(R1997) Distance Measures of Complex Fermatean Fuzzy Number and Their Application to Multi-criteria Decision-making Problem

Multi-criteria decision-making (MCDM) is the most widely used decision-making method to solve many complex problems. However, classical MCDM approaches tend to make decisions when the parameters are imprecise or uncertain. The concept of a complex fuzzy set is new in the field of fuzzy set theory. It is a set that can collect and interpret the membership grades from the unit circle in a plane instead of the interval [0,1]. CFS cannot deal with membership and non-membership grades, while complex intuitionistic fuzzy set and complex Pythagorean fuzzy set works only for a limited range of values. The concept of a complex Fermatean fuzzy set (CFFS) is proposed to deal with these problems. This paper presents the main ideas of CFFN and its properties are studied. The proposed new distance measures for real-world problems are also discussed. A comparative study of the proposed new work is also conducted

Multi-criteria decision-making based on Pythagorean cubic fuzzy Einstein aggregation operators for investment management

Pythagorean cubic fuzzy sets (PCFSs) are a more advanced version of interval-valued Pythagorean fuzzy sets where membership and non-membership are depicted using cubic sets. These sets offer a greater amount of data to handle uncertainties in the information. However, there has been no previous research on the use of Einstein operations for aggregating PCFSs. This study proposes two new aggregator operators, namely, Pythagorean cubic fuzzy Einstein weighted averaging (PCFEWA) and Pythagorean cubic fuzzy Einstein ordered weighted averaging (PCFEOWA), which extend the concept of Einstein operators to PCFSs. These operators offer a more effective and precise way of aggregating Pythagorean cubic fuzzy information, especially in decision-making scenarios involving multiple criteria and expert opinions. To illustrate the practical implementation of this approach, we apply an established MCDM model and conduct a case study aimed at identifying the optimal investment market. This case study enables the evaluation and validation of the established MCDM model's effectiveness and reliability, thus making a valuable contribution to the field of investment analysis and decision-making. The study systematically compares the proposed approach with existing methods and demonstrates its superiority in terms of validity, practicality and effectiveness. Ultimately, this paper contributes to the ongoing development of sophisticated techniques for modeling and analyzing complex systems, offering practical solutions to real-world decision-making problems

Novel possibility Pythagorean interval valued fuzzy soft set method for a decision making

We discuss the theory of possibility Pythagorean interval valued fuzzy soft set, possibility interval valued fuzzy soft set and define some related the operations namely complement, union, intersection, AND and OR. The possibility Pythagorean interval valued fuzzy soft sets are a generalization of soft sets. Notably, we showed DeMorgan’s laws that are valid in possibility Pythagorean interval valued fuzzy soft set theory. Also, we propose an algorithm to solve the decision making problem based on soft set method. To compare two possibilities Pythagorean interval valued fuzzy soft sets for dealing with decision making problems and find a similarity measure is obtained. Finally, an illustrative example is discussed to prove that they can be effectively used to solve problems with uncertainties.Publisher's Versio

Determine OWA operator weights using kernel density estimation

Some subjective methods should divide input values into local clusters before determining the ordered weighted averaging (OWA) operator weights based on the data distribution characteristics of input values. However, the process of clustering input values is complex. In this paper, a novel probability density based OWA (PDOWA) operator is put forward based on the data distribution characteristics of input values. To capture the local cluster structures of input values, the kernel density estimation (KDE) is used to estimate the probability density function (PDF), which fits to the input values. The derived PDF contains the density information of input values, which reflects the importance of input values. Therefore, the input values with high probability densities (PDs) should be assigned with large weights, while the ones with low PDs should be assigned with small weights. Afterwards, the desirable properties of the proposed PDOWA operator are investigated. Finally, the proposed PDOWA operator is applied to handle the multicriteria decision making problem concerning the evaluation of smart phones and it is compared with some existing OWA operators. The comparative analysis shows that the proposed PDOWA operator is simpler and more efficient than the existing OWA operator

Uncertain Multi-Criteria Optimization Problems

Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relationships used when modeling optimization problems. Moreover, the notion of symmetry has appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better solution with respect to one objective may compromise other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories such as probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems have not yet been explored in depth, and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed in various uncertain frameworks with special emphasis on optimization problems

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 systematic review on multi-criteria group decision-making methods based on weights: analysis and classification scheme

Interest in group decision-making (GDM) has been increasing prominently over the last decade. Access to global databases, sophisticated sensors which can obtain multiple inputs or complex problems requiring opinions from several experts have driven interest in data aggregation. Consequently, the field has been widely studied from several viewpoints and multiple approaches have been proposed. Nevertheless, there is a lack of general framework. Moreover, this problem is exacerbated in the case of experts’ weighting methods, one of the most widely-used techniques to deal with multiple source aggregation. This lack of general classification scheme, or a guide to assist expert knowledge, leads to ambiguity or misreading for readers, who may be overwhelmed by the large amount of unclassified information currently available. To invert this situation, a general GDM framework is presented which divides and classifies all data aggregation techniques, focusing on and expanding the classification of experts’ weighting methods in terms of analysis type by carrying out an in-depth literature review. Results are not only classified but analysed and discussed regarding multiple characteristics, such as MCDMs in which they are applied, type of data used, ideal solutions considered or when they are applied. Furthermore, general requirements supplement this analysis such as initial influence, or component division considerations. As a result, this paper provides not only a general classification scheme and a detailed analysis of experts’ weighting methods but also a road map for researchers working on GDM topics or a guide for experts who use these methods. Furthermore, six significant contributions for future research pathways are provided in the conclusions.The first author acknowledges support from the Spanish Ministry of Universities [grant number FPU18/01471]. The second and third author wish to recognize their support from the Serra Hunter program. Finally, this work was supported by the Catalan agency AGAUR through its research group support program (2017SGR00227). This research is part of the R&D project IAQ4EDU, reference no. PID2020-117366RB-I00, funded by MCIN/AEI/10.13039/ 501100011033.Peer ReviewedPostprint (published version