Rate of convergence, asymptotically attainable structures and sensitivity in non-homogeneous Markov systems with fuzzy states

Abstract

This paper is concerned with the rate of convergence, the asymptotically attainable structures and the sensitivity of a non-homogeneous Markov system (NHMS, in short) with fuzzy states. More specifically, it is proved that under some realistic assumptions easily met in practice, the convergence rate of the relative population structure to its limit is geometric. Furthermore, the asymptotically attainable structures in a NHMS with fuzzy states are given. More precisely, the problem of finding which states are possible as limiting ones in a NHMS with fuzzy states is studied, provided that the limit of the sequence of the input probability vectors is controlled. Moreover, the sensitivity of the limiting expected population structure on perturbations of the limiting input probabilities for the system is also studied. Two applications (in Cognitive Science and in Manpower Planning) are given, where the sensitivity of two NHMS with three states is studied, provided that the limiting input probability vector is perturbed.