Einstein Weighted Geometric Operator for Pythagorean Fuzzy Hypersoft with Its Application in Material Selection

Abstract

Hypersoft set theory is a most advanced form of soft set theory and an innovative mathematical tool for dealing with unclear complications. Pythagorean fuzzy hypersoft set (PFHSS) is the most influential and capable leeway of the hypersoft set (HSS) and Pythagorean fuzzy soft set (PFSS). It is also a general form of the intuitionistic fuzzy hypersoft set (IFHSS), which provides a better and more perfect assessment of the decision-making (DM) process. The fundamental objective of this work is to enrich the precision of decision-making. A novel mixed aggregation operator called Pythagorean fuzzy hypersoft Einstein weighted geometric (PFHSEWG) based on Einstein's operational laws has been developed. Some necessary properties, such as idempotency, boundedness, and homogeneity, have been presented for the anticipated PFHSEWG operator. Multi-criteria decision-making (MCDM) plays an active role in dealing with the complications of manufacturing design for material selection. However, conventional methods of MCDM usually produce inconsistent results. Based on the proposed PFHSEWG operator, a robust MCDM procedure for material selection in manufacturing design is planned to address these inconveniences. The expected MCDM method for material selection (MS) of cryogenic storing vessels has been established in the real world. Significantly, the planned model for handling inaccurate data based on PFHSS is more operative and consistent.

Optimizing construction company selection using einstein weighted aggregation operators for q-rung orthopair fuzzy hypersoft set

“…However, these AOs fail to deal with the decision outcomes when the sum of MD + NMD > 1 . Sunthrayuth et al 54 and Zulqarnain et al 55 prolonged the Einstein weighted average and geometric AOs for PFHSS and confirmed the novel MCDM techniques to solve MCDM obstacles because of the parameterization of sub-attributes. But these AOs also flop when the (MD) 2 + (NMD) 2 > 1 .…”

“…Sunthrayuth et al 54 and Zulqarnain et al 55 defined the Einstein weighted AOs for PFHSNs by above deliberated Einstein operational laws with confident environments…”

“…Siddique et al 53 delivered a creative MCDM system for PFHSS using their developed AOs. Sunthrayuth et al 54 and Zulqarnain et al 55 Motivation and drawback of existing approaches. The predominant Einstein-weighted AOs for PFHSS 54,55 only assess PFHSS impacts and only deliberate the PFHSS approximations, not the q-ROFHSS impacts.…”

“…Sunthrayuth et al 54 and Zulqarnain et al 55 Motivation and drawback of existing approaches. The predominant Einstein-weighted AOs for PFHSS 54,55 only assess PFHSS impacts and only deliberate the PFHSS approximations, not the q-ROFHSS impacts. Also, from the above AOs for q-ROFHSS 59 , it is stated that, in confident surroundings, these AOs deliver some disgusting consequences.…”

“…Meanwhile g d11 = 0.0, g d12 = 0.7, g d21 = 0.7, and g d22 = 0.2, which is unreasonable. The existing Einstein AOs 54,55 for PFHSS cannot handle the abovementioned problem. Because f d21 = 0.8 and g d21 = 0.7, where (0.8) 2 + (0.7) 2 > 1 .…”