New Challenges in Neutrosophic Theory and Applications

Neutrosophic theory has representatives on all continents and, therefore, it can be said to be a universal theory. On the other hand, according to the three volumes of “The Encyclopedia of Neutrosophic Researchers” (2016, 2018, 2019), plus numerous others not yet included in Encyclopedia book series, about 1200 researchers from 73 countries have applied both the neutrosophic theory and method. Neutrosophic theory was founded by Professor Florentin Smarandache in 1998; it constitutes further generalization of fuzzy and intuitionistic fuzzy theories. The key distinction between the neutrosophic set/logic and other types of sets/logics lies in the introduction of the degree of indeterminacy/neutrality (I) as an independent component in the neutrosophic set. Thus, neutrosophic theory involves the degree of membership-truth (T), the degree of indeterminacy (I), and the degree of non-membership-falsehood (F). In recent years, the field of neutrosophic set, logic, measure, probability and statistics, precalculus and calculus, etc., and their applications in multiple fields have been extended and applied in various fields, such as communication, management, and information technology. We believe that this book serves as useful guidance for learning about the current progress in neutrosophic theories. In total, 22 studies have been presented and reflect the call of the thematic vision. The contents of each study included in the volume are briefly described as follows. The first contribution, authored by Wadei Al-Omeri and Saeid Jafari, addresses the concept of generalized neutrosophic pre-closed sets and generalized neutrosophic pre-open sets in neutrosophic topological spaces. In the article “Design of Fuzzy Sampling Plan Using the Birnbaum-Saunders Distribution”, the authors Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam, and Abdur Razzaque Mughal discuss the use of probability distribution function of Birnbaum–Saunders distribution as a proportion of defective items and the acceptance probability in a fuzzy environment. Further, the authors Derya Bakbak, Vakkas Uluc¸ay, and Memet S¸ahin present the “Neutrosophic Soft Expert Multiset and Their Application to Multiple Criteria Decision Making” together with several operations defined for them and their important algebraic properties. In “Neutrosophic Multigroups and Applications”, Vakkas Uluc¸ay and Memet S¸ahin propose an algebraic structure on neutrosophic multisets called neutrosophic multigroups, deriving their basic properties and giving some applications to group theory. Changxing Fan, Jun Ye, Sheng Feng, En Fan, and Keli Hu introduce the “Multi-Criteria Decision-Making Method Using Heronian Mean Operators under a Bipolar Neutrosophic Environment” and test the effectiveness of their new methods. Another decision-making study upon an everyday life issue which empowered us to organize the key objective of the industry developing is given in “Neutrosophic Cubic Einstein Hybrid Geometric Aggregation Operators with Application in Prioritization Using Multiple Attribute Decision-Making Method” written by Khaleed Alhazaymeh, Muhammad Gulistan, Majid Khan, and Seifedine Kadry

A Pythagorean Fuzzy Multigranulation Probabilistic Model for Mine Ventilator Fault Diagnosis

In coal mining industry, the running state of mine ventilators plays an extremely significant role for the safe and reliable operation of various industrial productions. To guarantee the better reliability, safety, and economy of mine ventilators, in view of early detection and effective fault diagnosis of mechanical faults which could prevent unscheduled downtime and minimize maintenance fees, it is imperative to construct some viable mathematical models for mine ventilator fault diagnosis. In this article, we plan to establish a data-based mine ventilator fault diagnosis method to handle situations where engineers are absent or they are incapable of coming to a conclusion from multisource data. In the process of building the mine ventilator fault diagnosis model, considering that probabilistic rough sets (PRSs) could reduce the errors triggered by incompleteness, inconsistency, and inaccuracy without needing any additional assumptions and Pythagorean fuzzy multigranulation rough sets (PF MGRSs) over the two universes’ model could effectively handle data representation, fusion, and analysis issues, we generalize the existing PF MGRSs over the two universes’ model to the PRS setting, as well as to further establish a novel model named Pythagorean fuzzy multigranulation probabilistic rough sets (PF MG-PRSs) over two universes. In the granular computing paradigm, three types of PF MG-PRSs over two universes based on the risk attitude of engineers are proposed at first. Afterwards, several basic propositions of the newly proposed model are explored. Moreover, a PF multigranulation probabilistic model for mine ventilator fault diagnosis based on PF MG-PRSs over two universes is investigated. At last, a real-world case study of dealing with a mine ventilator fault diagnosis problem is given to illustrate the practicality of the presented model, and a validity test, a sensitivity analysis, and a comparison analysis are further explored to demonstrate the effectiveness of the presented model