Normalized Hamming Similarity Measure for Intuitionistic Fuzzy Multi Sets and Its Application in Medical Diagnosis

Abstract

As Similarity measure for fuzzy sets is one of the important research topics of fuzzy set theory, there are several methods to measure similarity between two fuzzy sets (FS), Intuitionistic fuzzy sets (IFS) and Intuitionistic fuzzy multi sets (IFMS). In this paper, the Normalized Hamming Similarity measure of Intuitionistic Fuzzy Multi sets (IFMS) is introduced. This new measure for IFMS is based on the geometrical interpretation of IFS which involves both similarity and dissimilarity. Using this measure, the application of medical diagnosis and pattern recognition are shown. Pattern Recognition, Medical Diagnosis. As various distance and similarity methods of IFS are extended for IFMS distance and similarity measures [16], [17], [18] and [19], this paper is an extension of the new similarity measure based on Normalized Hamming distance and Complement of IFS to IFMS. II. PRELIMINARIES Definition: 2.1Let X be a nonempty set. A fuzzy set A in X is given by A = {〈 , ( )〉/ ∈ }

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“…To compare the proposed approach with some existing approaches under IFSS environment, a comparison analysis has been performed with different approaches given in . The obtained results have been described in Table .…”

“…To compare the proposed approach with some existing approaches under IFSS environment, a comparison analysis has been performed with different approaches given in. 23,24,[26][27][28]30,38,43 The obtained results have been described in Table 10. From this table, it is noticed that the resulting values evaluated by utilizing the prevailing methods coincide with the proposed approach outcomes.…”

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