A Novel Fuzzified Markov Chain Approach to Model Monthly River Discharge

River discharge is a hydrological variable resulting from integrated processes at the basin scale, which proves challenging to be modeled due to the partial knowledge of forcings and basin characteristics. In this context, the Traditional Markov chain Model (hereafter TMM) has been extensively used in discharge modeling over the past few decades. This study addresses the key weaknesses of the TMM and enhances it using fuzzy logic, introducing the novel Fuzzy Markov Chain Model (FMM). This model integrates traditional formulas with concepts related to fuzzy membership functions (MFs). The effectiveness of FMM is investigated through two case studies: an example taken from the Literature, featuring eight cases, highlighting differences between TMM and FMM, and the case study of the monthly inflows to Zayandehrud Dam (IZD) in Isfahan, Iran. The results from the Literature example show clear distinctions between TMM and FMM. In the IZD case, the future condition, as predicted by the FMM method with a maximum probability of 0.53, indicates a moderate wet condition. In contrast, the TMM assigns an equal probability (0.33) to all three conditions (low, moderate, and high), highlighting the TMM’s inefficiency in modeling probabilities across different conditions.