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MicroRNAs (miRNAs) act as a major biomarker of cancer. All miRNAs in human body are not equally important for cancer identification. We propose a methodology, called FMIMS, which automatically selects the most relevant miRNAs for a particular type of cancer. In FMIMS, miRNAs are initially grouped by using a SVM-based algorithm; then the group with highest relevance is determined and the miRNAs in that group are finally ranked for selection according to their redundancy. Fuzzy mutual information is used in computing the relevance of a group and the redundancy of miRNAs within it. Superiority of the most relevant group to all others, in deciding normal or cancer, is demonstrated on breast, renal, colorectal, lung, melanoma and prostate data. The merit of FMIMS as compared to several existing methods is established. While 12 out of 15 selected miRNAs by FMIMS corroborate with those of biological investigations, three of them viz., "hsa-miR-519," "hsa-miR-431" and "hsa-miR-320c" are possible novel predictions for renal cancer, lung cancer and melanoma, respectively. The selected miRNAs are found to be involved in disease-specific pathways by targeting various genes. The method is also able to detect the responsible miRNAs even at the primary stage of cancer. The related code is available at http://www.jayanta.droppages.com/FMIMS.html .[1]