# Multi-Valued Interval Neutrosophic Soft Set: Formulation and Theory

## Authors

• Nor Liyana Amalini Mohd Kamal Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia
• Lazim Abdullah Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia
• Ilyani Abdullah Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia
• Shawkat Alkhazaleh Department of Mathematics, Faculty of science, Zarqa University, Az Zarqa, Jordan
• Faruk Karaaslan Department of Mathematics, Faculty of Sciences, Çankırı Karatekin University, 18100, Çankırı, Turkey

## Keywords:

multi-valued interval neutrosophic set, multi-valued interval neutrosophic soft set, neutrosophic set, soft set

## Abstract

Neutrosophic set is a powerful general formal framework. A lot of studies on neutrosophic had been proposed and recently, in multi-valued interval values. However, sometimes there is problem involving elements of ambiguity and uncertainties in which the function of membership is difficult to be set in a particular case. Clearly, these problems can be solved by soft set since it is able to solve the lack of parameterization tool of theory. Thus, this paper introduces a concept of multi-valued interval neutrosophic soft set which amalgamates multi-valued interval neutrosophic set and soft set. The proposed set extends the notions of fuzzy set, intuitionistic fuzzy set, neutrosophic set, interval-valued neutrosophic set, multi-valued neutrosophic set, soft set and neutrosophic soft set. Further, we study some basic operations such as complement, equality, inclusion, union, intersection, “AND” and “OR” for multi-valued interval neutrosophic soft elements and discuss its associated properties. Moreover, the derivation of its properties, related examples and some proofs on the propositions are included.

2019-12-10

## How to Cite

Mohd Kamal, N. L. A. ., Abdullah, . L. ., Abdullah, . I. ., Alkhazaleh, S. ., & Karaaslan, F. . (2019). Multi-Valued Interval Neutrosophic Soft Set: Formulation and Theory. Neutrosophic Sets and Systems, 30, 149-170. Retrieved from http://fs.unm.edu/NSS2/index.php/111/article/view/342

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