Interval-Valued Intuitionistic Hypersoft Sets and Their Algorithmic Approach in Multi-criteria Decision Making

Hypersoft set(HSS) is one of the recent topics developed by Smarandache in 2018 to be presented by replacing the single attribute function, used in soft set(SS), with a multi attribute function i.e a function can be further bifurcated using HSS. So, HSS provides more options to the decision-makers than SS to make precise and valid decisions. Also, the interval-valued intuitionistic fuzzy set (IVIFS) is developed to counter a kind of uncertain complex decision-making problem where the membership and non-membership values of a certain element are not precise. Basically, the IVIFS is the generalization of a fuzzy set(FS), interval-valued fuzzy set(IVFS), and intuitionistic fuzzy set(IFS). Therefore, the mixture of HSS and IVIFS will surely give a new field of study for the decision-makers to enhance their critical thinking ability to make a conclusive decisions. The main aim of the paper is to present the notion of interval-valued intuitionistic fuzzy hypersoft sets (IVIFHSSs) and study some fundamental operations on them which are worthy in critical decision making. The IVIFHSSs can be viewed as a hybrid structure that can be formed by combining interval-valued intuitionistic fuzzy sets (IVIFSs) and hypersoft sets (HSSs). On the idea of IVIFHSSs and their kinds, different operators such as complement, union, intersection, OR, AND etc have been introduced, and by using these operators we can encounter real-life-based problems that contain incomplete and parameterized information or data. A new algorithm based on IVIFHSSs has been initiated. Finally, a numerical example is employed to check the reliability and validity of the algorithm. In the future, we use the proposed concept practically in medical diagnosis, personality selection, weather forecasting, data clustering, parameter reduction, decision making, et