Similarity measure and sine exponential measure of possibility  interval-valued neutrosophic hypersoft sets and their  applications

Eman Hussein; Yousef Al-Qudah; HM Jaradat; Faisal Al-Sharqi; Saja Elnajar; Ali Jaradat

Authors

Eman Hussein Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, 11953, Jordan;
Yousef Al-Qudah Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, 11953, Jordan;
HM Jaradat Department of Mathematics, Faculty of Sciences, Al al-Bayt University, P.O. Box 130095, Al-Mafraq, 25113, Jordan;
Faisal Al-Sharqi Department of Mathematics, Faculty of Education for Pure Sciences, University of Anbar, Ramadi, 55431, Iraq;
Saja Elnajar Department of Basic Sciences and Humanitiess, Faculty of Arts and Science, Amman Arab University, Amman, 11953, Jordan;
Ali Jaradat Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, 11953, Jordan;

Keywords:

Interval-valued neutrosophic set; soft set; hypersoft set; interval-valued neutro sophic hypersoft set; possibility interval-valued neutrosophic hypersoft set; similarity measures; decision-making.

Abstract

The Hypersoft set (HSS) has been created as an extension of a soft set (SS) in order to address
limitations for the thought of disjoint attribute-valued sets corresponding to distinct attributes. The HSSs
melted with several fuzziness structures present in literature to handle real-world scenarios with complexity and
uncertainty. One such extension is the interval-valued neutrosophic hypersoft set (iv-NHSS), which focuses on
the partitioning of each attribute into its attribute-valued set with these attribute-valued sets, three iv-NHS
memberships degree line closed interval [0,1]. However, the iv-NHSS model is short of assessing the vague nature
of parameters and sub-parameters that cause some doubt in DM opinions. This work focuses primarily on show
the impact the degree of fuzzy possibility on e cient work of iv-NHSS when we introduce novel concepts of
possibility interval valued neutrosophic hyper soft set (in short piv-NHSS) by giving all iv-NHSs-values, the fuzzy
possibility degree increases the e ciency for the multi-argument approximately. Therefore, the axioms of set
theory such as piv-NHS-subset, piv-NHS-null set, piv-NHS-absolute set and piv-NHSS-complement de ned on
this concept, as well as we investigated the union, intersection, AND, OR of two piv-NHSSs, and relevant laws,
with the help of several numerical examples and piv-NHS-matrix representations. Moreover, we discovered both
similarities measure and sine exponential measure between two piv-NHSSs and these measures are successfully
applied in decision-making to judge choose the best tourist place. In the end, a conclusion of this work is
presented with some suggestions for future studies of this work.