Abstract
This paper proposes neutrosophic vague N-soft sets which is composed of neutrosophic vague sets and N-soft sets for the first time. The new hybrid model includes a pair of asymmetric functions: truth-membership and false-membership, and an indeterminacy-membership function. Some useful operations and propositions are given and illustrated by examples. Moreover, a method of priority relation ranking based on neutrosophic vague N-soft sets is presented. The validity of the method is verified by comparison. It is more flexible and reasonable to use this method in our daily life. Finally, a potential application of multi-attribute decision making is presented.
Highlights
Life is full of uncertainty, and people’s cognition begins with uncertainty
By comparing the ranking results of the existing methods and our proposed method, we observe that their result is the same, which means that there is a consistency among our proposed decision making method and the existing methods
We denote by NV(E) the set of all neutrosophic vague soft sets on U, we describe the mapping NV as : NV (e j ) = {< x1, TNV ( x1 ), ÎNV ( x1 ), FNV ( x1 ) >, · · ·, < xn, TNV, ÎNV, FNV >}
Summary
Life is full of uncertainty, and people’s cognition begins with uncertainty. By dealing with uncertain information, we can obtain more objective judgment. N-soft set is not enough to express content about rating or grades occurrence, nor can it describe the occurrence of vagueness For this purpose, as generalized models of N-soft sets, fuzzy N-soft sets, hesitant N-soft sets, hesitant fuzzy N-soft sets, interval valued hesitant fuzzy N-soft sets and intuitionistic fuzzy N-soft rough sets were introduced by Akram et al [23,24,25,26,27]. Peide Liu et al [29] proposed a new three-way decision model with intuitionistic fuzzy numbers to solve multiple attribute decision making problems. What’s more, priority relation ranking method based on neutrosophic vague N-soft sets is proposed for the first time.
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