{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:46:43Z","timestamp":1760147203129,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T00:00:00Z","timestamp":1673827200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at King Khalid University","award":["R.G.P.1\/383\/43"],"award-info":[{"award-number":["R.G.P.1\/383\/43"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The use of a single-valued neutrosophic set (svns) makes it much easier to manage situations in which one must deal with incorrect, unexpected, susceptible, faulty, vulnerable, and complicated information. This is a result of the fact that the specific forms of material being discussed here are more likely to include errors. This new theory has directly contributed to the expansion of both the concept of fuzzy sets and intuitionistic fuzzy sets, both of which have experienced additional development as a direct consequence of the creation of this new theory. In svns, indeterminacy is correctly assessed in a way that is both subtle and unambiguous. Furthermore, membership in the truth, indeterminacy, and falsity are all completely independent of one another. In the context of algebraic analysis, certain binary operations may be regarded as interacting with algebraic modules. These modules have pervasive and complicated designs. Modules may be put to use in a wide variety of different applications. Modules have applications in a diverse range of industries and market subsets due to their adaptability and versatility. Under the umbrella of the triplet (\u03bc,\u03bd,\u03c9) structure, we investigate the concept of svns and establish a relationship between it and the single-valued neutrosophic module and the single-valued neutrosophic submodule, respectively. The purpose of this study is to gain an understanding of the algebraic structures of single-valued neutrosophic submodules under the triplet structure of a classical module and to improve the validity of this method by analyzing a variety of important facets. In this article, numerous symmetrical features of modules are also investigated, which demonstrates the usefulness and practicality of these qualities. The results of this research will allow for the successful completion of both of these objectives. The tactics that we have devised for use in this article are more applicable to a wide variety of situations than those that have been used in the past. Fuzzy sets, intuitionistic fuzzy sets, and neutrosophic sets are some of the tactics that fall under this category.<\/jats:p>","DOI":"10.3390\/sym15010247","type":"journal-article","created":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T05:30:07Z","timestamp":1673847007000},"page":"247","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Some Results on Submodules Using (\u03bc,\u03bd,\u03c9)-Single-Valued Neutrosophic Environment"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1652-6811","authenticated-orcid":false,"given":"Muhammad Shazib","family":"Hameed","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0418-193X","authenticated-orcid":false,"given":"Esmail Hassan Abdullatif","family":"Al-Sabri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Arts, King Khalid University, Abha 62529, Saudi Arabia"},{"name":"Department of Mathematics and Computer, Faculty of Science, IBB University, Ibb 70270, Yemen"}]},{"given":"Zaheer","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5998-0053","authenticated-orcid":false,"given":"Shahbaz","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Islamia University of Bahawalpur, Rahim Yar Khan Campus 64200, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9916-2031","authenticated-orcid":false,"given":"Muhammad Usman","family":"Ghani","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,16]]},"reference":[{"key":"ref_1","unstructured":"Smarandache, F. 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