Determining the membership degrees in the range (0, 1) for hypersoft sets independently of the decision-maker

Abstract

Today, Molodtsov's soft set has been generalised to hypersoft sets, and the use of hypersoft set theory for uncertain data has become more preferable than soft sets. However, the membership degree of an object in hypersoft sets is 0 or 1. In order to express this situation in the range $(0,1)$, many mathematical models have been constructed by considering hypersoft sets together with fuzzy sets and their derivatives. However, these mathematical models require the decision-maker to express the membership degrees. It is a very difficult task for a decision-maker to determine a value in $(0,1)$ and the probability of an error is very high. For this reason, the concepts relational hypersoft membership degree and inverse relational hypersoft membership degree, which are given less dependent on decision-makers, are proposed in this paper. Moreover, two decision-making algorithms are given to use these concepts in an environment of uncertainty. Finally, the decision-making process for the given algorithms is analysed.

Keywords:

• Relational hypersoft membership function
• inverse relational hypersoft membership function
• decision making

2010 Mathematics Subject Classifications:

• 03E72
• 03E75
• 91B06

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Orhan Dalkılıç

Orhan Dalkılıç received his M.Sc. in Mathematics in 2020 from the University of Mersin, Turkey and is now a Ph.D. student in the same field. His research interests are topology fuzzy set theory, rough set theory, soft set theory, neutrosophic set theory, decision making and their applications. He is the founder of virtual fuzzy parameterized soft sets with his co-authors.