Markov chains and rough sets
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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.
KeywordsRough 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.
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Conflict of interest
The authors declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
- Ciucci D (2008) A unifying abstract approach for rough models. Lect Notes Artif Int 5009:371–378Google Scholar
- Fan ZP (1996) Complicated multiple attribute decision making: theory and applications. Dissertation, Northeastern UniversityGoogle Scholar
- Kedukodi BS, Kuncham SP, Jagadeesha B (2017) Interval valued L-fuzzy prime ideals, triangular norms and partially ordered groups. Soft Comput. https://doi.org/10.1007/s00500-017-2798-x
- Opricovic S (1998) Multicriteria optimization of civil engineering systems. Fac Civ Eng Belgrade 2:5–21Google Scholar
- Page L, Brin S, Motwani R, Winograd T (1998) The PageRank citation ranking: Bringing order to the web. Technical report, Stanford digital library technologies project, USAGoogle Scholar