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

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

Robot sensors process based on generalized Fermatean normal different aggregation operators framework

Novel methods for multiple attribute decision-making problems are presented in this paper using Type-Ⅱ Fermatean normal numbers. Type-Ⅱ Fermatean fuzzy sets are developed by further generalizing Fermatean fuzzy sets and neutrosophic sets. The Type-Ⅱ Fermatean fuzzy sets with basic aggregation operators are constructed. The concept of a Type-Ⅱ Fermatean normal number is compatible with both commutative and associative rules. This article presents a new proposal for Type-Ⅱ Fermatean normal weighted averaging, Type-Ⅱ Fermatean normal weighted geometric averaging, Type-Ⅱ generalized Fermatean normal weighted averaging, and Type-Ⅱ generalized Fermatean normal weighted geometric averaging. Furthermore, these operators can be used to develop an algorithm that solves MADM problems. Applications for the Euclidean distance and Hamming distances are discussed. Finally, the sets that arise as a result of their connection to algebraic operations are emphasized in our discourse. Examples of real-world applications of enhanced Hamming distances are presented. A sensor robot's most important components are computer science and machine tool technology. Four factors can be used to evaluate the quality of a robotics system: resolution, sensitivity, error and environment. The best alternative can be determined by comparing expert opinions with the criteria. As a result, the proposed models' outcomes are more precise and closer to integer number $\delta$. To demonstrate the applicability and validity of the models under consideration, several existing models are compared with the ones that have been proposed

Decision support algorithm under SV-neutrosophic hesitant fuzzy rough information with confidence level aggregation operators

To deal with the uncertainty and ensure the sustainability of the manufacturing industry, we designed a multi criteria decision-making technique based on a list of unique operators for single-valued neutrosophic hesitant fuzzy rough (SV-NHFR) environments with a high confidence level. We show that, in contrast to the neutrosophic rough average and geometric aggregation operators, which are unable to take into account the level of experts' familiarity with examined objects for a preliminary evaluation, the neutrosophic average and geometric aggregation operators have a higher level of confidence in the fundamental idea of a more networked composition. A few of the essential qualities of new operators have also been covered. To illustrate the practical application of these operators, we have given an algorithm and a practical example. We have also created a manufacturing business model that takes sustainability into consideration and is based on the neutrosophic rough model. A symmetric comparative analysis is another tool we use to show the feasibility of our proposed enhancements

Multiple-Criteria Decision Making

Decision-making on real-world problems, including individual process decisions, requires an appropriate and reliable decision support system. Fuzzy set theory, rough set theory, and neutrosophic set theory, which are MCDM techniques, are useful for modeling complex decision-making problems with imprecise, ambiguous, or vague data.This Special Issue, “Multiple Criteria Decision Making”, aims to incorporate recent developments in the area of the multi-criteria decision-making field. Topics include, but are not limited to:- MCDM optimization in engineering;- Environmental sustainability in engineering processes;- Multi-criteria production and logistics process planning;- New trends in multi-criteria evaluation of sustainable processes;- Multi-criteria decision making in strategic management based on sustainable criteria

q-Rung orthopair fuzzy information aggregation and their application towards material selection

Material selection is a complex process that involves selecting the best material for a given application. It is a critical process in engineering, and the importance of selecting the right material for the job cannot be overstated. Multi-criteria decision-making (MCDM) is an important tool that can be used to help engineers make informed decisions about material selection. The logistic function can be extended using the soft-max function, which is widely used in stochastic classification methods like neural nets, soft-max extrapolation, linear differential analysis, and Naïve Bayes detectors. This has inspired researchers to develop soft-max-based fuzzy aggregation operators (AOs) for q-rung orthopair fuzzy sets (q-ROPFS) and to propose an MCDM approach based on these AOs. To test the effectiveness of this approach, the researchers applied it to a practical problem using q-rung orthopair fuzzy data and conducted a numerical example to validate the suggested procedures

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches

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

Collected Papers (on Neutrosophic Theory and Applications), Volume VIII

This eighth volume of Collected Papers includes 75 papers comprising 973 pages on (theoretic and applied) neutrosophics, written between 2010-2022 by the author alone or in collaboration with the following 102 co-authors (alphabetically ordered) from 24 countries: Mohamed Abdel-Basset, Abduallah Gamal, Firoz Ahmad, Ahmad Yusuf Adhami, Ahmed B. Al-Nafee, Ali Hassan, Mumtaz Ali, Akbar Rezaei, Assia Bakali, Ayoub Bahnasse, Azeddine Elhassouny, Durga Banerjee, Romualdas Bausys, Mircea Boșcoianu, Traian Alexandru Buda, Bui Cong Cuong, Emilia Calefariu, Ahmet Çevik, Chang Su Kim, Victor Christianto, Dae Wan Kim, Daud Ahmad, Arindam Dey, Partha Pratim Dey, Mamouni Dhar, H. A. Elagamy, Ahmed K. Essa, Sudipta Gayen, Bibhas C. Giri, Daniela Gîfu, Noel Batista Hernández, Hojjatollah Farahani, Huda E. Khalid, Irfan Deli, Saeid Jafari, Tèmítópé Gbóláhàn Jaíyéolá, Sripati Jha, Sudan Jha, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, M. Karthika, Kawther F. Alhasan, Giruta Kazakeviciute-Januskeviciene, Qaisar Khan, Kishore Kumar P K, Prem Kumar Singh, Ranjan Kumar, Maikel Leyva-Vázquez, Mahmoud Ismail, Tahir Mahmood, Hafsa Masood Malik, Mohammad Abobala, Mai Mohamed, Gunasekaran Manogaran, Seema Mehra, Kalyan Mondal, Mohamed Talea, Mullai Murugappan, Muhammad Akram, Muhammad Aslam Malik, Muhammad Khalid Mahmood, Nivetha Martin, Durga Nagarajan, Nguyen Van Dinh, Nguyen Xuan Thao, Lewis Nkenyereya, Jagan M. Obbineni, M. Parimala, S. K. Patro, Peide Liu, Pham Hong Phong, Surapati Pramanik, Gyanendra Prasad Joshi, Quek Shio Gai, R. Radha, A.A. Salama, S. Satham Hussain, Mehmet Șahin, Said Broumi, Ganeshsree Selvachandran, Selvaraj Ganesan, Shahbaz Ali, Shouzhen Zeng, Manjeet Singh, A. Stanis Arul Mary, Dragiša Stanujkić, Yusuf Șubaș, Rui-Pu Tan, Mirela Teodorescu, Selçuk Topal, Zenonas Turskis, Vakkas Uluçay, Norberto Valcárcel Izquierdo, V. Venkateswara Rao, Volkan Duran, Ying Li, Young Bae Jun, Wadei F. Al-Omeri, Jian-qiang Wang, Lihshing Leigh Wang, Edmundas Kazimieras Zavadskas