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This article proposes a neighbors' similarity-based fuzzy community detection (FCD) method, which we call ``NeSiFC.'' In the proposed NeSiFC approach, we compute the similarity between two neighbors by introducing a modified local random walk (mLRW). Basically, in a network, a node and its' neighbors with noticeable similarities among them construct a community. To measure this similarity, we introduce a new metric, called the peripheral similarity index (PSI). This PSI is used to construct the transition probability matrix for the mLRW.