Research Article Extended Perturbed Mixed Variational-Like Inequalities for Fuzzy Mappings Muhammad Bilal Khan , 1 Muhammad Aslam Noor , 1 Khalida Inayat Noor, 1 AhmadTermimiAbGhani , 2 and Lazim Abdullah 2 1 Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan 2 Management Science Research Group, Faculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu, Terengganu, Malaysia Correspondence should be addressed to Lazim Abdullah; lazim_m@umt.edu.my Received 19 November 2020; Revised 9 December 2020; Accepted 23 December 2020; Published 18 January 2021 Academic Editor: Xiaolong Qin Copyright©2021MuhammadBilalKhanetal.isisanopenaccessarticledistributedundertheCreativeCommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this article, our aim is to consider a class of fuzzy mixed variational-like inequalities (FMVLIs) for fuzzy mapping known as extended perturbed fuzzy mixed variational-like inequalities (EPFMVLIs). As exceptional cases, some new and classically defined “FMVLIs” are also attained. We have also studied the auxiliary principle technique of auxiliary “EPFMVLI” for “EPFMVLI.” By using this technique and some new analytic results, some existence results and efficient numerical techniques of “EPFMVLI” are established. Some advanced and innovative iterative algorithms are also obtained, and the convergence criterion of iterative sequences generated by algorithms is also proven. In the end, some new and previously known existence results and algorithms are also studied. Results secured in this paper can be regarded as purification and development of previously familiar results. 1.Introduction e boundless research work of fuzzy set and systems [1] has been devoted in advancement of different fields. It con- tributes to a vast class knowledge and appears in pure mathematics and applied sciences as well as operation re- search, computer science, managements sciences, artificial intelligence, control engineering, and decision sciences [2]. As a part of these knowledge developments, Chang and Zhu [3] initiated to introduce a new type of variational inequality for fuzzy mapping, which is known as fuzzy variational inequality. In fuzzy optimization, Noor [4–6] studied the characterization of minimum of convex fuzzy mapping through fuzzy variational inequality and fuzzy mixed vari- ational inequality and obtained some advanced and effective iterative algorithms. Moreover, they showed the parallel correlation by linking fuzzy variational inequalities and fuzzy Wiener–Hopf equations. Similarly, they established parallel correspondence between fuzzy variational inequal- ities and the resolvent equations for fuzzy mappings and encouraged some important and novel new iterative algo- rithms and discussed their convergence criteria. ey also introduced fuzzy mixed variational inequalities, and by using the classical auxiliary principle technique, some new existence theorems and iterative algorithms for fuzzy mixed variational inequalities are attained. It is worthy to mention here that one of the most considered generalizations of convex fuzzy mappings is preinvex fuzzy mapping. e idea of fuzzy preinvex mapping on the invex set was introduced and studied by Noor [7]. Moreover, any local minimum of a preinvex fuzzy mapping is a global minimum on invex set, and necessary and sufficient condition for fuzzy mapping is to be preinvex if its epigraph is an invex set. Furthermore, it has been verified that fuzzy optimality conditions of differentiable fuzzy preinvex mappings can be distinguished by variational-like inequalities. Motivated and inspired by the ongoing research work, many authors dis- cussed fuzzy variational inequalities and its important generalizations and its applications in different fields [8, 9]. In the subsequent text, we will review the applications and Hindawi Journal of Mathematics Volume 2021, Article ID 6652930, 16 pages https://doi.org/10.1155/2021/6652930