Simplified Neutrosophic Sets Research Articles

Dynamic nonlinear simplified neutrosophic sets for multiple-attribute group decision making

In this paper, the concept of a dynamic nonlinear simplified neutrosophic set (DNSNS) is proposed for describing the real-time changing expert preference information. Furthermore, the DNSNS aggregation model and decision algorithm are provided to solve the actual multiple-attribute group decision making (MAGDM) problems. The basic notions, the similarity measure, the entropy measure, and the index of distance of DNSNS are presented first. Secondly, the univariate time series of DNSNS are projected into dynamic nonlinear simplified neutrosophic curves in three-dimensional space. The areas of the surface enclosed by the curves represent the variance among the DNSNSs. Thus, the DNSNS aggregation model is established correctly without preprocessing the original data. Afterward, the aggregation algorithm extended from the plant growth simulation algorithm (PGSA) is proposed for calculating the optimal aggregation preference curve and constructing the collective matrix. Additionally, a novel corresponding decision algorithm based on TOPSIS and projection theory is proposed for obtaining the overall ranking of alternatives in the actual MAGDM problem. Finally, a typical example is presented to illustrate the feasibility and effectiveness of the proposed model and algorithm.

Lagrange-enhanced GRA framework for probabilistic simplified neutrosophic multiple-attributes decision-making and applications to painting teaching quality evaluation

Universities are important talent training bases in China and the main driving force for achieving the strategic layout of “revitalizing the country through science and education” and “strengthening the country through talent". Oil painting is a global art with rich humanistic and artistic value. Most art colleges in China have set up oil painting courses. Analyze the current situation and value of oil painting course teaching in local art (teacher training) majors, and leverage the educational role of oil painting courses by enriching course offerings, emphasizing the integration of humanistic innovation, improving teacher literacy, and striving to further improve the quality and efficiency of oil painting course teaching. The quality evaluation of oil painting teaching in universities is viewed as multiple-attribute decision-making (MADM). The grey relational analysis (GRA) is a useful tool to cope with the MADM issue. The probabilistic simplified Neutrosophic set (PSNSs) is easy to characterize uncertain information during the quality evaluation of oil painting teaching in universities. In this paper, in order to obtain the weight information, an optimization model implemented to obtain a simple and exact formula which can be employed to derive the attribute weights values based on the Lagrange function and the probabilistic simplified neutrosophic number grey relational analysis (PSNN-GRA) technique is implemented for MADM to rank the alternatives. Finally, a numerical example for quality evaluation of oil painting teaching in universities is used to verify the practicability of the PSNN-GRA technique and compares it with other techniques.

Improving computer network security evaluation with grey relational analysis and probabilistic simplified neutrosophic sets

The popularity of computer network has provided great convenience for people’s work and life, but it has also brought corresponding information security problems. It is very important to do a good job in computer network security evaluation. Conventional computer network security evaluation can be realized with the help of firewalls, antivirus software, etc., while in the face of complex computer network applications, it is necessary to adopt a security evaluation method with good operability and wider application range. The computer network security evaluation is viewed as multiple attribute decision-making (MADM) issue. In this paper, an extended probabilistic simplified neutrosophic number grey relational analysis (PSNN-GRA) method is established for computer network security evaluation. The PSNN-GRA method integrated with Criteria Importance Though Intercrieria Correlation (CRITIC) method in probabilistic simplified neutrosophic sets (PSNSs) circumstance is applied to rank the optional alternatives and a numerical example for computer network security evaluation is used to proof the newly proposed method’s practicability along with the comparison with other methods. The results display that the approach is uncomplicated, valid and simple to compute.

Lagrange-enhanced GRA method for probabilistic simplified neutrosophic MADM: Yaozhou porcelain decoration design quality evaluation

Yaozhou ware is located in Huangbao Town, Tongchuan City. It began in the Song Dynasty and flourished in the Tang Dynasty. Its warm and jade like glaze color, exquisite decorative techniques, and rich and varied utensil shapes all give it a very important position in history. The traditional Yaozhou porcelain contains the ancient people’s concept of creation and their attitude towards humans and nature. Each artifact of Yaozhou porcelain contains the designer’s understanding and emotions about the world, establishing a dialogue between people and objects to form a desired lifestyle. The production method of Yaozhou porcelain that has been preserved for thousands of years shares many similarities with modern design ideas. The quality evaluation of Yaozhou porcelain decoration design is viewed as multiple-attribute decision-making (MADM). The grey relational analysis (GRA) is a useful tool to cope with the MADM issue. The probabilistic simplified Neutrosophic set (PSNSs) is easy to characterize uncertain information during the quality evaluation of Yaozhou porcelain decoration design. In this paper, in order to obtain the weight information, an optimization model is constructed to obtain a simple and exact formula which can be employed to derive the attribute weights values based on the Lagrange function and the probabilistic simplified neutrosophic (PSN) grey relational analysis (PSN-GRA) method is originated for MADM to rank the decision alternatives. Finally, a numerical example for quality evaluation of Yaozhou porcelain decoration design is used to verify the practicability of the PSN-GRA method and compares it with other methods.

An improved GRA algorithm for teaching quality evaluation of college physical education based on the probabilistic simplified neutrosophic sets

With the emergence of various new teaching concepts and teaching models in colleges and universities, the original evaluation system can no longer fully meet the requirements of the current development of physical education curriculum teaching in colleges and universities. Thus, reducing the judgment and guidance of evaluation on physical education curriculum teaching shall result in the development of physical education curriculum teaching quality evaluation lagging behind the development of teaching and being in a passive position. Therefore, it is particularly important to establish a new evaluation standard system for the teaching quality of physical education courses. The teaching quality evaluation of college physical education (PE) is viewed as multiple attribute decision-making (MADM). In this paper, an enhanced probabilistic simplified neutrosophic grey relational analysis (PSN-GRA) method is designed for MADM. Then, in the environment of probabilistic simplified neutrophil set (PSNSs), the PSN-GRA method and CRITIC method are combined to rank the alternative schemes, and a numerical example of college physical education teaching quality evaluation proves the practicability of the new method and compares it with other methods. The results show that this method is simple, effective and simple in calculation.

GRA method for probabilistic simplified neutrosophic MADM and application to talent training quality evaluation of segmented education

The “3 + 2” segmented training between higher vocational colleges and applied undergraduate courses has opened up the rising channel of vocational education from junior college level to undergraduate level, and promoted the organic connection between higher vocational colleges and Universities of Applied Sciences. It is one of the important ways to establish a modern vocational education system. Exploring the monitoring mechanism of talent training quality is an important measure to ensure the achievement of the segmented training goal, and it is a necessary condition to successfully train high-quality skilled applied talents. The talent training quality evaluation of segmented education is viewed as multiple attribute decision-making (MADM) issue. In this paper, an extended probabilistic simplified neutrosophic number GRA (PSNN-GRA) method is established for talent training quality evaluation of segmented education. The PSNN-GRA method integrated with CRITIC method in probabilistic simplified neutrosophic sets (PSNSs) circumstance is applied to rank the optional alternatives and a numerical example for talent training quality evaluation of segmented education is used to proof the newly proposed method’s practicability along with the comparison with other methods. The results display that the approach is uncomplicated, valid and simple to compute.

Selecting the Best Health Care Systems: An Approach Based on Opinion Mining and Simplified Neutrosophic Sets

Measuring what hospital offers the best services is very difficult, for that reason, the opinions from previous patients have become an essential tool for the new possible clients to decide which services they must select. Many online platforms deal with opinions to analyze their services/products, primarily, by means of aspect-based sentiment analysis techniques. These techniques are mainly based on the detection of features from services/products to model the feelings toward them. Most models primarily cope with positiveness, negativeness and neutrality; nevertheless, these do not reflect other situations in which there are positive and negative aspects, but the overall sentiment is not neutral, but indeterminate. To face this issue, simplified neutrosophic sets can be a useful tool. Therefore, this study presents a novel application of the simplified neutrosophic sets to hospital ranking. The application, first, detects the hospital features, second, models the feelings toward them using simplified neutrosophic sets, and finally, ranks the hospitals according to the patients’ preferences. It has been tested using opinions from a real website and compared against other fuzzy logic-based approaches. The achieved results outperform the ones obtained by other proposals, revealing that simplified neutrosophic sets can be an interesting solution to model feelings.

Novel Generalized Divergence Measure and Aggregation Operators With Applications for Simplified Neutrosophic Sets

The amount of information on which researchers work increases continuously due to the new developments around the world. This information contains data which is uncertain, incomplete and cannot be fully expressed using crisp numbers. To manage such information, the theory of fuzzy sets, intuitionistic fuzzy sets and neutrosophic sets are used. Neutrosophic sets were introduced as the generalization of fuzzy and intuitionistic fuzzy sets to show incomplete, imprecise, inconsistent and uncertain information that exists in real situations. In this paper, a generalized neutrosophic divergence measure is proposed along with the proof of its validity and neutrosophic aggregation operators are discussed. The proposed measure is applied in decision-making for simplified neutrosophic sets. An illustrative example is provided to demonstrate the application and effectiveness of the developed approach and to test its practicality and legitimacy.

Q-INDETERMINATE CORRELATION COEFFICIENT BETWEEN SIMPLIFIED NEUTROSOPHIC INDETERMINATE SETS AND ITS MULTICRITERIA DECISION-MAKING METHOD

Owing to the indeterminacy, incompleteness, and inconsistency of decision makers’ arguments/cognitions regarding complicated decision-making problems, the truth, falsity, and indeterminacy degrees given by decision makers may imply the partial certainty and partial uncertainty information. In this case, a simplified neutrosophic set (SNS) cannot express the uncertainty degrees of the truth, falsity, indeterminacy arguments. To depict the hybrid information of SNS and neutrosophic (indeterminate) numbers (NNs) together, this study presents a simplified neutrosophic indeterminate set (SNIS) to describe the uncertainty degrees of the truth, falsity, indeterminacy, and then based on the de-neutrosophication technology using the parameterized SNSs of SNISs we introduce the q-indeterminate correlation coefficients of SNISs with a parameter q ∈ [0, 1]. Next, a simplified neutrosophic indeterminate multicriteria decision-making method using the qindeterminate correlation coefficients of SNISs is established along with decision makers’ risk attitudes, such as the small risk for q = 0, the moderate risk for q = 0.5, and the large risk for q = 1, to carry out multicriteria decision-making problems in SNIS setting. Eventually, the proposed decision-making approach is applied in an example of selecting a satisfactory slope design scheme for an open pit mine to indicate the practicality and flexibility in SNIS setting.

Entropy measures of simplified neutrosophic sets and their decision-making approach with positive and negative arguments

Regarding the insufficiency of existing entropy measures-based decision-making approaches, this paper presents trigonometric functions (cosine and sine functions)-based entropy measures of simplified neutrosophic sets (SNSs), including the entropy measures of single-valued neutrosophic sets (SvNSs) and interval-valued neutrosophic sets (IvNSs). Next, a decision-making (DM) approach is developed regarding the ranking method of both entropy values and positive and negative arguments in SNS setting, and then the comparative analysis with existing DM approaches based on the entropy measures of SNSs (SvNSs and IvNSs) is indicated by a numerical DM example to illustrate the effectiveness and rationality of the developed DM approach in SNS setting. Lastly, two actual DM examples are provided to indicate the practicability and sufficiency of the developed DM approach. However, this study not only enriches the simplified neutrosophic entropy measure but also enhances/improves existing DM approaches based on the entropy measures.

Multiple Attribute Group Decision Making Based on Simplified Neutrosophic Integrated Weighted Distance Measure and Entropy Method

Simplified neutrosophic set (SNS) is a popular tool in modelling potential, imprecise, and uncertain information within complex environments. In this paper, a method based on the integrated weighted distance measure and entropy weight is proposed for handling SNS multiple attribute group decision-making (MAGDM) problems. To this end, the simplified neutrosophic (SN) integrated weighted distance (SVNIWD) measure is first developed for overcoming the limitations of the existing methods. Afterward, the proposed SNIWD’s several properties and particular status are studied. Moreover, a flexible and useful MAGDM approach that combines the strengths of the SNIWD and the SNS is proposed, wherein the SN entropy measure is applied to calculate the unknown weight information regarding attributes. Finally, a numerical case of investment evaluation and subsequent comparative analysis are conducted to prove the superiority of the proposed framework.

SIMPLIFIED NEUTROSOPHIC INDETERMINATE DECISION MAKING METHOD WITH DECISION MAKERS’ INDETERMINATE RANGES

There exists the indeterminate situations of truth, falsity, indeterminacy degrees due to the uncertainty and inconsistency of decision makers’ arguments in a complicated decision making (DM) problem. Then, existing neutrosophic set cannot describe the indeterminate information of truth, falsity, indeterminacy degrees. It is noted that the simplified neutrosophic set (SNS) is depicted by truth, falsity, indeterminacy degrees, while a neutrosophic number (NN) can be flexibly depicted by its determinate part and its indeterminate part. Regarding the indeterminate situations of truth, falsity, indeterminacy degrees in indeterminate DM problems, this study first presents a simplified neutrosophic indeterminate set (SNIS) to express the hybrid information of SNS and NN and defines the score, accuracy, and certainty functions of simplified neutrosophic indeterminate elements (SNIEs) with indeterminate ranges to compare SNIEs. Then, we introduce a SNIE weighted arithmetic averaging (SNIEWAA) operator and a SNIE weighted geometric averaging (SNIEWGA) operator to aggregate simplified neutrosophic indeterminate information. Next, a multi-attribute DM approach with decision makers’ indeterminate ranges is established regarding the SNIEWAA and SNIEWGA operators in SNIS setting. Finally, the proposed DM approach is applied in a DM example on choosing a suitable slope design scheme to indicate the applicability and suitability of the proposed approach.

Generalized Ordered Weighted Simplified Neutrosophic Cosine Similarity Measure for Multiple Attribute Group Decision Making

The paper proposes a generalized ordered weighted simplified neutrosophic cosine similarity (GOWSNCS) measure by combining the cosine similarity measure of simplified neutrosophic sets (SNSs) with the generalized ordered weighted averaging (GOWA) operator and investigates its properties and special cases. Then, the author develops a simplified neutrosophic group decision-making method based on the GOWSNCS measure to handle multiple attribute group decision-making problems with simplified neutrosophic information. The prominent characteristics of the GOWSNCS measure are that it not only is a generalization of the cosine similarity measure but also considers the associated weights for attributes and decision makers in the aggregation of the cosine similarity measures of SNSs to alleviate the influence of unduly large or small similarities in the process of information aggregation. Finally, an illustrative example of investment alternatives is provided to demonstrate the application and effectiveness of the developed approach.

A simplified neutrosophic multiplicative set‐based TODIM using water‐filling algorithm for the determination of weights

AbstractDue to the technological developments around the world, the amount of information that researchers work on increases continuously. This information density contains incomplete and uncertain data that cannot be fully expressed with crisp numbers. Fuzzy sets, intuitionistic fuzzy sets, and neutrosophic sets are useful tools to manage such information, but these concepts use a symmetrical and uniform scale to express data, whereas real‐life problems contain nonsymmetrical and non‐uniform information. Intuitionistic multiplicative sets (IMSs) are effective tools for dealing with these real‐life problems. However, IMSs cannot handle real‐life problems completely because indeterminate information depends on membership and non‐membership information of IMSs, which is a restriction for decision makers and also for decision problems. To overcome this limitation, this paper generalizes the IMSs by using simplified neutrosophic set and introduces a novel approach that is called simplified neutrosophic multiplicative sets (SNMSs). Firstly, we define SNMS, show their set‐based operations, and then give a description of simplified neutrosophic multiplicative numbers (SNMNs). Based on SNMNs, we develop two simplified neutrosophic multiplicative aggregation operators on SNMNs that are called simplified neutrosophic multiplicative weighted arithmetic average operator and simplified neutrosophic multiplicative weighted geometric average operator. Furthermore, we define some simplified neutrosophic multiplicative distance measures. Finally, using a model based on water‐filling algorithm for determining criteria weights, we give a numerical example to demonstrate the effectiveness of the introduced concept with the proposed simplified neutrosophic multiplicative simplified neutrosophic multiplicative‐TODIM method.

Fault diagnosis of rolling element bearing based on symmetric cross entropy of neutrosophic sets

A novel symmetric single-valued neutrosophic cross entropy (SVNCE) measure based upon a newly developed symmetric measure of fuzzy cross entropy is established and then applied it for identifying defects of bearings installed in a test rig and axial piston pump. A 3-level wavelet packet transformation (WPT) is used for extracting and decomposing the fault features associated with the vibrational signals. The new evaluated SVNCE values between knowledge of various faults types and real testing samples provide useful evaluation information of fault types. The concluded results reveal that the proposed SVNCE measure furnishes better fault identification accuracy when compared with the existing model based upon correlation coefficient of simplified neutrosophic sets (SNSs). Furthermore, the proposed SVNCE measure offers consistent and feasible results and is capable for holding the optimal fault type selection under sensitive analysis.

Data Envelopment Analysis for Simplified Neutrosophic Sets

In recent years, therehas been a growing interest in neutrosophic theory, and there are several methods for solving various problems under neutrosophic environment. However, a few papers have discussed the Data envelopment analysis (DEA) with neutrosophic sets. So, in this paper, we propose an input-oriented DEA model with simplified neutrosophic numbers and present a new strategy to solve it. The proposed method is based on the weighted arithmetic average operator and has a simple structure. Finally, the new approach is illustrated with the help of a numerical example.

Multi-criteria decision making approach based on PROMETHEE with probabilistic simplified neutrosophic sets

Probabilistic simplified neutrosophic set $$ \left( {PSNS} \right) $$ is an important tool to describe the vagueness existing in the real life. In this study, we define a PSNS and discuss some of theoretical set operations of $$ PSNSs $$. Also we propose the concepts of module on $$ PSNSs $$, as well as inner product and projection operator between two $$ PSNSs $$. In relation to this new set, we introduce a probabilistic simplified neutrosophic number $$ \left( {PSNN} \right) $$. A $$ PSNN $$ has three components which is called probabilistic-valued truth membership degree, probabilistic-valued indeterminacy membership degree and probabilistic-valued falsity membership degree, respectively. We give some of algebraic operational rules, a score function and an accuracy function on $$ PSNNs $$. Furthermore, we introduce two aggregation operators called the probabilistic simplified neutrosophic weighted arithmetic average operator and the probabilistic simplified weighted geometric average operator on $$ PSNNs $$. Furthermore, we determine weights of criteria with a method that is based on fuzzy measure and develop a method based on preference function to determine weight of each decision maker. We present an extended PROMETHEE method based on $$ PSNSs $$ for group decision problems. Finally, as an application of this theory, we give a practice on a multi-criteria group decision making problem based on $$ PSNNs $$ by using extended PROMETHEE method to ensure stability of the proposed method.

Simplified Neutrosophic Sets Based on Interval Dependent Degree for Multi-Criteria Group Decision-Making Problems

Simplified Neutrosophic Sets Based on Interval Dependent Degree for Multi-Criteria Group Decision-Making Problems

Generalized Distance-Based Entropy and Dimension Root Entropy for Simplified Neutrosophic Sets

Generalized Distance-Based Entropy and Dimension Root Entropy for Simplified Neutrosophic Sets

Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems

Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems