Probabilistic Single-Valued (Interval) Neutrosophic Hesitant Fuzzy Set and Its Application in Multi-Attribute Decision Making

The uncertainty and concurrence of randomness are considered when many practical problems are dealt with. To describe the aleatory uncertainty and imprecision in a neutrosophic environment and prevent the obliteration of more data, the concept of the probabilistic single-valued (interval) neutrosophic hesitant fuzzy set is introduced

A hierarchical integration method under social constraints to maximize satisfaction in multiple criteria group decision making systems

Aggregating multiple opinions or assessments in a decision has always been a challenging field topic for researchers. Over the last decade, different approaches, mainly based on weighting data sources or decision-makers (DMs), have been proposed to resolve this issue, although social choice theory, focused on frameworks to combine individual opinions, is generally overlooked. To resolve this situation, a novel methodology is developed in this paper based on social choice theory and statistical mathematics. This method innovates by dividing the assessment into components which provides a multiple assessment analysis, assigning weights to each source regarding their position compared to the group for each considered criteria. This multiple-weighting process maximises individual and group satisfaction. Furthermore, the method makes it possible to manage previously assigned influence. An example is given to illustrate the proposed methodology. Additionally, sensitivity analysis is performed and comparisons with other methods are made. Finally, conclusions are presented.The first author acknowledges support from the Spanish Ministry of Education, Culture and Sports [grant number FPU18/01471]. The second and third author wish to recognise their support from the Serra Hunter programme. 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

Interval-valued probabilistic hesitant fuzzy set-based framework for group decision-making with unknown weight information

This paper aims at presenting a new decision framework under an interval-valued probabilistic hesitant fuzzy set (IVPHFS) context with fully unknown weight information. At first, the weights of the attributes are determined by using the interval-valued probabilistic hesitant deviation method. Later, the DMs’ weights are determined by using a recently proposed evidence theory-based Bayesian approximation method under the IVPHFS context. The preferences are aggregated by using a newly extended generalized Maclaurin symmetric mean operator under the IVPHFS context. Further, the alternatives are prioritized by using an interval-valued probabilistic hesitant complex proportional assessment method. From the proposed framework, the following significances are inferred; for example, it uses a generalized preference structure that provides ease and flexibility to the decision-makers (DMs) during preference elicitation; weights are calculated systematically to mitigate inaccuracies and subjective randomness; interrelationship among attributes are effectively captured; and alternatives are prioritized from different angles by properly considering the nature of the attributes. Finally, the applicability of the framework is validated by using green supplier selection for a leading bakery company, and from the comparison, it is observed that the framework is useful, practical and systematic for rational decision-making and robust and consistent from sensitivity analysis of weights and Spearman correlation of rank values, respectively

EDAS method for multiple attribute group decision making with probabilistic dual hesitant fuzzy information and its application to suppliers selection

Probabilistic dual hesitant fuzzy set (PDHFS) is a more powerful and important tool to describe uncertain information regarded as generalization of hesitant fuzzy set (HFS) and dual HFS (DHFS), not only reflects the hesitant attitude of decision-makers (DMs), but also reflects the probability information of DMs. Score function of fuzzy number and weighting method are very important in multi-attribute group decision-making (MAGDM) issues. In many fuzzy environments, the score function and entropy measure have been proposed one after another. Firstly, based on the detailed analysis of the existed score function of PDHF element (PDHFE) and with the help of previous references, we build a novel score function for PDHFE. Secondly, a combined weighting method is built based on the minimum identification information principle by fusing PDHF entropy and Criteria Importance Through Intercriteria Correlation (CRITIC) method. Thirdly, a novel PDHF MAGDM approach (PDHF-EDAS) is built by extending evaluation based on distance from average solution (EDAS) approach to the PDHF environment to solve the issue that the decision attribute information is PDHFE. Finally, the practicability and effectiveness of the PDHF MAGDM technique is verified by suppliers selection (SS) and comparing analysis with existing methods. First published online 23 January 202

Investment decision making along the B&R using critic approach in probabilistic hesitant fuzzy environment

The Belt and Road (B&R) Initiative receives enthusiastic response, the aim of which is to develop cooperative partnerships with countries along the routes and build a community of common destiny. So far, Chinese companies have invested in many different countries along the B&R. Generally, the investment decision making problems are characterized by high risk and uncertainty. Then how to make an appropriate investment decision will be a thorny issue. In this paper, probabilistic hesitant fuzzy set (PHFS) is used for handling uncertainty in multiple attribute decision making (MADM), and the criteria importance through intercriteria correlation (CRITIC) approach is extended to obtain attribute weights, no matter whether the weight information is incompletely known or not. Considering that the existing probabilistic hesitant fuzzy distance measures fail to meet the condition of distance measure, a new distance between PHFSs is proposed and applied to investment decision making for countries along the B&R. In the last, comparative analyses are performed to illustrate the advantages of the presented approach

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

Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value

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