Communications in Mathematics and Applications Vol. 13, No. 2, pp. 595–602, 2022 ISSN 0975-8607 (online); 0976-5905 (print) Published by RGN Publications http://www.rgnpublications.com DOI: 10.26713/cma.v13i2.1746 Research Article M-N Homomorphism of an M-N Fuzzy Soft Subgroups and Its Level M-N Subgroups M. Kaliraja* 1 and S. Rumenaka 2 PG and Research Department of Mathematics, H.H. The Rajah’s College (Bharathidasan University ), Pudukottai 622001, Tiruchirappalli, Tamilnadu, India *Corresponding author: mkr.maths009@gmail.com Received: December 1, 2021 Accepted: April 25, 2022 Abstract. We examined the notion of M-N homomorphism of fuzzy soft subgroups in this study, then defined the M-N level subsets of a fuzzy soft subgroup and discussed some of its basic aspects. Keywords. Fuzzy group, M-N fuzzy group, M-N fuzzy soft subgroups, M-N level subset, M-N homomorphism of fuzzy soft subgroups Mathematics Subject Classification (2020). 20N25, 06D72, 20E15, 22F05 Copyright © 2022 M. Kaliraja and S. Rumenaka. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction In the actual world, there are many different forms of uncertainties, yet few traditional mathematical techniques are suited for modelling these uncertainties. Undefined data is at the heart of many complex problems in economics, social science, engineering, medicine, and other domains. These difficulties that one encounters in life cannot be solved with traditional mathematical methods. A mathematical model of an object is devised in classical mathematics, but the concept of the exact solution of this model is not yet specified. The exact solution cannot be found because the standard mathematical model is too complex. There are a number of well- known ideas that can be used to describe uncertainty. For example, Rosenfeld [11] presented the notion of fuzzy subgroup in 1971, and Zadeh [12] inspired the theory of fuzzy sets. In addition, Molodtsov [8] introduced the concept of soft sets in 1999. Maji et al. [6] presented the concept of fuzzy soft sets in 2009, and Jacobson [3] introduced the concept of M-group M-subgroup.