Wearable technology allows users to monitor and track various fitness-related activities and data, including calories burned, distance traveled, heart rate, and sleep patterns. To choose best app for fitness, here introduced a new innovation in fuzzy algebra named as complex interval valued picture fuzzy soft relations (CIVPFSR) by defining the cartesian product (CP) of two complex interval valued picture fuzzy soft sets (CIVPFSS). Additionally, the many kinds of CIVPFS relations are described, and their outcomes are also mentioned in this article. The CIVPFSS has a complex structure that includes multidimensional variables for membership, abstinence, and non-membership degrees. As a result, this research offers modeling techniques for wearable technology that are based on CIVPFSR. The score function for best human decision making is also formulated in this process. Lastly, a comparison of current structures is done to demonstrate the viability of the suggested work with the conclusion highlighting its potential to significantly advance wearable technology. Additionally, a topological space is developed for CIVPFSR, providing a geometric interpretation of these relations and offering insights into their behavior in multi-dimensional decision spaces. The basic operations, operators, related theorems, and results are discussed. Results concerning the interiors and closures are also addressed.

In Digital Geometry, a gap is a location of a digital object through which a discrete ray can penetrate with no intersection. More specifically, for a 3D digital object we distinguish between 0- and 1-gaps depending on the relative position of such a ray. Although in some applications it is important to know how many gaps has a set of voxels, it is quite complicated to find an efficient algorithm to directly count them. In this paper, we provide a formula that states the number of 1-gaps of a generic 3D object using the notion of free cell of dimension 1 and 2.