How to Handle Uncertainty

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Exact Tools for Analysis of Non-Exact Problems

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Software Tool For Voice Disorder Diagnostics

Causes of voice disorders may vary the same way as treatment techniques. Surgical intervention is the most used treatment method. As for not so serious cases, vocal exercises can be efficiently used instead. Still, there are only few methods to find right diagnosis or classify the scale of impact on patient’s voice. Nowadays, it is possible to extract key features (fundamental frequency, sound pressure level and less common such as cepstral coefficients, zero crossing rate or spectral energy) from patient’s speech using state-of-the-art voice processing methods. So, the software called Voice disorder diagnostician was designed. The tool that can store patient’s data and immediately provide the results of analysis.Příčiny vzniku poruch hlasu mohou být různé stejně tak jako jejich léčba. Nejčastěji se poruchy hlasu léčí chirurgicky tj. operací nebo v méně závažnějších případech hlasovými cvičeními. Přesto však v současné době existuje jen velmi málo metod, které mohou spolehlivě určit diagnózu pacienta a míru poškození hlasu. S využitím aktuálních metod pro zpracování řeči je možné určit klíčové parametry jako je základní tón hlasu, hladina akustického tlaku, ale i méně běžné jako například kepstrální koeficienty, počet průchodů nulou, či spektrální energie. Pro tyto účely byla vytvořena aplikace s názvem Voice disorder diagnostician. Nástroj, který umožňuje ukládat data od pacientů a provádět jejich okamžitou analýzu

Two approaches to fuzzification of payments in NTU coalitional game

There exist several possibilities of fuzzification of a coalitional game. It is quite usual to fuzzify, e.\,g., the concept of coalition, as it was done in [1]. Another possibility is to fuzzify the expected pay-offs, see [3,4]. The latter possibility is dealt even here. We suppose that the coalitional and individual pay-offs are expected only vaguely and this uncertainty on the "input" of the game rules is reflected also by an uncertainty of the derived "output" concept like superadditivity, core, convexity, and others. This method of fuzzification is quite clear in the case of games with transferable utility, see [6,3]. The not transferable utility (NTU) games are mathematically rather more complex structures. The pay-offs of coalitions are not isolated numbers but closed subsets of n-dimensional real space. Then there potentially exist two possible approaches to their fuzzification. Either, it is possible to substitute these sets by fuzzy sets (see, e.g.[3,4]). This approach is, may be, more sophisticated but it leads to some serious difficulties regarding the domination of vectors from fuzzy sets, the concept of superoptimum, and others. Or, it is possible to fuzzify the whole class of (essentially deterministic) NTU games and to represent the vagueness of particular properties or components of NTU game by the vagueness of the choice of the realized game (see [5]). This approach is, perhaps, less sensitive regarding some subtile variations in the the fuzziness of some properties but it enables to transfer the study of fuzzy NTU coalitional games into the analysis of classes of deterministic games. These deterministic games are already well known, which fact significantly simplifies the demanded analytical procedures. This brief contribution aims to introduce formal specifications of both approaches and to offer at least elementary comparison of their properties

Additivities in fuzzy coalition games with side-payments

summary:The fuzzy coalition game theory brings a more realistic tools for the mathematical modelling of the negotiation process and its results. In this paper we limit our attention to the fuzzy extension of the simple model of coalition games with side-payments, and in the frame of this model we study one of the elementary concepts of the coalition game theory, namely its “additivities”, i. e., superadditivity, subadditivity and additivity in the strict sense. In the deterministic game theory these additivites indicate the structure of eventual cooperation, namely the extent of finally formed coalitions, if the cooperation is possible. The additivities in fuzzy coalition games play an analogous role. But the vagueness of the input data about the expected coalitional incomes leads to consequently vague validity of the superadditivity, subadditivity and additivity. In this paper we formulate the model of this vagueness depending on the fuzzy quantities describing the expected coalitional pay-offs, and we introduce some elementary results mostly determining the links between additivities in a deterministic coalition game and its fuzzy extensions

Fuzzy coalitional structures (alternatives)

The uncertainty of expectations and vagueness of the interests belong to natural components of cooperative situations, in general. Therefore, some kind of formalization of uncertainty and vagueness should be included in realistic models of cooperative behaviour. This paper attempts to contribute to the endeavour of designing a universal model of vagueness in cooperative situations. Namely, some initial auxiliary steps toward the development of such a model are described. We use the concept of fuzzy coalitions suggested in [1], discuss the concepts of superadditivity and convexity, and introduce a concept of the coalitional structure of fuzzy coalitions. The first version of this paper [10] was presented at the Czech-Japan Seminar in Valtice 2003. It was obvious that the roots of some open questions can be found in the concept of superadditivity (with consequences on some other related concepts), which deserve more attention. This version of the paper extends the previous one by discussion of alternative approaches to this topic