2.1 The Main Theorem We first start with the simplest case where A and B are both subsets of the real line R. Let x ∈ A. The number pA(x) means that, in the infinitesimal interval [x, x+ δx), there exists pA(x)δx amount of “probability mass.” Here, δx is a “differential quantity” such that (δx) = 0. Assume that f is continuous and infinitely differentiable. The function f sends the interval [x,...

Decision making is still an open issue in the application of Dempster-Shafer evidence theory. A lot of works have been presented for it. In the transferable belief model (TBM), pignistic probabilities based on the basic probability assignments are used for decision making. In this paper, multiscale probability transformation of basic probability assignment based on the belief function and the p...

Our team of research works on diagnosis by pattern recognition using Fuzzy Pattern Matching (FPM) as a classification method, for data coming from industrial and medical sectors. FPM uses a transformation from probability to possibility in order to construct densities of possibilities. These densities are used to assign each new sample to its suitable class which corresponds to a functioning mo...

abstract spi is based on fitting a gamma distribution to precipitation amounts in selected periods. based on current research, the gamma distribution may not be fitted to annual precipitation of some regions. in order to evaluate this subject, annual precipitation have been used during 1958- 2007 at 11 synoptic stations in iran. in first step, values of spi and frequency of different classes of...

This article reports a study that tests whether the internal consistency of the standard gamble can be improved upon by incorporating loss weighting and probability transformation parameters in the standard gamble valuation procedure. Five alternatives to the standard EU formulation are considered: (1) probability transformation within an EU framework; and, within a prospect theory framework, (...

Smets proposes the Pignistic Probability Transformation (PPT) as decision layer in Transferable Belief Model (TBM), which argues when there is no more information, we have to make a using Mass Function (PMF). In this paper, Evolution Network (BEN) and full causality function are proposed by introducing Hierarchical Hypothesis Space (HHS). Based on BEN, interpret PPT from an information fusion v...