An Extensive Review of the Literature Using the Diophantine Equations to Study Fuzzy Set Theory

Every field in mathematics has made significant progress in research with fuzzy sets. Numerous application fields were discovered in both empirical and theoretical investigations, ranging from information technology to medical technology, from the natural sciences to the physical sciences, and from technical education to fine arts education. However, it has limitations of its own and has not been able to function in real-world situations. An interdisciplinary approach of fuzzy theory with number theory, especially Diophantine equations, needs to be accomplished to overcome this problem. A thorough literature study of the Diophantine equations, fuzzy sets, and the combination known as the linear Diophantine fuzzy set (LDFS) is accomplished in the present study. New forms of LDFSs have been added recently, and these additions have found use in a variety of fields, including the disciplines of pharmacology, power, healthcare, goods, and finance. The genesis of these expansions is also examined in this study of the literature. Hence, in the present work, some applications of LDFS are described in detail. Further in the present study, the existing primary constraints in the research on LDFS are highlighted. Also, the last section of the review is dedicated to outlining some future directions for the study of LDFS.