Decision-Making Approach Based on Neutrosophic Rough Information

Dynamic aggregation operators and Einstein operations based on interval-valued picture hesitant fuzzy information and their applications in multi-period decision making

The traditional picture hesitant fuzzy aggregation operators are generally suitable for aggregating information acquired in the form of picture hesitant fuzzy numbers, but they will fail in dealing with interval-valued picture hesitant fuzzy information. In this paper, we describe the notion of interval-valued picture hesitant fuzzy set and the operational laws of interval-valued picture hesitant fuzzy variables. Moreover, we derive some dynamic interval-valued picture hesitant fuzzy aggregation operators (based on Einstein operators) to aggregate the interval-valued picture hesitant fuzzy information collected at different periods. Some desirable properties of these aggregation operators are discussed in detail. In addition, we develop the approaches to tackle the multi-period decision-making problems, where all decision information takes the form of interval-valued picture hesitant fuzzy information collected at different periods. In an attempt to illustrate the applications of the proposed approaches, two numerical examples are given to measure the impact of Coronavirus Disease 2019 (COVID-19) in daily life and to identify the optimal investment opportunity. Finally, a comparative analysis of the proposed and existing studies are conducted to demonstrate the effectiveness of the proposed approaches. The presented interval-valued picture hesitant fuzzy operations, aggregation operators, and decision-making approaches can widely apply to dynamic decision analysis and multi-stage decision analysis in real life.

A neutrosophic clinical decision-making system for cardiovascular diseases risk analysis

Cardiovascular diseases are the leading cause of death worldwide. Early diagnosis of heart disease can reduce this large number of deaths so that treatment can be carried out. Many decision-making systems have been developed, but they are too complex for medical professionals. To target these objectives, we develop an explainable neutrosophic clinical decision-making system for the timely diagnose of cardiovascular disease risk. We make our system transparent and easy to understand with the help of explainable artificial intelligence techniques so that medical professionals can easily adopt this system. Our system is taking thirty-five symptoms as input parameters, which are, gender, age, genetic disposition, smoking, blood pressure, cholesterol, diabetes, body mass index, depression, unhealthy diet, metabolic disorder, physical inactivity, pre-eclampsia, rheumatoid arthritis, coffee consumption, pregnancy, rubella, drugs, tobacco, alcohol, heart defect, previous surgery/injury, thyroid, sleep apnea, atrial fibrillation, heart history, infection, homocysteine level, pericardial cysts, marfan syndrome, syphilis, inflammation, clots, cancer, and electrolyte imbalance and finds out the risk of coronary artery disease, cardiomyopathy, congenital heart disease, heart attack, heart arrhythmia, peripheral artery disease, aortic disease, pericardial disease, deep vein thrombosis, heart valve disease, and heart failure. There are five main modules of the system, which are neutrosophication, knowledge base, inference engine, de-neutrosophication, and explainability. To demonstrate the complete working of our system, we design an algorithm and calculates its time complexity. We also present a new de-neutrosophication formula, and give comparison of our the results with existing methods.

TODIM Method for Multiple Attribute Group Decision Making under 2-Tuple Linguistic Neutrosophic Environment

In this article, we extend the original TODIM (Portuguese acronym for Interactive Multi-Criteria Decision Making) method to the 2-tuple linguistic neutrosophic fuzzy environment to propose the 2TLNNs TODIM method. In the extended method, we use 2-tuple linguistic neutrosophic numbers (2TLNNs) to present the criteria values in multiple attribute group decision making (MAGDM) problems. Firstly, we briefly introduce the definition, operational laws, some aggregation operators and the distance calculating method of 2TLNNs. Then, the calculation steps of the original TODIM model are presented in simplified form. Thereafter, we extend the original TODIM model to the 2TLNNs environment to build the 2TLNNs TODIM model, our proposed method, which is more reasonable and scientific in considering the subjectivity of DM’s behaviors and the dominance of each alternative over others. Finally, a numerical example for the safety assessment of a construction project is proposed to illustrate the new method, and some comparisons are also conducted to further illustrate the advantages of the new method.

Energy of Pythagorean Fuzzy Graphs with Applications

Pythagorean fuzzy sets (PFSs), an extension of intuitionistic fuzzy sets (IFSs), inherit the duality property of IFSs and have a more powerful ability than IFSs to model the obscurity in practical decision-making problems. In this research study, we compute the energy and Laplacian energy of Pythagorean fuzzy graphs (PFGs) and Pythagorean fuzzy digraphs (PFDGs). Moreover, we derive the lower and upper bounds for the energy and Laplacian energy of PFGs. Finally, we present numerical examples, including the design of a satellite communication system and the evaluation of the schemes of reservoir operation to illustrate the applications of our proposed concepts in decision making.

Certain Notions of Energy in Single-Valued Neutrosophic Graphs

A single-valued neutrosophic set is an instance of a neutrosophic set, which provides us an additional possibility to represent uncertainty, imprecise, incomplete and inconsistent information existing in real situations. In this research study, we present concepts of energy, Laplacian energy and signless Laplacian energy in single-valued neutrosophic graphs (SVNGs), describe some of their properties and develop relationship among them. We also consider practical examples to illustrate the applicability of the our proposed concepts.