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Crude oil, the backbone of modern industry, holds unparalleled significance as a global energy cornerstone. Unlocking its potential hinges on effective pretreatment techniques, ensuring purity, and maximizing efficiency. This study extends the established Spherical Fuzzy Set paradigm to explore the domain of Disc Spherical Fuzzy Sets (D-SFSs) in critical decision-making for crude oil preparation. Investigating D-SFSs within the Aczel Alsina norm, the research employs comparison rules, conversion rules, and distance metrics. Primary operations of the Aczel Alsina norm in D-SFSs are examined, laying the groundwork for introducing unique aggregation operations within this framework. The paper's primary aim is to propose a hybrid method, termed MEREC-SWARA-MARCOS-D-SFSs Multiple Attribute Group Decision Making, which integrates the aforementioned aggregation procedures. A case study on crude oil pretreatment validates the effectiveness of the proposed method. Furthermore, a comprehensive comparison with CoCoSo underscores the reliability of the method. This study represents a significant stride in enhancing decision-making by providing a robust framework to tackle complex situations, particularly in the critical domain of crude oil pretreatment. [ABSTRACT FROM AUTHOR]

Spherical q-linear Diophantine fuzzy sets (Sq-LDFSs) showed a significant improvement to handling uncertainty in multi-criteria decision-making (MADM). It is advantageous for two-parametric data as well as for data with three variable parameters. One of the most crucial functions of supply chain management is to increase competitive pressure. The study's standout innovation, Multi-Attributive Ideal Real Comparative Analysis (MAIRCA), has been implemented to give powerful group decision-making. An ecological perspective is becoming more prevalent due to the competitive climate and customer perception. Green supplier selection (GSS) has become a significant issue. In this study, we address the problem of GSS, which aims for flexibility, robustness, ecological sensitivity, leanness, and feasibility. The feasibility criteria in recycling, environmental, carbon footprints, and water consumption are different from those in standard supplier selection. The aim of our work is to introduced the weighted Average/Geometric aggregation operators based on Sq-LDFSs. For this we defined some operational rules as a foundation of aggregation operators. Secondly we proposed a MAIRCA approach for Sq-LDFSs to address these issues. The MAIRCA strategy, which uses multi-criteria group decision-making (MCGDM) to evaluate and choose traditional and environmental conventionalities, is used to reduce instability and ambiguity. The spherical q-linear Diophantine fuzzy MAIRCA approach provides comparative analysis of decision-makers and criteria. By merging Sq-LDFS and MAIRCA, a hybrid strategy is formed, successfully selecting the best provider among options based on the order of significance. These numerical examples demonstrate the suggested MCGDM approaches that were applied in actual situations, giving a realistic appreciation of their efficacy. The comparative study of the final ranking further supports the idea that these strategies are dependable in decision-making processes in addition to being practical and usable. [ABSTRACT FROM AUTHOR]

Simulation software replicates the behavior of real electrical equipment using mathematical models. This is efficient not only in regard to time savings but also in terms of investment. It, at large scale for instance airplane pilots, chemical or nuclear plant operators, etc., provides valuable experiential learning without the risk of a catastrophic outcome. But the selection of a circuit simulator with effective simulation accuracy poses significant challenges for today's decision-makers because of uncertainty and ambiguity. Thus, better judgments with increased productivity and accuracy are crucial. For this, we developed a complex probabilistic hesitant fuzzy soft set (CPHFSS) to capture ambiguity and uncertain information with higher accuracy in application scenarios. In this manuscript, the novel concept of CPHFSS is explored and its fundamental laws are discussed. Additionally, we investigated several algebraic aspects of CPHFSS, including union, intersections, soft max-AND, and soft min-OR operators, and we provided numerical examples to illustrate these key qualities. The three decision-making strategies are also constructed using the investigated idea of CPHFSS. Furthermore, numerical examples related to bridges and circuit simulation are provided in order to assess the validity and efficacy of the proposed methodologies. The graphical expressions of the acquired results are also explored. Finally, we conclude the whole work. [ABSTRACT FROM AUTHOR]

Due to the frequent occurrence of numerous emergency events that have significantly damaged society and the economy, the need for emergency decision-making has been manifest recently. It assumes a controllable function when it is critical to limit property and personal catastrophes and lessen their negative consequences on the natural and social course of events. In emergency decision-making problems, the aggregation method is crucial, especially when there are more competing criteria. Based on these factors, we first introduced some basic concepts about SHFSS, and then we introduced some new aggregation operators such as the spherical hesitant fuzzy soft weighted average, spherical hesitant fuzzy soft ordered weighted average, spherical hesitant fuzzy weighted geometric aggregation, spherical hesitant fuzzy soft ordered weighted geometric aggregation, spherical hesitant fuzzy soft hybrid average, and spherical hesitant fuzzy soft hybrid geometric aggregation operator. The characteristics of these operators are also thoroughly covered. Also, an algorithm is developed within the spherical hesitant fuzzy soft environment. Furthermore, we extend our investigation to the Evaluation based on the Distance from Average Solution method in multiple attribute group decision-making with spherical hesitant fuzzy soft averaging operators. And a numerical illustration for "supply of emergency aid in post-flooding the situation" is given to show the accuracy of the mentioned work. Then a comparison between these operators and the EDAS method is also established in order to further highlight the superiority of the established work. [ABSTRACT FROM AUTHOR]

Artificial intelligence (AI)-enabled energy efficiency in buildings leverages AI to optimize energy consumption, enhancing sustainability and aiding decision-makers in selecting cost-effective and environmentally friendly solutions. Pythagorean fuzzy Z ̃ number sets, capable of handling high uncertainty, play a crucial role in representing fuzzy information in decision-making. This research introduces novel operational laws and weighted aggregation operators, focusing on neutral addition and scalar multiplication. Comprehensive investigations into the properties of these laws lead to groundbreaking aggregation operators tailored for Pythagorean fuzzy Z ̃ number information. These include weighted, ordered weighted, and hybrid neutral averaging aggregation operators, along with a novel approach for calculating attribute weights. Relationships and characteristics of these operators are explored, and an algorithm for solving multiple attribute group decision-making problems is provided. A practical example illustrates the approach's superiority, supported by comparative results. • The advanced Pythagorean fuzzy Z-number-based neutrality aggregation model is given. • Fundamental operational guidelines for neutrality AOs for PFZNs are introduced. • The theoretic algorithm to tackle MAGDM problems in the PFZN environment is proposed. • The problem of AI-enabled energy efficiency is addressed from the MAGDM aspect. • Guidance for experts when evaluating energy-efficient building solutions is offered. [ABSTRACT FROM AUTHOR]

The main purpose of this manuscript is to present a novel idea on the q-rung orthopair fuzzy rough set (q-ROFRS) by the hybridized notion of q-ROFRSs and rough sets (RSs) and discuss its basic operations. Furthermore, by utilizing the developed concept, a list of q-ROFR Einstein weighted averaging and geometric aggregation operators are presented which are based on algebraic and Einstein norms. Similarly, some interesting characteristics of these operators are initiated. Moreover, the concept of the entropy and distance measures is presented to utilize the decision makers' unknown weights as well as attributes' weight information. The EDAS (evaluation based on distance from average solution) methodology plays a crucial role in decision-making challenges, especially when the problems of multicriteria group decision-making (MCGDM) include more competing criteria. The core of this study is to develop a decision-making algorithm based on the entropy measure, aggregation information, and EDAS methodology to handle the uncertainty in real-word decision-making problems (DMPs) under q-rung orthopair fuzzy rough information. To show the superiority and applicability of the developed technique, a numerical case study of a real-life DMP in agriculture farming is considered. Findings indicate that the suggested decision-making model is much more efficient and reliable to tackle uncertain information based on q-ROFR information. [ABSTRACT FROM AUTHOR]

Spherical fuzzy sets have recently become more popular in various fields. It was proposed as a generalization of picture fuzzy sets and Pythagorean fuzzy sets in order to deal with uncertainty and fuzziness information. This paper presents a multi-attribute group decision making method based on novel sine aggregation operators to help decision makers choose the optimal alternative. Moreover, the well-known sine trigonometry function preserves the periodic and symmetric nature about the origin, and hence, it satisfies the decision makers preferences over the multi-time phase parameters. Keeping these features and the importance of the spherical fuzzy (SF) sets, the objective of this paper is to present some robust sine trigonometric (ST) operation laws for SF sets. Associated with these laws, we define some series of new aggregation operators (AOs) named as ST-weighted averaging and geometric operators to aggregate the spherical fuzzy information. Afterward, we present group decision making techniques to solve the multi-attribute group decision making problems based on proposed AOs and illustrate with a numerical example of an internet finance soft power evaluation problem to validate it. Also, we conduct some comparison analysis to study the reasonability and practicality of the proposed method. [ABSTRACT FROM AUTHOR]

The spherical fuzzy set (SFS) is one of the most important concepts to accommodate more uncertainties than the intuitionistic fuzzy set, Pythagorean fuzzy set, picture fuzzy set and hence its applications are more extensive. Keeping the feature and the importance of the SFS, the objective of this paper is to present some robust symmetric operational laws for SFSs. Associated with these laws, we define some series of new aggregation operators named as spherical fuzzy (SF) symmetric weighted averaging, SF ordered weighted averaging and SF hybrid weighted averaging operators to aggregate the SF information. Afterwards, we present a group decision making technique to solve the multi attribute group decision making (MAGDM) based on proposed symmetric aggregation operators and illustrate with a numerical example of renewable energy source selection as a real-life practical example to validate it. A comparative analysis is also conducted to show the superiorities of the proposed method. [ABSTRACT FROM AUTHOR]

The linguistic picture fuzzy set (LPFS) is an extension of the linguistic intuitionistic fuzzy set (LIFS), and can contain more information than the LIFS. In this paper, the degrees of positive, neutral and non-membership of PFSs are expressed in linguistic terms, which can more easily describe the uncertain and vague information existing in the real world. By combining the PFS and the linguistic term, we define the LPFS and propose operational rules for linguistic picture fuzzy numbers (LPFNs). We further propose weighted averaging and weighted geometric operators and discuss their properties. Additionally, we propose an approach to deal with a multiple-attribute group decision-making (MAGDM) problem based on the developed aggregation operators. Finally, we present an illustrative example to demonstrate the effectiveness and advantages of the developed method by comparing it with existing methods. In addition, our method can be utilized not only to solve problems with linguistic intuitionistic fuzzy numbers (LIFNs), but also to deal with problems with LPFNs, and is a generalization of a number of existing methods. [ABSTRACT FROM AUTHOR]

AIMS Mathematics, 2023, 8(3): 5148-5174. doi: 10.3934/math.2023258 2 Muhammad Naeem, Aziz Khan, Shahzaib Ashraf, Saleem Abdullah, Muhammad Ayaz, Nejib Ghanmi. Keywords: Correction EN Correction 1 2 2 05/15/23 20230601 NES 230601 A correction on A novel decision aid approach based on spherical hesitant fuzzy Aczel-Alsina geometric aggregation information by Aziz Khan, Shahzaib Ashraf, Saleem Abdullah, Muhammad Ayaz, Thongchai Botmart. [Extracted from the article]

Kamran, S. Ashraf, N. Salamat, M. Naeem, T. Botmart, Cyber security control selection based decision support algorithm under single valued neutrosophic hesitant fuzzy Einstein aggregation information, AIMS Math., 8 (2023), 5551-5573. https://doi.org/10.3934/math.2023280 doi: 10.3934/math.2023280 Cyber security control selection based decision support algorithm under single valued neutrosophic hesitant fuzzy Einstein aggregation information. [Extracted from the article]

The information aggregation operator plays a key rule in the group decision making problems. The aim of this paper is to investigate the information aggregation operators method under the picture fuzzy environment with the help of Einstein norms operations. The picture fuzzy set is an extended version of the intuitionistic fuzzy set, which not only considers the degree of acceptance or rejection but also takes into the account of neutral degree during the analysis. Under these environments, some basic aggregation operators namely picture fuzzy Einstein weighted and Einstein ordered weighted operators are proposed in this paper. Some properties of these aggregation operators are discussed in detail. Further, a group decision making problem is illustrated and validated through a numerical example. A comparative analysis of the proposed and existing studies is performed to show the validity of the proposed operators. [ABSTRACT FROM AUTHOR]

The primary goal of this paper is to solve the investment problem based on linguistic picture decision making method under the linguistic triangular picture linguistic fuzzy environment. First to define the triangular picture linguistic fuzzy numbers. Further, we define operations on triangular picture linguistic fuzzy numbers and their aggregation operator namely, triangular picture fuzzy linguistic induce OWA (TPFLIOWA) and triangular picture fuzzy linguistic induce OWG (TPFLIOWG) operators. Multi-criteria group decision making method is developed based on TPFLIOWA and TPFLIOWG operators and solve the uncertainty in the investment problem. We study the applicability of the proposed decision making method under triangular picture linguistic fuzzy environment and construct a descriptive example of investment problem. We conclude from the comparison and sensitive analysis that the proposed decision making method is more effective and reliable than other existing models. [ABSTRACT FROM AUTHOR]

The main objective of proposed work is to introduce a series of picture fuzzy weighted geometric aggregation operators by using t-norm and t-conorm. In this paper, we discussed generalized form of weighted geometric aggregation operator for picture fuzzy information. Further, the proposed geometric aggregation operators of picture fuzzy number are applied to multi-attribute group decision making problems. Also, we propose the TOPSIS method to aggregate the picture fuzzy information. To implement the proposed models, we provide some numerical applications of group decision making problems. Also compared with previous model, we conclude that the proposed technique is more effective and reliable. [ABSTRACT FROM AUTHOR]

Spherical fuzzy sets (SFSs) are a new extension of Cuong's picture fuzzy sets (PFSs). In SFSs, membership degrees satisfy the condition 0≤P2(x)+I2(x)+N2(x)≤1 instead of 0≤P(x)+I(x)+N(x)≤1 as is in PFSs. In the present work, we extend different strict archimedean triangular norm and conorm to aggregate spherical fuzzy information. Firstly, we define the SFS and discuss some operational rules. Generalized spherical aggregation operators for spherical fuzzy numbers utilizing these strict Archimedean t‐norm and t‐conorm are proposed. Finally, based on these operators, a decision‐making method has been established for ranking the alternatives by utilizing a spherical fuzzy environment. The suggested technique has been demonstrated with a descriptive example for viewing their effectiveness as well as reliability. A test checking the reliability and validity has also been conducted for viewing the supremacy of the suggested technique. [ABSTRACT FROM AUTHOR]

Emergency decision-making is vital for nations or communities because it increases emergency management's effectiveness and legitimacy, which in turn greatly minimizes environmental damage, fatalities, and economic loss. The evaluation of emergency judgements must take into account significant inaccuracy, fuzzyness, and ambiguity. While high risk and uncertainty are frequently characteristics of emergency decision-making (EDM) circumstances. The current EDM methodologies do not take into account the psychological behavior of the decision makers in addition to the various emergency situations and the various responses. In this paper, we presented a new method based on a Complex Probabilistic Hesitant Fuzzy Soft Set (CPHFSS) as represented by membership in 2-D with hesitant probability. The idea that is being put forth captures the ambiguity and takes into account emergency situations while also taking into account the psychological state of the decision-makers involved in the EDM procedure. The introduction of a new score function for the CPHFSS serves as the second objective of this paper, which is to address a number of comparability issues. We examine a novel family of hybrid operators for CPHFSS that utilize numerous independent variables as a solution to these unforeseen issues. The group decision-making strategy and EDAS technique are then suggested employing these operators. Later, an emergency decision-making situation involving a major fire in China is used to demonstrate the validity of the algorithms. • Concept of complex probabilistic hesitant fuzzy soft set is presented. • Introduce a new score function for the CPHFSS. • Group decision-making strategy and EDAS technique presented. • Emergency decision-making problems discussed in the study. • Case study related to industrial disaster emergency decision-making discuss. [ABSTRACT FROM AUTHOR]

Reference 1 Qiyas M, Abdullah S, Khan S. Multi-attribute group decision making based on sine trigonometric spherical fuzzy aggregation operators. Retraction Note to: Soft Computing (2021) 25:8549-8572 https://doi.org/10.1007/s00500-021-057... The Editors-in-Chief have retracted this article because it is highly similar to a previously published article by Qiyas et al. ([1]). [Extracted from the article]

Spherical fuzzy set (SFS) is one of the most important and extensive concept to accommodate more uncertainties than existing fuzzy set structures. In this article, we will describe a novel enhanced TOPSIS-based procedure for tackling multi attribute group decision making (MAGDM) issues under spherical fuzzy setting, in which the weights of both decision-makers (DMs) and criteria are totally unknown. First, we study the notion of SFSs, the score and accuracy functions of SFSs and their basic operating laws. In addition, defined the generalized distance measure for SFSs based on spherical fuzzy entropy measure to compute the unknown weights information. Secondly, the spherical fuzzy information-based decision-making technique for MAGDM is presented. Lastly, an illustrative example is delivered with robot selection to reveal the efficiency of the proposed spherical fuzzy decision support approach, along with the discussion of comparative results, to prove that their results are feasible and credible. [ABSTRACT FROM AUTHOR]

The aims of this study are to propose the linguistic picture fuzzy Dombi (LPFD) aggregation operators and decision-making approach to deal with uncertainties in the form of linguistic picture fuzzy sets. LPFD operators have more flexibility due to the general fuzzy set. Utilizing the Dombi operational rule, the series of Dombi aggregation operators were proposed, namely linguistic picture fuzzy Dombi arithmetic/geometric, ordered arithmetic/ordered geometric and Hybrid arithmetic/Hybrid geometric aggregation operators. The distinguished feature of these proposed operators is studied. At that point, we have used these Dombi operators to design a model to deal with multiple attribute decision-making (MADM) issues under linguistic picture fuzzy information. Finally, an illustrative example to evaluate the emerging technology enterprises is provided to demonstrate the effectiveness of the proposed approach, together with a sensitivity analysis and comparison analysis, proving that its results are feasible and credible. [ABSTRACT FROM AUTHOR]

Keeping in view the importance of new defined and well growing spherical fuzzy sets, in this study, we proposed a novel method to handle the spherical fuzzy multi-criteria group decision-making (MCGDM) problems. Firstly, we presented some novel logarithmic operations of spherical fuzzy sets (SFSs). Then, we proposed series of novel logarithmic operators, namely spherical fuzzy weighted average operators and spherical fuzzy weighted geometric operators. We proposed the spherical fuzzy entropy to find the unknown weights information of the criteria. We study some of its desirable properties such as idempotency, boundary and monotonicity in detail. Finally, the detailed steps for the spherical fuzzy decision-making problems were developed, and a practical case was given to check the created approach and to illustrate its validity and superiority. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantages of our proposed method. Results indicate that the proposed method is suitable and effective for the decision process to evaluate their best alternative. [ABSTRACT FROM AUTHOR]

The key objective of the proposed work in this paper is to introduce a generalized form of linguistic picture fuzzy set, so-called linguistic spherical fuzzy set (LSFS), combining the notion of linguistic fuzzy set and spherical fuzzy set. In LSFS we deal with the vague and defective information in decision making. LSFS is characterized by linguistic positive, linguistic neutral and linguistic negative membership degree which satisfies the conditions that the square sum of its linguistic membership degrees is less than or equal to 1. In this paper, we investigate the basic operations of linguistic spherical fuzzy sets and discuss some related results. We extend operational laws of aggregation operators and propose linguistic spherical fuzzy weighted averaging and geometric operators based on spherical fuzzy numbers. Further, the proposed aggregation operators of linguistic spherical fuzzy number are applied to multi-attribute group decision-making problems. To implement the proposed models, we provide some numerical applications of group decision-making problems. In addition, compared with the previous model, we conclude that the proposed technique is more effective and reliable. [ABSTRACT FROM AUTHOR]