A Rough Set Approach to Estimating the Game Value and the Shapley Value from Data

A value of a game v is a function which to each coalition S assigns the value v(S) of this coalition, meaning the expected pay–off for players in that coalition. A classical approach of von Neumann and Morgenstern [6] had set some formal requirements on v which contemporary theories of value adhere to. A Shapley value of the game with a value v [14] is a functional Φ giving for each player p the value Φ_p(v) estimating the expected pay-off of the player p in the game. Game as well as conflict theory have been given recently much attention on the part of rough and fuzzy set communities [11,8,1,4,7,2]. In particular, problems of plausible strategies [1] in conflicts as well as problems related to Shapley's value [3,2] have been addressed.We confront here the problem of estimating a value as well as Shapley's value of a game from a partial data about the game. We apply to this end the rough set ideas of approximations, defining the lower and the upper value of the game and, respectively, the lower and upper Shapley value. We also define a notion of an exact coalition, on which both values coincide giving the true value of the game; we investigate the structure of the family of exact sets showing its closeness on complements, disjoint sums, and intersections of coalitions covering the set of players. This work sets open a new area of rough set applications in mining constructs from data. The construct mined in this case are values as well as Shapley values of games.     

Mo–Si–B alloys for ultra-high-temperature space and ground applications: liquid-assisted fabrication under various temperature and time conditions

Journal of Materials Science - Boron-doped molybdenum silicides have been already recognized as attractive candidates for space and ground ultra-high-temperature applications far beyond limits of...     

Wetting Behavior and Reactivity of Molten Silicon with h-BN Substrate at Ultrahigh Temperatures up to 1750 °C

For a successful implementation of newly proposed silicon-based latent heat thermal energy storage systems, proper ceramic materials that could withstand a contact heating with molten silicon at temperatures much higher than its melting point need to be developed. In this regard, a non-wetting behavior and low reactivity are the main criteria determining the applicability of ceramic as a potential crucible material for long-term ultrahigh temperature contact with molten silicon. In this work, the wetting of hexagonal boron nitride (h-BN) by molten silicon was examined for the first time at temperatures up to 1750 °C. For this purpose, the sessile drop technique combined with contact heating procedure under static argon was used. The reactivity in Si/h-BN system under proposed conditions was evaluated by SEM/EDS examinations of the solidified couple. It was demonstrated that increase in temperature improves wetting, and consequently, non-wetting-to-wetting transition takes place at around 1650 °C. The contact angle of 90° ± 5° is maintained at temperatures up to 1750 °C. The results of structural characterization supported by a thermodynamic modeling indicate that the wetting behavior of the Si/h-BN couple during heating to and cooling from ultrahigh temperature of 1750 °C is mainly controlled by the substrate dissolution/reprecipitation mechanism.     

A Calculus on Granules from Rough Inclusions in Information Systems

1 Introduction In thiswork ,we addresstheproblems of Granu - larComputing , thebranch of Approximate (or, Soft) Computing ,whose underlyingideaistocompute with granulesofobjects,i.e.,“clumps of objects(…) which are drawn togetherby indistinguishabil,its…     

Silicon-Boron Alloys as New Ultra-High Temperature Phase-Change Materials: Solid/Liquid State Interaction with the h-BN Composite

Silicon-boron alloys have been recently pointed out as novel ultra-high temperature phase change materials for applications in Latent Heat Thermal Energy S     

Left ventricular outflow obstruction as a result of external cardiac compression by a mediastinal tumor

A case of left ventricular outflow tract stenosis resulted from compression of the heart is presented. This symptomatic cardiovascular lesion was produced by extensive growth of mediastinal tumour. Numerous noninvasive methods were necessary to establish this difficult diagnosis. The patient underwent surgery that disclosed a benign process (of neurofibroma). After tumour's resection marked hemodynamic signs subsided.     

Rough Mereological Calculi of Granules: A Rough Set Approach To Computation

Rough Mereology is a paradigm allowing for a synthesis of main ideas of two potent paradigms for reasoning under uncertainty: Fuzzy Set Theory and Rough Set Theory. Approximate reasoning is based in this paradigm on the predicate of being a part to a degree . We present applications of Rough Mereology to the important theoretical idea put forth by Lotfi Zadeh (1996, 1997), i.e., Granularity of Knowledge: We define granules of knowledge by means of the operator of mereological class and we extend the idea of a granule over complex objects like decision rules as well as decision algorithms. We apply these notions and methods in the distributed environment discussing complex problems of knowledge and granule fusion. We express the mechanism of complex granule formation by means of a formal grammar called Synthesis Grammar defined over granules of knowledge, granules of classifying rules, or over granules of classifying algorithms. We finally propose hybrid rough-neural schemes bridging rough and neural computations.