A NovelMethod for Determining Tourism Carrying Capacity in a Decision-Making Context Using q−Rung Orthopair Fuzzy Hypersoft Environment

Tourism is a popular activity that allows individuals to escape their daily routines and explore new destinations for various reasons,including leisure,pleasure,or business.A recent study has proposed a unique mathematical concept called a q−Rung orthopair fuzzy hypersoft set(q−ROFHS)to enhance the formal representation of human thought processes and evaluate tourism carrying capacity.This approach can capture the imprecision and ambiguity often present in human perception.With the advanced mathematical tools in this field,the study has also incorporated the Einstein aggregation operator and score function into the q−ROFHS values to supportmultiattribute decision-making algorithms.By implementing this technique,effective plans can be developed for social and economic development while avoiding detrimental effects such as overcrowding or environmental damage caused by tourism.A case study of selected tourism carrying capacity will demonstrate the proposed methodology.

Aggregation Operators for Decision Making Based on q-Rung Orthopair Fuzzy Hypersoft Sets:An Application in Real Estate Project

In this paper,a decision-making problem with a q-rung orthopair fuzzy hypersoft environment is developed,and two operators of ordered weighted average and induced ordered weighted average are developed.Several fundamental features are also derived.The induced ordered weighted average operator is essential in a q-ROFH environment as the induced ordered aggregation operators are special cases of the existing aggregation operators that already exist in q-ROFH environments.The main function of these operators is to help decision-makers gain a complete understanding of uncertain facts.The proposed aggregation operator is applied to a decision-making problem,with the aim of selecting the most promising real estate project for investment.

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

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.

Aggregation Operators for Interval-Valued Pythagorean Fuzzy Hypersoft Set with Their Application to Solve MCDM Problem

Experts use Pythagorean fuzzy hypersoft sets(PFHSS)in their investigations to resolve the indeterminate and imprecise information in the decision-making process.Aggregation operators(AOs)perform a leading role in perceptivity among two circulations of prospect and pull out concerns from that perception.In this paper,we extend the concept of PFHSS to interval-valued PFHSS(IVPFHSS),which is the generalized form of intervalvalued intuitionistic fuzzy soft set.The IVPFHSS competently deals with uncertain and ambagious information compared to the existing interval-valued Pythagorean fuzzy soft set.It is the most potent method for amplifying fuzzy data in the decision-making(DM)practice.Some operational laws for IVPFHSS have been proposed.Based on offered operational laws,two inventive AOs have been established:interval-valued Pythagorean fuzzy hypersoft weighted average(IVPFHSWA)and interval-valued Pythagorean fuzzy hypersoft weighted geometric(IVPFHSWG)operators with their essential properties.Multi-criteria group decision-making(MCGDM)shows an active part in contracts with the difficulties in industrial enterprise for material selection.But,the prevalent MCGDM approaches consistently carry irreconcilable consequences.Based on the anticipated AOs,a robust MCGDMtechnique is deliberate formaterial selection in industrial enterprises to accommodate this shortcoming.A real-world application of the projectedMCGDMmethod for material selection(MS)of cryogenic storing vessels is presented.The impacts show that the intended model is more effective and reliable in handling imprecise data based on IVPFHSS.

Decision Making Algorithmic Approaches Based on Parameterization of Neutrosophic Set under Hypersoft Set Environment with Fuzzy, Intuitionistic Fuzzy and Neutrosophic Settings

Hypersoft set is an extension of soft set as it further partitions each attribute into its corresponding attribute-valued set.This structure is more flexible and useful as it addresses the limitation of soft set for dealing with the scenarios having disjoint attribute-valued sets corresponding to distinct attributes.The main purpose of this study is to make the existing literature regarding neutrosophic parameterized soft set in line with the need of multi-attribute approximate function.Firstly,we conceptualize the neutrosophic parameterized hypersoft sets under the settings of fuzzy set,intuitionistic fuzzy set and neutrosophic set along with some of their elementary properties and set theoretic operations.Secondly,we propose decision-making-based algorithms with the help of these theories.Moreover,illustrative examples are presented which depict the structural validity for successful application to the problems involving vagueness and uncertainties.Lastly,the generalization of the proposed structure is discussed.