Chapter 9 ______________________________________________________________________________________ A Novel Approach to Mappings on Hypersoft Classes with Application Muhammad Saeed 1 , Muhammad Ahsan 1∗ , Atiqe Ur Rahman 2 1,2 Department of Mathematics, University of Management and Technology Lahore, Pakistan. E-mail: muhammad.saeed@umt.edu.pk , E-mail: ahsan1826@gmail.com , E-mail: aurkhb@gmail.com Abstract: The soft set is inadequate to tackle the problems involving attribute-valued sets. Hypersoft set, an extension of the soft set, can tackle such issues efficiently. This work aims to adequate the existing concepts of mappings on fuzzy soft and soft classes for multi attribute-valued functions. First, mapping is characterized under a hypersoft set environment, then some of its essential properties like HS images, HS inverse images, etc., are developed with more generalized results. Moreover, practical application and comparative study is given to show the validity and predominance of the proposed technique. Keywords: Fuzzy soft classes; Soft classes, Hypersoft set, Hypersoft classes, Hypersoft images, Hypersoft inverse images. 1. Introduction For solving multifaceted problems in robotics, engineering, shortest-path selection, economics, and the environment, we cannot practice the conventional means successfully. Despite the variety of incomplete information, there are four theories specific to these problems Probability set theory (PST), Fuzzy set theory (FST) Zadeh [1], Rough set theory (RST) Pawlak [2] and Period mathematics (PM) can be assumed as a mathematical tool for dealing with lacking information. Every one of these apparatuses acquires the pre-determination of few parameters, to begin with, density function (DF) in PST, membership degree in FST, and a congruence relation in RST. Such a prerequisite, observed in the scrim of flawed or deficient information, escalate numerous issues. Simultaneously, fragmented information stays the most glaring attribute of humanitarian, organic, monetary, social, political, and large man-machine frameworks of different kinds. Heilpern [3], presented the idea of fuzzy mapping and demonstrated a fixed-point theory for fuzzy contraction mappings, which speculates the fixed-point hypothesis for multi-valued mappings of Nadler [4]. Estruch and Vidal give a fixed-point theory for fuzzy contraction mappings over a complete metric space, which is a generalization of the fundamental Heilpern’s fixed point hypothesis [5]. In the pioneer research of Zhu and Xiao [6] they have examined the convexity, and quasiconvexity of fuzzy mappings