Exponentially Preinvex Fuzzy Mappings and Fuzzy Exponentially Mixed Variational-Like Inequalities

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Muhammad Bilal Khan
Muhammad Aslam Noor
Khalida Inayat Noor
Hassan Almusawa
Kottakkaran Sooppy Nisar

Abstract

In this article, our aim is to consider a class of nonconvex fuzzy mapping known as exponentially preinvex fuzzy mapping. With the support of some examples, the notions of exponentially preinvex fuzzy mappings are explored and discussed in some special cases. Some properties are also derived and relations among the exponentially preinvex fuzzy mappings (exponentially preinvex-FMs), exponentially invex fuzzy mappings (exponentially-IFMs), and exponentially monotonicity are established under some mild conditions. In the end, using the fact that fuzzy optimization and fuzzy variational inequalities have close relationships, we have proven that the optimality conditions of exponentially preinvex fuzzy mapping can be distinguished by exponentially fuzzy variational-like inequality and exponentially fuzzy mixed variational-like inequality. These inequalities render the very interesting outcomes of our main results and appear to be the new ones. Presented results in this paper can be considered and the development of previously obtained results.

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