In 1951, K.J. Arrow proved that, under certain assumptions, it is impossible to have group decision-making rules that satisfy reasonable conditions like symmetry. This Impossibility Theorem is often cited as a proof that reasonable group decision-making is impossible. We start our article by remarking that Arrow's result covers only those situations when the only information we have about individual preferences is their binary preferences between the alternatives. If we follow the main ideas of modern decision making and game theory and also collect information about the preferences between lotteries (i.e., collect the utility values of different alternatives), then reasonable decision-making rules are possible, e.g., Nash's rule in which we select an alternative for which the product of utilities is the largest possible. We also deal with two related issues: how we can detect individual preferences if all we have is preferences of a subgroup and how we take into account the mutual attraction between participants. © 2008 Wiley Periodicals, Inc.

The problem of optimal bit rate allocation for 3-D JPEG2000 compression is dicussed. In this paper we consider data where the 2-D slices are compressed using JPEG2000, and the third dimension is decorrelated using the Karhunen-Loeve Transform. Here two new methods are proposed. The first approach is called the Rate Distortion Optimal (RDO) method and is based on Post-Compression Rate-Distortion (PCRD) optimization concept. The second approach is here called the Mixed Model (MM) approach and consists of extending the traditional high-resolution model with a region that is accurate for low bit rates. The proposed bit allocation methods are tested by applying them to Meteorological (Met) data. The specific data set used was generated by the Battlescale Forecast Model (BFM). The test results shows that these approach significantly reduces the computational complexity.

The formal concept of logical equivalence in fuzzy logic, while theoretically sound, seems impractical. The misinterpretation of this concept has led to some pessimistic conclusions. Motivated by practical interpretation of truth values for fuzzy propositions, we take the class (lattice) of all subintervals of the unit interval [0, 1] as the truth value space for fuzzy logic, subsuming the traditional class of numerical truth values from [0, 1]. The associated concept of logical equivalence is stronger than the traditional one. Technically, we are dealing with much smaller set of pairs of equivalent formulas, so that we are able to check equivalence algorithmically. The checking is done by showing that our strong equivalence notion coincides with the equivalence in logic programming. © 1996 John Wiley & Sons, Inc.