In this paper, a new class of generalized convex (concave) fuzzy mappings are introduced, which is called intuitionistic convex (concave) fuzzy mappings from the convex set ${K\subseteq \mathbb{R}}^n$ to the set of intuitionistic fuzzy numbers. By using the concept of epigraph, the characterization of intuitionistic convex fuzzy mappings is also discussed. Different types of intuitionistic convex (concave) fuzzy mappings are defined and their properties are investigated. Then, we discuss some applications of intuitionistic fuzzy convex mappings in fuzzy optimization. Additionally, some variational inequalities, known as intuitionistic fuzzy variational inequality and intuitionistic fuzzy variational mixed inequalities, are introduced. The results obtained in this paper can be regarded as refinements and extensions of previously established results.

In this study, we derived pricing formulas for various forward-start style exotic options based on an uncertain stock models with periodic dividends. Specifically, we present valuations for forward-start, Cliquet/Ratchet, and spread options. In addition, we conducted numerical simulations of these formulas and compared them to pricing formulas for the same options based on a dividend-paying stock model driven by standard Brownian motion.

Applying a parametric approach, in this paper we studied a new class of multidimensional extremization models with data uncertainty. Concretely, first, we derived the robust conditions of necessary optimality. Thereafter, we established robust sufficient optimality conditions by employing the various forms of convexity of the considered functionals. In addition, we formulated an illustrative example to validate the theoretical results.