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Coarsest granularity-based optimal reduct using A* search


The optimal reduct computation problem aims to obtain the best reduct out of all possible reducts of a given decision system. In the rough set literature, two optimality criteria exist for computing an optimal reduct: shortest length based and coarsest granular space based. The coarsest granular space-based optimal reduct has the ability to induce a better generalizable classification model. The \(A^*RSOR\) is an existing \(A^*\) search-based optimal reduct computation algorithm that uses the coarsest granular space as an optimality criterion. This article proposes an improved coarsest granularity-based optimal reduct approach \(MA^*\_RSOR\) through analyzing the search process’s behaviour in \(A^*RSOR\) algorithm. To minimize the search space utilization and arrive at an optimal reduct in less time, suitable modifications are incorporated using the domain knowledge of rough set theory. The relevance of \(MA^*\_RSOR\) is demonstrated through theoretical analysis and comparative experimental validation with state-of-the-art algorithms. The experimental results with benchmark data sets established that \(MA^*\_RSOR\) achieves significant computational time gain (\(49-99\%\)) and space reduction (\(37-96\%\)) over \(A^*RSOR\). The \(MA^*\_RSOR\) could induce classification models with significantly better classification accuracies than state-of-the-art shortest length-based optimal/near-optimal reduct computation algorithms. In addition, a coefficient of variation based \(CV_{\text {NonCore}}\) heuristic is proposed for predicting when the \(MA^*\_RSOR\) algorithm is appropriate to use. Experimental results validate the relevance of the heuristic as its prediction turned out correctly in 8 out of 10 data sets.

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  1. Note: Without loss of generality, \(U/IND(\emptyset )\) is taken as \(\{U\}\). That means objects are not distinguishable in absence of any attributes information.


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This research acknowledges the financial support of UoH-IoE by MHRD (F11/9/2019-U3(A)). The first author acknowledges the support of the Senior Research Fellowship from the Council of Scientific and Industrial Research (CSIR) (09/414(1117)/2016-EMR-I), Ministry of Science and Technology, Government of India.

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Correspondence to Abhimanyu Bar, Anil Kumar or P. S. V. S. Sai Prasad.

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Bar, A., Kumar, A. & Sai Prasad, P.S.V.S. Coarsest granularity-based optimal reduct using A* search. Granul. Comput. 8, 45–66 (2023).

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  • Feature selection
  • Optimal reduct computation
  • Rough set theory
  • \(A^*\) search
  • Granular computing