Abstract
In this paper, we investigate several fuzzy differential subordinations that are connected with the Borel distribution series B(lambda,alpha,beta)(z) of the Mittag-Leffler type, which involves the two-parameter Mittag-Leffler function E-alpha,E-beta(z). Using the above-mentioned operator B(lambda,alpha,beta), we also introduce and study a class M-lambda,alpha,beta(F)(eta) of holomorphic and univalent functions in the open unit disk Delta. The Mittag-Leffler-type functions, which we have used in the present investigation, belong to the significantly wider family of the Fox-Wright function (p)psi(q)(z), whose p numerator parameters and q denominator parameters possess a kind of symmetry behavior in the sense that it remains invariant (or unchanged) when the order of the p numerator parameters or when the order of the q denominator parameters is arbitrarily changed. Here, in this article, we have used such special functions in our study of a general Borel-type probability distribution, which may be symmetric or asymmetric. As symmetry is generally present in most works involving fuzzy sets and fuzzy systems, our usages here of fuzzy subordinations and fuzzy membership functions potentially possess local or non-local symmetry features.