In this paper, we present applications of Markov rough approximation framework (MRAF). The concept of MRAF is defined based on rough sets and Markov chains. MRAF is used to obtain the probability distribution function of various reference points in a rough approximation framework. We consider a set to be approximated together with its dynamacity and the effect of dynamacity on rough approximations is stated with the help of Markov chains. An extension to Pawlak’s decision algorithm is presented, and it is used for predictions in a stock market environment. In addition, suitability of the algorithm is illustrated in a multi-criteria medical diagnosis problem. Finally, the definition of fuzzy tolerance relation is extended to higher dimensions using reference points and basic results are established.
We define $$2n+1$$
2
n
+
1
and 2n fuzzy numbers, which generalize triangular and trapezoidal fuzzy numbers, respectively. Then, we extend the fuzzy preference relation and relative preference relation to rank $$2n+1$$
2
n
+
1
and 2n fuzzy numbers. When the data is representable in terms of $$2n+1$$
2
n
+
1
fuzzy number, we generalize the FMCDM (fuzzy multi-criteria decision making) model constructed with TOPSIS and relative preference relation. Lastly, we give an example from telecommunications to present the proposed FMCDM model and validate the results obtained.
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