Markov chains and rough sets

  • Kavitha Koppula
  • Babushri Srinivas Kedukodi
  • Syam Prasad Kuncham
Methodologies and Application


In this paper, we present a link between markov chains and rough sets. A rough approximation framework (RAF) gives a set of approximations for a subset of universe. Rough approximations using a collection of reference points gives rise to a RAF. We use the concept of markov chains and introduce the notion of a Markov rough approximation framework (MRAF), wherein a probability distribution function is obtained corresponding to a set of rough approximations. MRAF supplements well-known multi-attribute decision-making methods like TOPSIS and VIKOR in choosing initial weights for the decision criteria. Further, MRAF creates a natural route for deeper analysis of data which is very useful when the values of the ranked alternatives are close to each other. We give an extension to Pawlak’s decision algorithm and illustrate the idea of MRAF with explicit example from telecommunication networks.


Rough set Markov chain Rough approximation framework Ring 



The authors acknowledge the anonymous reviewers and the editor for their valuable comments and suggestions. All authors acknowledge the support and encouragement of Manipal Institute of Technology, Manipal Academy of Higher Education (MAHE), India.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Manipal Institute of TechnologyManipal Academy of Higher Education (MAHE)ManipalIndia

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