With respect to decision making problems by using probabilities, immediate probabilities and information that can be represented with hesitant fuzzy information, some new decision analysis are proposed. Then, we have developed some new probability aggregation operators with hesitant fuzzy information: probability hesitant fuzzy weighted average (P-HFWA) operator, immediate probability hesitant ...

Repairable system analysis is in nature an evaluation of repair effects. Recent tendency in reliability engineering literature was imposing repair regimes and estimate system repair effects or linking repair to certain covariate to extract repair impacts. Hinted by engineering tune up exercises, we propose a repair model in terms of random variable distribution with a fuzzy parameter because fu...

Intuitionistic fuzzy probabilities are an extension of the concept of probabilities with application in several practical problem solving tasks. The former are probabilities represented through intuitionistic fuzzy numbers, to indicate the uncertainty of the membership and nonmembership degrees in the value assigned to probabilities. Moreover, a dual hesitant fuzzy set (DHFS) is an extension of...

In this paper, we investigate the probabilistic decision making problems with hesitant fuzzy information, some new probabilistic decision making analysis methods are developed. Then, we have developed some new probability aggregation operators with hesitant fuzzy information: probability hesitant fuzzy Hamacher weighted average(P-HFHWA) operator, immediate probability hesitant fuzzy Hamacher or...

We give a detailed sketch of how the exponential, Poisson, gamma, beta, normal, χ, t, and F distributions arise in “natural” ways. Our only prerequisite distributions will be the binomial distribution and the uniform distribution on [0, 1]. The details of the (more than) healthy dose of multivariable calculus along the way may certainly be slurred over by those looking for a sense of how the di...

Probability density functions (PDFs) of scale-dependent energy fluctuations, P[deltaE(l)] , are studied in high-resolution direct numerical simulations of Navier-Stokes and incompressible magnetohydrodynamic (MHD) turbulence. MHD flows with and without a strong mean magnetic field are considered. For all three systems it is found that the PDFs of inertial range energy fluctuations exhibit self-...