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

An FMEA model for risk assessment of university sustainability: using a combined ITARA with TOPSIS-AL approach based neutrosophic sets

It is necessary to emphasize both the process and results of performance management to find the balance between quality and quantity needed to ensure the sustainable development of universities to make the best use of limited educational resources and meet the diverse needs of students. This study applies failure mode and effects analysis (FMEA) to analyze obstacles to university sustainability by constructing complete risk assessment modes and reference indicators. The neutrosophic set theory was incorporated into the FMEA to account for information uncertainty and asymmetry. A specialist team then evaluated the importance of the risk factors using neutrosophic indifference threshold-based attribute ratio analysis to determine objective weights for the risk factors. Furthermore, the neutrosophic technique for order preference by similarity to the ideal solution based on aspiration level (N-TOPSIS-AL) is employed to aggregate the total risk scores of the failure modes. Using neutrosophic sets to measure truth, falsity, and indeterminacy in the assessment significantly improve the adaptability of the fuzzy theory to real-world problems. The study results indicate that when assessing university affairs management and analyzing possible risks, priority must be given to the occurrence of risks and that the lack of educational facilities is the riskiest item in the specialist assessment. The proposed assessment model can be applied as a basis for university sustainability assessments to accelerate the development of other forward-looking approaches.

Multi-attribute decision-making method based on a novel distance measure of linguistic intuitionistic fuzzy sets

Linguistic intuitionistic fuzzy sets can qualitatively rather than quantitatively express data in the form of membership degree. But quantitative tools are required to handle qualitative information. Therefore, an improved linguistic scale function, which can more accurately manifest the subjective feelings of decision-makers, is employed to deal with linguistic intuitionistic information. Subsequently, due to some commonly used distance measures do not comprehensively evaluate the information of linguistic intuitionistic fuzzy sets, an improved distance measure of linguistic intuitionistic fuzzy sets is designed. It considers the cross-evaluation information to get more realistic reasoning results. In addition, a new similarity measure defined by nonlinear Gaussian diffusion model is proposed, which can provide different response scales for different information between various schemes. The properties of these measures are also studied in detail. On this basis, a method in linguistic intuitionistic fuzzy environment is developed to handle multi-attribute decision-making problems. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method and the influence of the parameters is analyzed.

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

The neighborhood rough set theory was adopted for attributes reduction and the weight distribution of condition attributes based on the concept of importance level. Smart elderly care coverage rate is low in China. A decisive role in the adoption of smart elderly care is still a problem that needs to be addressed. This study contributes to the adoption of smart elderly care was selected as the decision attribute. The remaining attributes are used as conditional attributes and the multi-level symmetric attribute set for assessing acceptance of smart elderly care. Prior studies are not included smart elderly care adoption attributes in multi-levels; hence, this problem needs to be addressed. The results of this study indicate that the condition attribute of gender has the greatest influence on the decision attribute. The condition attribute of living expenses for smart elderly care has the second largest impact on decision attribute. Children’s support for the elderly decency of the novel elderly care system and the acceptance of non-traditional elderly care methods belong to the primary condition attribute of traditional concept. The result indicates traditional concepts have a certain impact on the adoption of smart elderly care and a condition attribute of residence also has a slight influence on the symmetric decision attribute. The sensitivity analysis shows the insights for uncertainties and provides as a basis for the analysis of the attributes in the smart elderly care service adoption.

A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty

To handle indeterminate and incomplete data, neutrosophic logic/set/probability were established. The neutrosophic truth, falsehood and indeterminacy components exhibit symmetry as the truth and the falsehood look the same and behave in a symmetrical way with respect to the indeterminacy component which serves as a line of the symmetry. Soft set is a generic mathematical tool for dealing with uncertainty. Rough set is a new mathematical tool for dealing with vague, imprecise, inconsistent and uncertain knowledge in information systems. This paper introduces a new rough set model based on neutrosophic soft set to exploit simultaneously the advantages of rough sets and neutrosophic soft sets in order to handle all types of uncertainty in data. The idea of neutrosophic right neighborhood is utilised to define the concepts of neutrosophic soft rough (NSR) lower and upper approximations. Properties of suggested approximations are proposed and subsequently proven. Some of the NSR set concepts such as NSR-definability, NSR-relations and NSR-membership functions are suggested and illustrated with examples. Further, we demonstrate the feasibility of the newly rough set model with decision making problems involving neutrosophic soft set. Finally, a discussion on the features and limitations of the proposed model is provided.

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (<A>, <neutA>, <antiA>), where <A> is an entity (i.e. element, concept, idea, theory, logical proposition, etc.), <antiA> is the opposite of <A>, while <neutA> is the neutral (or indeterminate) between them, i.e., neither <A> nor <antiA> [...]

New Multigranulation Neutrosophic Rough Set with Applications

After the neutrosophic set (NS) was proposed, NS was used in many uncertainty problems. The single-valued neutrosophic set (SVNS) is a special case of NS that can be used to solve real-word problems. This paper mainly studies multigranulation neutrosophic rough sets (MNRSs) and their applications in multi-attribute group decision-making. Firstly, the existing definition of neutrosophic rough set (we call it type-I neutrosophic rough set (NRSI) in this paper) is analyzed, and then the definition of type-II neutrosophic rough set (NRSII), which is similar to NRSI, is given and its properties are studied. Secondly, a type-III neutrosophic rough set (NRSIII) is proposed and its differences from NRSI and NRSII are provided. Thirdly, single granulation NRSs are extended to multigranulation NRSs, and the type-I multigranulation neutrosophic rough set (MNRSI) is studied. The type-II multigranulation neutrosophic rough set (MNRSII) and type-III multigranulation neutrosophic rough set (MNRSIII) are proposed and their different properties are outlined. We found that the three kinds of MNRSs generate tcorresponding NRSs when all the NRs are the same. Finally, MNRSIII in two universes is proposed and an algorithm for decision-making based on MNRSIII is provided. A car ranking example is studied to explain the application of the proposed model.

A Multi-Granularity 2-Tuple QFD Method and Application to Emergency Routes Evaluation

Quality function deployment (QFD) is an effective approach to satisfy the customer requirements (CRs). Furthermore, accurately prioritizing the engineering characteristics (ECs) as the core of QFD is considered as a group decision making (GDM) problem. In order to availably deal with various preferences and the vague information of different experts on a QFD team, multi-granularity 2-tuple linguistic representation is applied to elucidate the relationship and correlation between CRs and ECs without loss of information. In addition, the importance of CRs is determined using the best worst method (BWM), which is more applicable and has good consistency. Furthermore, we propose considering the relationship matrix and correlation matrix method to prioritize ECs. Finally, an example about evaluating emergency routes of metro station is proposed to illustrate the validity of the proposed methodology.

Some Results on Multigranulation Neutrosophic Rough Sets on a Single Domain

As a generalization of single value neutrosophic rough sets, the concept of multi-granulation neutrosophic rough sets was proposed by Bo et al., and some basic properties of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators were studied. However, they did not do a comprehensive study on the algebraic structure of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators. In the present paper, we will provide the lattice structure of the pessimistic multigranulation neutrosophic rough approximation operators. In particular, in the one-dimensional case, for special neutrosophic relations, the completely lattice isomorphic relationship between upper neutrosophic rough approximation operators and lower neutrosophic rough approximation operators is proved.