Multi-Granulation Neutrosophic Rough Sets on a Single Domain and Dual Domains with Applications

Abstract

It is an interesting direction to study rough sets from a multi-granularity perspective. In rough set theory, the multi-particle structure was represented by a binary relation. This paper considers a new neutrosophic rough set model, multi-granulation neutrosophic rough set (MGNRS). First, the concept of MGNRS on a single domain and dual domains was proposed. Then, their properties and operators were considered. We obtained that MGNRS on dual domains will degenerate into MGNRS on a single domain when the two domains are the same. Finally, a kind of special multi-criteria group decision making (MCGDM) problem was solved based on MGNRS on dual domains, and an example was given to show its feasibility.

Using Neighborhood Rough Set Theory to Address the Smart Elderly Care in Multi-Level Attributes

“…Rough sets theory is to deal with inaccurate discontinuous and other incomplete information [21][22][23]. Rough set theory analyzes incomplete data find out the relationship between the data and extract core data to overcome the subjectivity of traditional method evaluation parameter selection.…”

“…Object U is mapped to obtain V Z under the condition of the attribute set Z. This has an equation V = ∪ z∈Z V Z so V is a collection of attribute values [23,24,45].…”

A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty

“…To illustrate the features of our model, we compare it with traditional rough approach [5,33], neutrosophic rough set approaches [10,[23][24][25], and fuzzy and intuitionistic fuzzy rough soft approaches [34][35][36].…”

“…Therefore, all properties of traditional rough set approximations will be satisfied. We continue our discussion by comparing the proposed neutrosophic soft rough approach with other approaches which combine rough set to neutrosophic set [10,[23][24][25]. It can be seen that these approaches have the inadequacy of the parametrization tool to facilitate the representation of parameters, while the soft set in the proposed model can represent the problem parameters in a more complete manner.…”

“…Smarandache [16,17] proposed neutrosophic set to handle problems containing imprecise, incomplete, uncertain and indeterminate data. Neutrosophic sets progressed rapidly to neutrosophic oversets, neutrosophic undersets, neutrosophic offsets [18], neutrosophic cubic sets [19], neutrosophic and generalised neutrosophic soft sets [20][21][22], neutrosophic rough sets [23][24][25][26], neutrosophic vague sets [27,28] and complex neutrosophic sets [29][30][31][32].…”