AHP PRIORITIES AND MARKOV-CHAPMAN-KOLMOGOROV STEADY-STATES PROBABILITIES

The Fractional Chapman Kolmogorov Equation

The Chapman–Kolmogorov equation with fractional integrals is derived. An integral of fractional order is considered as an approximation of the integral on fractal. Fractional integrals can be used to describe the fractal media. Using fractional integrals, the fractional generalization of the Chapman–Kolmogorov equation is obtained. From the fractional Chapman–Kolmogorov equation, the Fokker–Pla...

Priorities in Thurstone Scaling and Steady-State Probabilities in Markov Stochastic Modeling

The Fractional Chapman - Kolmogorov Equation Vasily

The Chapman-Kolmogorov equation with fractional integrals is derived. An integral of fractional order is considered as an approximation of the integral on fractal. Fractional integrals can be used to describe the fractal media. Using fractional integrals, the fractional generalization of the Chapman-Kolmogorov equation is obtained. From the fractional Chapman-Kolmogorov equation, the Fokker-Pla...

An Analysis of Ahp Comparisons and Priorities

In the Analytic Hierarchy Process (AHP/ANP), the local preference values v1p,v2p,...,vnp of n alternatives A1,A2,...,An with respect to a criterion Cp are measured in ratio scale (Saaty, 2006). Estimated values for the relative ratios vip/vjp (i,j=1,2,...,n) of the local preference values are elicited directly from decision maker (DM) via ratio-scaled pairwise comparisons. These estimated value...

A Logic with Kolmogorov Style Conditional Probabilities

In this paper we investigate a probability logic with conditional probability operators. The logic (denoted LPP ) allows making statements such as CP≥s(α | β), with the intended meaning ”the conditional probability of α given β is at least s”. Conditional probabilities are defined in the usual Kolmogorv style: P (α | β) = P (α∧β) P (β) , P (β) > 0. A possible-world approach is used to give sema...