Abstract
This paper introduces a pioneering theoretical framework for the best approximation and projection operator of the vectors onto the fuzzy sets, utilizing the innovative concept of r -cuts within the Euclidean norm. We meticulously define these operators and establish their fundamental properties. Particularly noteworthy is our demonstration that, under specific conditions, the projection of a vector onto a fuzzy set in terms of r -cuts is not only feasible but also unique, highlighting a significant advantage of our method. Furthermore, we provide a detailed characterization of this projection, enhancing its practical utility and reliability. Finally, through a series of illustrative examples, we demonstrate the practical significance of our approach by showcasing its effectiveness in solving constrained optimization problems within the domain of r -cuts.
Keywords
Get full access to this article
View all access options for this article.
