<p>Firstly, a new version of fuzzy sets called bi-quadratic fuzzy sets is presented in this work. We checked the capability of bi-quadratic fuzzy sets based on suitable examples and compared them with intuitionistic fuzzy sets, Pythagorean fuzzy sets, and Fermatean fuzzy sets. We also stated some set-theoretic operations, score, and accuracy functions. Further, to strengthen and better handle real-life optimization problems, a new concept and model called the bi-quadratic fuzzy optimization technique with bi-quadratic membership and bi-quadratic non-membership functions are introduced in this article. Many modifications of fuzzy optimization techniques have been presented using ordinary linear membership and non-membership functions. However, membership and non-membership can be bi-quadratic instead of linear. Therefore, in the domain of uncertainty and hesitation, the bi-quadratic membership and non-membership functions may play a vital role in real-life optimization problems rather than ordinary ones. Here, we construct the bi-quadratic membership and non-membership functions in a developed computational algorithm. Secondly, it is interesting to note that in real-life problems, the value of data changes very fast, so linear membership does not work properly. For example, the income of the person in a country, in such a case, piecewise linear membership may play a perfect role. So, to deal with problems with piecewise linearity, a piecewise linear optimization technique is constructed based on it, and a computational algorithm designed to show its application is also discussed in this paper. Finally, the outcomes of the developed algorithms are compared via the degree of closeness with the outcomes of the existing algorithms.</p>