Generalized interval neutrosophic rough sets and its application in multi-attribute decision making

Abstract

Abstract. Neutrosophic set (NS) was originally proposed by Smarandache to handle indeterminate and inconsistent information. It is a generalization of fuzzy sets and intuitionistic fuzzy sets. Wang and Smarandache proposed interval neutrosophic sets (INS) which is a special case of NSs and would be extensively applied to resolve practical issues. In this paper, we put forward generalized interval neutrosophic rough sets based on interval neutrosophic relations by combining interval neutrosophic sets with rough sets. We explore the hybrid model through constructive approach as well as axiomatic approach. On one hand, we define generalized interval neutrosophic lower and upper approximation operators through constructive approach. Moreover, we investigate the relevance between generalized interval neutrosophic lower (upper) approximation operators and particular interval neutrosophic relations. On the other hand, we study axiomatic characterizations of generalized interval neutrosophic approximation operators, and also show that different axiom sets of theoretical interval neutrosophic operators make sure the existence of different classes of INRs that yield the same interval neutrosophic approximation operators. Finally, we introduce generalized interval neutrosophic rough sets on two universes and a universal algorithm of multi-attribute decision making based on generalized interval neutrosophic rough sets on two universes. Besides, an example is given to demonstrate the validity of the new rough set model.

An overview of MULTIMOORA for multi-criteria decision-making: Theory, developments, applications, and challenges

“…Mukherjee [155] developed IVNS, IVNSS, and discussed different types of IVNSS relations. Yang et al [156] proposed GINRS supported on interval neutrosophic relations and evaluate the hybrid methodology using constructive technique and axiomatic approach. Yang et al [157] studied HFRS based on constructive and axiomatic approaches.…”

Multi-Attribute Group Decision Making Based on Multigranulation Probabilistic Models with Interval-Valued Neutrosophic Information

“…To handle MAGDM information fusion and analysis with IN information effectively, GrC-based approaches own unique superiorities in constructing problem addressing approaches via multi-view problem solving tactics [23,24]. During the past several years, taking full advantage of GrC-based approaches, many scholars and practitioners have obtained fruitful results in merging NSs with rough sets [25][26][27][28][29][30][31][32], formal concept analysis [33,34], three-way decisions [35][36][37], and others [38,39]. In the current article, we plan to propose a new IN MAGDM method via multigranulation probabilistic models, which can provide a risk-based information synthesis scheme with the capability of error tolerance in light of GrC-based approaches.…”

Single-stage and two-stage total failure-based group-sampling plans for the Weibull distribution under neutrosophic statistics

“…Gulistan and Salma [25] discussed the application of neutrosophic logic using complex fuzzy sets. More information about neutrosophic logic can be seen in Yang [55], Peng and Dai [42], Zhang et al [58], and Zhang et al [59].…”