, not by using many alternative t-norms and t-conorms. In floppy logic, we can use the whole apparatus of Kolmogorov’s probability theory. This theory allows to work consistently with systems that are described by fuzzy sets, probability distributions and accurate values simultaneously.
This article provides a simple and practical tutorial on how to use floppy logic. The floppy logic is a method suitable for systems control and description. It preserves the simplicity of the fuzzy logic and the accuracy of the probability theory. The floppy logic allows to work consistently and simultaneously with data in the form of exact numbers, probability distributions and fuzzy sets.
One of the most difficult tasks in field of the operative hydrology is the prediction of occurrence and course of the flash floods. It is difficult to predict torrential rainfalls because their character (great intensity, short duration, small affected area). Usage of the nowcasting methods (weather forecast with two hour validity) holds hope. The torrential rainfall prediction should be followed by suitable hydrological model able to estimate at least the resultant peak outflow. The hydrological models construction interferes with high measure of uncertainty, inherent in the rainfall prediction, rainfall-runoff process and its simulation. The way how to eliminate influence of uncertainty is to use the fuzzy logic and other artificial intelligence methods. The fuzzy model was compiled through the Fuzzy Logic Toolbox in the developmental environment of MATLAB. A model was calibrated with the help of genetic algorithm, neural networks and different optimization methods. and V příspěvku jsou prezentovány výsledky experimentálního výzkumu pohybu rotující kulovité částice ve vodě. Kulovitá částice vyrobená z gumy o hustotě blízké hustotě vody byla uvedena do pohybu v šikmé štěrbině, kde získala rotační i translační rychlost v osové rovině štěrbiny. Trajektorie částic ve vodě byly snímány standardní video kamerou a byl vyhodnocen vliv dvou bezrozměrných parametrů (Reynoldsova čísla a rotačního Reynoldsova čísla) na pohyb částice. Z experimentálních údajů byly určeny hodnoty odporového koeficientu a odporového momentu částice a tyto hodnoty byly porovnány s výsledky numerické simulace pohybu částice. Byly vyhodnoceny vztahy vhodné pro využití při numerickém modelování a popisující vzájemné závislosti výše uvedených veličin a vzájemný vliv translačního a rotačního pohybu částice.
This article is a continuation of a previous one named Fuzzy model use for prediction of the state of emergency of river basin in the case of flash flood (Janál & Starý, 2009), where the potential applications of fuzzy logic in the field of flash flood forecasting were described. Flash flood forecasting needs a specific approach because of the character of torrential rainfall. Storms are very difficult to forecast in space and time. The hydrological models designed for flash flood prediction have to be able to work with very uncertain input data. Moreover, the models have to be capable of evaluating the level of danger in as short a time as possible because of the highly dynamic character of the modeled process. The fuzzy model described in the previous article was modified into a form usable in operational hydrology and a simulation of its operational application was run using this model. The selected time period for the simulation was the summer of 2009, when numerous flash floods occurred in Czech Republic. The topic of this article is the preparation of the model for practical use and the results of the simulation of its operation. and Článek navazuje na předchozí článek s názvem Fuzzy model pro předpověď stupně ohroženosti povodí povodněmi z přívalových dešťů (Janál, Starý, 2009a). V úvodním článku byly popsány možnosti využití fuzzy logiky v problematice operativních předpovědí povodní způsobených přívalovými srážkami. Předpověď tohoto druhu povodní vyžaduje specifický přístup, jelikož výskyt přívalových srážek v prostoru a čase lze, díky jejich charakteru, jen stěží předpovídat. Hydrologické modely, určené pro předpověď povodní jimi způsobenými musí být schopny pracovat s velmi neurčitými vstupy. Díky vysoké dynamice předpovídaného procesu musí být navíc schopny vyhodnotit vstupní data ve velmi krátkém čase. Fuzzy model, popsaný v prvním díle, byl upraven do podoby využitelné v operativní hydrologii a byl otestován pomocí simulace operativního provozu ve zvoleném období z léta 2009, kdy byla ČR zasažena četnými povodněmi z přívalových srážek. Úpravy modelu pro praktické využití a vyhodnocení zpětné simulace jeho provozu jsou předmětem předloženého navazujícího článku.
The paper introduces a novel proposal of a security management system destined primarily for application in the field of IT. Its core is formed by a triplet of cooperating knowledge-based (expert) systems, the knowledge bases of which consist of vague If-Then rules. The knowledge bases were created by experts on the problem domain and multiple times tested and verified on actual scenarios and real systems. With the system, a comprehensive methodology that is a part of a more complex approach to a decision making process is introduced. The proposed fuzzy tool is demonstrated on examples and problems from the area of information security. The paper also briefly reviews other used approaches to information security management - mainly qualitative and quantitative methodologies.
Information retrieval in information systems (IS) with large amounts of data is not only a matter of an effective IS architecture and design and technical parameters of computer technology used for operation of the IS, but also of an easy and intuitive orientation in a number of offers and information provided by the IS. Such retrievals in IS are, however, frequently carried out with indeterminate information, which requires other models of orientation in the environment of the IS.
It is well known that the fuzzy sets theory can be successfully used in quantum models ([5, 26]). In this paper we give first a review of recent development in the probability theory on tribes and their generalizations - multivalued (MV)-algebras. Secondly we show some applications of the described method to develop probability theory on IF-events.
Some basic properties of α-planes of type-2 fuzzy sets are investigated and discussed in connection with the similar properties of α-cuts of type-1 fuzzy sets. It is known, that standard intersection and standard union of type-1 fuzzy sets (it means intersection and union under minimum t-norm and maximum t-conorm, respectively) are the only cutworthy operations for type-1 fuzzy sets. Recently, a similar property was declared to be true also for α-planes of type-2 fuzzy sets in a few papers. Thus, we study under which t-norms and which \mbox{t-conorms} are intersection and union of the type-2 fuzzy sets preserved in the α-planes. Note that understanding of the term α-plane is somewhat confusing in recent type-2 fuzzy sets literature. We discuss this problem and show how it relates to obtained results.