In this study, we introduce some well-known definitions and properties for multi-valued functions. We present new such as, m-retraction, m-section, m-homeomorphism, m-HEP reducible function. give a result on the relation between multi-homotopy groups m-homeomorphism. also deal with of m-HEP.

Motivated by multi-task machine learning with Banach spaces, we propose the notion of vector-valued reproducing kernel Banach spaces (RKBSs). Basic properties of the spaces and the associated reproducing kernels are investigated. We also present feature map constructions and several concrete examples of vector-valued RKBSs. The theory is then applied to multi-task machine learning. Especially, ...

We present eÆcient algorithms for the bi-decomposition of arbitrary incompletely speci ed functions in variable-valued logic. Several special cases are discussed. The algorithms are especially applicable for Data Mining applications, because, in contrast to the general multi-valued approaches to function decomposition that decompose to arbitrary tables, we create a network from multi-valued two...

Abstract This paper aims to present the concept of multi-valued mappings in fuzzy cone metric spaces and prove some basic lemmas, a Hausdorff metric, fixed point results for set-valued cone-contraction mappings. We theorem rational type cone-contractions spaces. Our extend improve given literature.

This work extends the game-based framework of μ-calculus model checking to the multi-valued setting. In multi-valued model checking a formula is interpreted over a Kripke structure defined over a lattice. The value of the formula is also an element of the lattice. This problem has many applications in verification, such as handling abstract or partial models, analyzing systems in the presence o...