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In current piece of writing, we bring in the new notion of induced bipolar neutrosophic (BN) AOs by utilizing Einstein operations as the foundation for aggregation operators (AOs), as well as to endow having a real-world problem-related application. The neutrosophic set can rapidly and more efficiently bring out the partial, inconsistent, and ambiguous information. The fundamental definitions and procedures linked to the basic bipolar neutrosophic (BN) set as well as the neutrosophic set (NS), are presented first. Our primary concern is the induced Einstein AOs, like, induced bipolar neutrosophic Einstein weighted average (I-BNEWA), induced bipolar neutrosophic Einstein weighted geometric (I-BNEWG), as well as their different types and required properties. The main advantage of employing the offered methods is that they give decision-makers a more thorough analysis of the problem. These strategies whenever compare to on hand methods, present complete, progressively precise, and accurate result. Finally, utilizing a numerical representation of an example for selection of robot, for a problem involving multi-criteria community decision making, we propose a novel solution. The suitability ratings are then ranked to select the most suitable robot. This demonstrates the practicality as well as usefulness of these novel approaches. [ABSTRACT FROM AUTHOR]

The distribution of emergency shelter materials in emergency cases around the world is a hard task, the goal of this research is to offer a Complex Non-linear Diophantine Fuzzy (C-NLDF) decision-making model for earthquake shelter construction. Essentially, the article is divided into three sections to acquire acceptable and precise measures in emergency decision-making situations. First, we present the Complex Non-Linear Diophantine Fuzzy Set (CN-LDFS), a new generalization of the complex linear Diophantine fuzzy set (CLDFS) and q-linear Diophantine fuzzy set (q-LDFS), as well as explore its key aspects. Furthermore, aggregation operators are useful for aggregating uncertainty in decision-making issues. As a result, algebraic norms for CN-LDFSs are produced based on certain operational laws. In the second section of the work, we offer a series of averaging and geometric aggregation operators under CN-LDFS that are based on defined operating laws. In the final section of the work, under complex Non-linear Diophantine fuzzy information, the ranking algorithms based on suggested aggregation operators are present to address the case study regarding emergency situation of earthquakes. In comparison section, results of existing and proposed operators explore the effectiveness of proposed methodologies and provide accurate emergency measures to address the global uncertainty about the construction of emergency shelters in earthquakes. [ABSTRACT FROM AUTHOR]

Due to the rapid development of machine learning and artificial intelligence (AI), the analysis of AI cloud platforms is now a key area of research. Assessing the wide range of frameworks available and choosing the ideal AI cloud providers that may accommodate the demands and resources of a company is mandatory. There are several options, all having their own benefits and limitations. The evaluation of artificial intelligence cloud platforms is a multiple criteria group decision-making (MCGDM) process. This article establishes a collection of Einstein geometric aggregation operators (AoPs) and a novel Fractional Fuzzy VIKOR and Fractional Fuzzy Extended TOPSIS based on the entropy weight of criteria in fractional fuzzy sets (FFSs) for this scenario. The FFSs provide an evaluation circumstance containing more information, which makes the final decision-making results more accurate. Finally, this framework is then implemented in a computational case study for the evaluation of artificial intelligence cloud platforms and comparison of this model with other existing approaches, such as the extended GRA approach, to check the consistency and accuracy of the proposed technique. The most optimal artificial intelligence cloud platform is I 1 [ABSTRACT FROM AUTHOR]

Deep learning (DL), a branch of machine learning and artificial intelligence, is nowadays considered as a core technology. Due to its ability to learn from data, DL technology originated from artificial neural networks and has become a hot topic in the context of computing, it is widely applied in various application areas. However, building an appropriate DL model is a challenging task, due to the dynamic nature and variations in real-world problems and data. The aim of this work was to develope a new method for appropriate DL model selection using complex spherical fuzzy rough sets (CSFRSs). The connectivity of two or more complex spherical fuzzy rough numbers can be defined by using the Hamacher t-norm and t-conorm. Using the Hamacher operational laws with operational parameters provides exceptional flexibility in dealing with uncertainty in data. We define a series of Hamacher averaging and geometric aggregation operators for CSFRSs, as well as their fundamental properties, based on the Hamacher t-norm and t-conorm. Further we have developed the proposed aggregation operators and provide here a group decision-making approach for solving decision making problems. Finally, a comparative analysis with existing methods is given to demonstrate the peculiarity of our proposed method. [ABSTRACT FROM AUTHOR]

In real life, with the trend of outsourcing logistics activities, choosing a third-party logistics (3PL) provider has become an inevitable choice for shippers. One of the most difficult decisions logistics consumers are facing the selecting the 3PL provider that best meets their needs. Decision making (DM) is an important in dealing with such situations because it allows them to make reliable decisions in a short period of time, as incorrect decisions can result in huge financial losses. In this regard, this article provides a new multi criteria group decision making method (MCGDM) under Pythagorean fuzzy rough (PyFR) set. A series of new PyFR Einstein weighted averaging aggregation operators and their basic aspects are described in depth. To evaluate the weights of decision experts and criteria weights we established the PyFR entropy measure. Further, using multiple aggregation methods based on PyFR information, a novel algorithm is offered to solve issues with ambiguous or insufficient data to obtain reliable and preferable results. First, decision-experts use PyFR sets to represent their evaluation information on alternatives based on the criteria. Then, apply all these proposed PyFR Einstein aggregation lists to rank all alternatives and find the best optimal result. Finally, to demonstrate the feasibility of the proposed PyFR decision system, a real example of choosing a 3PL is given. [ABSTRACT FROM AUTHOR]

Finding the best transportation project and logistic service provider is one for the most important aspects of the development of a country. This task becomes more complicated from time to time as different criteria are involved. Hence, this paper proposes an approach to the linguistic three-way decision-making (TWDs) problem for selecting sustainable transportation investments and logistic service providers with unknown criteria and expert weight information. To this end, we first propose a new tool, the Pythagorean double hierarchy linguistic term sets (PyDHLTSs), which is a combination of first hierarchy linguistic term sets and second hierarchy linguistic term sets which can describe uncertainty and fuzziness more flexibly in decision-making (DM) problems. In addition, we propose some aggregation operators and basic operational laws for PyDHLTSs. A new decision-making technique for PyDHLTSs based on decision-theoretic rough sets (DTRSs) is proposed in the three-way decisions. Next, the conditional probability is computed using grey relational analysis in a PyDHLTSs environment, which improves decision-making. The loss function is computed by using the proposed aggregation operator, and the decision's results are determined by the minimum-loss principle. Finally, a real-world case study of a transportation project and logistic service provider is considered to demonstrate the efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

A neural network is a very useful tool in artificial intelligence (AI) that can also be referred to as an ANN. An artificial neural network (ANN) is a deep learning model that has a broad range of applications in real life. The combination and interrelationship of neurons and nodes with each other facilitate the transmission of information. An ANN has a feed-forward neural network. The neurons are arranged in layers, and each layer performs a particular calculation on the incoming data. Up until the output layer, which generates the network's ultimate output, is reached, each layer's output is transmitted as an input to the subsequent layer. A feed-forward neural network (FFNN) is a method for finding the output of expert information. In this research, we expand upon the concept of fuzzy neural network systems and introduce feed-forward double-hierarchy linguistic neural network systems (FFDHLNNS) using Yager–Dombi aggregation operators. We also discuss the desirable properties of Yager–Dombi aggregation operators. Moreover, we describe double-hierarchy linguistic term sets (DHLTSs) and discuss the score function of DHLTSs and the distance between any two double-hierarchy linguistic term elements (DHLTEs). Here, we discuss different approaches to choosing a novel water purification technique on a commercial scale, as well as some variables influencing these approaches. We apply a feed-forward double-hierarchy linguistic neural network (FFDHLNN) to select the best method for water purification. Moreover, we use the extended version of the Technique for Order Preference by Similarity to Ideal Solution (extended TOPSIS) method and the grey relational analysis (GRA) method for the verification of our suggested approach. Remarkably, both approaches yield almost the same results as those obtained using our proposed method. The proposed models were compared with other existing models of decision support systems, and the comparison demonstrated that the proposed models are feasible and valid decision support systems. The proposed technique is more reliable and accurate for the selection of large-scale water purification methods. [ABSTRACT FROM AUTHOR]

In decision support systems, linguistic fuzzy information played an important role and the linguistic fuzzy aggregation operators (AOs) worked in group decision support systems. Recently, we proposed the linguistic picture fuzzy (LPF) sets, which is the extension of the linguistic intuitionist fuzzy sets, to reflect the ambiguity and vagueness of knowledge in decision-making (DM) problem. The goal of this research work is to define a new family of LPF AOs through the use of Dombi operations and Heronian mean (HM) operator. In addition to fusing individual attribute values, the evolved operators are good ability to handle the common association between the attributes, making them more appropriate to effectively solve difficult multi-attribute DM (MADM) problems. Therefore, we developed an approach for MADM problem based on LPF Dombi HM operators and solved an emergency programme selection problem. The comparison section provides the effectiveness, reliability and practicality. [ABSTRACT FROM AUTHOR]

In fuzzy artificial intelligent decision support systems, three-way intelligent-decision making (TWIDM) has played a very important role in ranking objects under the double hierarchy linguistic variable (DHLV). The 8 × 8 S-boxes are very important for image encryption in secure communication. Therefore, the aim of the present study is to develop a new approach to artificial intelligent three-way decision making via DHLV and apply it to S-box image encryption. Artificial intelligent based three-way decision-making problems with double hierarchy hesitant linguistic terms are developed. The first and second hierarchy hesitant linguistic term sets make up the double hierarchy hesitant linguistic term set, which allows for more flexible expressions of doubt and fuzziness. First, we define the Einstein operational laws, score function, and Einstein aggregation operators; i.e., double hierarchy hesitant linguistic Einstein weighted averaging and weighted geometric operators. First, the unknown weight vector for decision experts is determined by using aggregation operators and entropy measures for DHLV. Then, we find the weight vector for our criteria by using the distance measure. In TWIDM, conditional probability is determined by using the extended TOPSIS method for evaluating the S-boxes for image encryption. The expected losses are then computed by aggregating the loss functions with the help of Einstein-weighted averaging aggregation operators. Finally, we apply the minimum-loss decision rules for the selection of S-box to image encryption. The proposed decision technique has been compared with existing three-way decisions and the result of proposed three-way decision making for analyzing and ranking the S-box is very good and reliable for decision making. [ABSTRACT FROM AUTHOR]

The degree of credibility of the fuzzy assessment value demonstrates its significance and necessity in the fuzzy decision making problem. The fuzzy assessment values should be closely related to their credibility measures in order to increase the credibility levels and degrees of fuzzy assessment values. This will increase the abundance and the credibility of the assessment information. As a new extension of the intuitionistic fuzzy concept, this study suggests the idea of an intuitionistic fuzzy credibility number (IFCN). So, based on Dombi norms, we proposed some new operational laws for intuitionistic fuzzy credibility numbers. Different intuitionistic fuzzy credibility aggregation operators are defined using Dombi t-norm and t-conorm operations. i.e., intuitionistic fuzzy credibility Dombi weighted averaging (IFCDWA), intuitionistic fuzzy credibility Dombi ordered weighted averaging (IFCDOWA), intuitionistic fuzzy credibility Dombi hybrid weighted averaging (IFCDHWA) operators. Next, we defined multiple criteria group decisions (MCGDM) approach. To ensure that their results are reliable and applicable, we also gave an example of railway train selection and discussed comparative result analysis. [ABSTRACT FROM AUTHOR]

In daily life, the decision making problem is a complicated work related to uncertainties and vagueness. To overcome this vagueness and uncertainties, many fuzzy sets and theories have been presented by different scholars and researchers. EDAS (Evaluation based on distance from average solution) method plays a major role in decision-making problems. Especially, when multi-attribute group decision-making (MAGDM) problems have more conflicting attribute. In this paper, a new approach known as Spherical fuzzy rough-EDAS (SFR-EDAS) method is used to handle these uncertainties in the MAGDM problem. The aggregation operators have the ability to combine different sources of information, which plays an essential role in decision making (DM) problem. Keeping in view the increasing complexity of the DM problem, it will be useful to combine the aggregation operators with the fuzzy sets in solving DM problem. Therefore, an aggregation operator known as SFR-EDAS method is utilized. For this propounded some new averaging and geometric aggregation is investigated. Moreover, the essential and desirable properties with some particular cases are deliberated and discussed detail. To evaluate the emergency program, a MAGDM approach is used based on the new introduced operators. Later on, the viability and applicability the proposed method is certified by a detailed analysis with the other existing approaches. [ABSTRACT FROM AUTHOR]

The best mathematical tools for combining numerous inputs into a single result are aggregation operators. The aggregation operators work to combine all of the individual evaluation values provided in a uniform form, and they are very useful for evaluating the options provided in the decision-making process. To provide a larger space for decision makers, complex q -rung orthopair fuzzy rough sets can express their uncertain information. As a generalization of the algebraic operations, the Einstein t -norm and t -conorm, Hamacher operations have become significant in aggregation theory. The Hamacher aggregation operator's major characteristic is that it can capture the interrelationship between several input arguments. In this article, some Hamacher aggregation operators for complex q -rung orthopair fuzzy rough sets are presented. We define a complex q -rung orthopair fuzzy rough Hamacher operation laws and a new score function. In addition, we propose a serious of averaging aggregation operators for complex q -rung orthopair fuzzy rough set. We present the essential properties of these operators. We use the defined operators and modified EDAS (evaluation based on distance from average solution) method to propose an approach for solving a multicriteria decision making problem. To demonstrate the practicality and effectiveness of our propose model, we consider a numerical example of area selection for an arboretum. Finally, a comparison between the suggested approach with existing operators has been presented for authenticity and reliability. [ABSTRACT FROM AUTHOR]

In order to ensure effective hand over management, network selection is very important. The process of selecting a network that offers a reliable and satisfactory service to the end user is known as network selection. Some existing approaches are utilized for network selection, however, they are reactive and can lead to erroneous conclusions due to inadequate information. These methods, however, have drawbacks due to their computational complexity and need for excessive and frequent hand over. Thus, we defined fractional orthotriple fuzzy Rough sets (FOFRSs), that can easily deal with ambiguity and insufficient information. The concepts of fractional orthotriple fuzzy rough Hamacher averaging and geometric operators are also introduced. The fundamental properties of the defined operators are discussed in detail. An algorithm to cope with uncertainty and ambiguity information for a multiple attribute group decision making (MAGDM) problem are proposed. Finally, a numerical example of the real-life is provided. The proposed method is compared to several existing methods, and the results show that the proposed method is more effective and helpful than the others. [ABSTRACT FROM AUTHOR]

Nanomaterials are the most important component of nanosensors, and the selection of the most desirable nanomaterial for nanosensors is a challenge for companies. The classical decision making procedure is very difficult and uncertain to select the desirable nanomaterial. Therefore, we develop a decision making model based on a fuzzy credibility neural network. In this article, we introduce a novel fuzzy credibility neural network using Dombi t-norms and co-norms and also using the score function of fuzzy credibility numbers. Further, the fuzzy credibility neural network applies to the decision making model for the selection of the best nanomaterial for nanosensors. In this approach or decision making model, we first collect data from three experts in the form of fuzzy credibility numbers and then use a neural network to aggregate the data with the help of Dombi t-norm and t-conorm. We consider the expert decision making criteria, which correspond to the input signals of the fuzzy credibility neural network, and calculate the weight of the input signal using distance measure techniques. Next, we compute the hidden layer information and the output layer information by using the fuzzy credibility neural network with the Dombi aggregation operator. The proposed approach is compared with other existing models of decision making and the results of the comparison show that the proposed technique is applicable and reliable for the decision support model. [ABSTRACT FROM AUTHOR]

In daily life, decision-making (DM) problem is a complicated work related to uncertainties and vagueness. To overcome these imprecisions, many fuzzy sets and theories have been presented by different scholars. Probabilistic models are the communal models proposed for the management of uncertainties. On the other hand, if these uncertainties are not probabilistic in nature, then other models such as fuzzy linguistic and fuzzy logic are developed. Here, a new approach known as the complex Pythagorean fuzzy Maclaurin symmetric mean (CPFMSM) operator is used to handle these uncertainties in DM issues. This complex Pythagorean fuzzy set (CPFS) is a modified form of the Pythagorean fuzzy set (PFS) and of the complex intuitionistic fuzzy set (CIFS). The aggregation operators have the ability to combine different sources of information. Therefore, an aggregation operator known as the MSM operator is utilized under the complex Pythagorean fuzzy (CPF) environment to extend the theory and applications of traditional MSM. For this purpose, we devised new operators known as CPFMSM and CPF dual Maclaurin symmetric mean (CPFDMSM) to aggregate CPF data. To evaluate an emergency program, the MAGDM approach is used, which is based on the newly introduced operators. Furthermore, the viability and applicability of the propounded method are certified by a detailed analysis with the other approaches researched in the past. [ABSTRACT FROM AUTHOR]

The operational law plays an important role in the aggregation operator for group decision system. The aggregation information has high influence in aggregating group decision information. Therefore, the main objective of the proposed work is to develop some operational laws as aggregation operator for fuzzy credibility numbers based on Dombi norms. Dombi operations can benefit from the best operational parameter flexibility. To the best of our knowledge, Dombi operations have so far not been used in for fuzzy credibility numbers (FCNs). Using these Dombi t-norm and t-conorm to define some different fuzzy credibility aggregation operators. i.e., fuzzy credibility Dombi weighted averaging (FCDWA) operator, fuzzy credibility Dombi ordered weighted averaging (FCDOWA) operator, fuzzy credibility Dombi hybrid weighted averaging (FCDHWA) operator. Next, we used TOPSIS method procedure for multi-attribute grouped decision-making (MAGDM). Finally, we provided an example, as well as a discussion of the comparative result analysis, to ensure that their findings are credible and practical. [ABSTRACT FROM AUTHOR]

In this article, we introduce bipolar neutrosophic (BN) aggregation operators (AOs) as a revolutionary notion in aggregation operators (AOs) by applying Einstein operations to bipolar neutrosophic aggregation operators (AOs), with its application related to a real-life problem. The neutrosophic set is able to drawout the incomplete, inconsistent and indeterminate information pretty efficiently. Initially, we present essential definitions along with operations correlated to the neutrosophic set (NS) and its generalization, the bipolar neutrosophic set (BNS). The Einstein aggregation operators are our primary targets, such asthe BN Einstein weighted average (BNEWA), BN Einstein ordered weighted average (BNEOWA), BN Einstein hybrid average (BNEHA), BN Einstein weighted geometric (BNEWG), BN Einstein ordered weighted geometric (BNEOWG) and BN Einstein hybrid geometric (BNEHG), as well as their required properties. The most important benefit of using the suggested approaches is that they provide decision-makers with complete sight of the issue. These techniques, when compared to other methods, provide complete, progressive and precise findings. Lastly, by means of diverse types of newly introduced aggregation operators and a numerical illustration by an example, we suggest an innovative method to be used for multi-criteria community decision-making (DM). This illustrates the utility and applicability of this new strategy when facing real-world problems. [ABSTRACT FROM AUTHOR]

Due to the vagueness and uncertainty of human cognition/judgments as related to complicated decision-making problems, existing fuzzy decision-making approaches merely signal fuzzy assessment values and lack degrees/levels of credibility for the fuzzy assessment values in alternatives over attributes. As a result, the fuzzy evaluative value’s credibility degree highlights its significance and importance in the fuzzy decision-making problem. To improve the degrees/levels of credibility of fuzzy evaluation values, the fuzzy assessment values should be tightly linked to their credibility measures, which would result in more abundant and reliable assessment information. The major goal of this research was to describe new procedures for credible fuzzy numbers based on the Dombi t-norm and Dombi t-conorm. Dombi operations can benefit from the operational parameter’s best tractability. These operations are more generalized for credibility fuzzy numbers. Furthermore, using the basic operational laws of Dombi t-norm and Dombi t-conorm, we develop a series of fuzzy credibility Dombi aggregation operators, like the fuzzy credibility Dombi geometric aggregation operator, fuzzy credibility Dombi ordered geometric aggregation operator and fuzzy credibility Dombi hybrid geometric aggregation operator. To handle this sort of decision-making problem, an extended TOPSIS (technique for order of preference by similarity to ideal solution) is proposed. Finally, we present an example, along with a discussion of the comparative results to check the accuracy and validation of the proposed methods, to confirm that their results are credible and feasible. [ABSTRACT FROM AUTHOR]

The goal of the present research work is to develop a new family of aggregation operators (AOs) under the fractional orthotriple fuzzy (FOF) information and apply them to MCDM problems. At the start, the Archimedean coupla and co-coupla are extended to handle FOF information, and some operational law for fractional orthotriple fuzzy numbers (FOFNs) based on extended Archimedean copula (EAC) and extended Archimedean co-copula (EACC) is presented. The fractional orthotriple fuzzy Banzhaf Choquet-Copula aggregation operator and fractional orthotriple fuzzy Banzhaf Choquet-Copula geometric operators are defined based on the proposed operational laws of FOFNs. In addition, the modified maximum deviation approach and the Banzhaf function model are created to objectively determine the fuzzy measure (FM) of criteria sets. Finally, based on the defined AOs, the appropriate decision-making procedures are developed. The proposed approaches can effectively overcome the FMs of criteria sets that are subjectively assigned by decision makers, as well as some decision-making problems in which the weights of the criteria are incomplete (completely) unknown, and there is a correlation between all criteria set. [ABSTRACT FROM AUTHOR]

In this manuscript, we give the idea of Spherical 2-tuple linguistic fuzzy set (S2TLFS) for the multi criteria decision making (MCDM) problem with the information. We utilized some operation to define some Spherical 2-tuple linguistic fuzzy (S2TLF) aggregation operators (AOs). We discussed some properties of the developed operators. Then, to solve an MCDM problem using the Spherical 2-tuple linguistic information, we proposed an approach, and utilized these operators. Lastly, a numerical example of the green supplier selection for chemical processing industry is given to show the advantage of the defined approach and to show its practicability and performance. [ABSTRACT FROM AUTHOR]

The objectives of this paper are to define novel aggregation operators (AOs) for aggregating different complex spherical fuzzy numbers (CSFNs) under the influence of their membership grades. The uncertainties included in the information are dealt with in contemporary studies of the fuzzy set and its extensions by membership grades, which are a subset of real numbers that lose some relevant information and hence alter the decision results. The conversion to these complex spherical fuzzy sets addresses the classes' uncertainty, whose ranges differ from the specific subset of the complex subset of the unit disk. For this purpose, we defined new CSF power AOs. Some of the desirable properties of these operators have also been investigated. A multiattribute group decision-making (MAGDM) approach is implemented in the structure developed by the CSFNs on the basis of these operators. A numerical example concerning the selection of the best alternatives is given to demonstrate the effectiveness of the defined method and is tested by comparing its results with the various methods. [ABSTRACT FROM AUTHOR]

The triangular linguistic cubic fuzzy sets (TLCFSs) can express the fuzzy data easily and is also very useful in modeling of uncertain data in decision making (DM) problems. First of all, on the basis of Dombi t-norm and t-conorm (DTT), we propose novel operational rules of triangular linguistic cubic fuzzy numbers (TLCFNs). We propose some new aggregation operators of TLCFNs based on the newly developed operations, i.e., triangular linguistic cubic fuzzy Dombi weighted averaging (TLCFDWA), triangular linguistic cubic fuzzy Dombi weighted geometric (TLCFDWG), triangular linguistic cubic fuzzy Dombi order weighted averaging (TLCFDOWA), triangular linguistic cubic fuzzy Dombi order weighted geometric (TLCFDOWG), triangular linguistic cubic fuzzy Dombi hybrid weighted averaging (TLCFDHWA), and triangular linguistic cubic fuzzy Dombi hybrid weighted geometric (TLCFDHWG) operators. Furthermore, a new method is proposed with the help of the proposed operators to solve the decision making problem. Finally, a numerical example is provided to illustrate the effectiveness of the new method. Comparative analysis is used to demonstrate the proposed method's superiority. [ABSTRACT FROM AUTHOR]

Industrial control system (ICS) attacks are usually targeted attacks that use the ICS entry approach to get a foothold within a system and move laterally throughout the organization. In recent decades, powerful attacks such as Stuxnet, Duqu, Flame, and Havex have served as wake-up calls for industrial units. All organizations are faced with the rise of security challenges in technological innovations. This paper aims to develop aggregation operators that can be used to address the decision-making problems based on a spherical fuzzy rough environment. Meanwhile, some interesting properties of idempotence, boundedness, and monotonicity for the proposed operators are analyzed. Moreover, we use this newly constructed framework to select ICS security suppliers and validate its acceptability. Furthermore, a different test has been performed based on a new operator to strengthen the suggested approach. Additionally, comparative analysis based on the novel extended TOPSIS method is presented to demonstrate the superiority of the proposed technique. The results show that the conventional approach has a larger area for information representation, better adaptability to the evaluation environment, and higher reliability of the evaluation results. [ABSTRACT FROM AUTHOR]

With the frequent occurrences of emergency events, emergency decision making (EDM) plays an increasingly significant role in coping with such situations and has become an important and challenging research area in recent times. It is essential for decisionmakers tomake reliable and reasonable emergency decisions within a short span of time, since inappropriate decisions may result in enormous economic losses and social disorder. To handle emergency effectively and quickly, this paper proposes a new EDM method based on the novel concept of q-rung orthopair fuzzy rough (q-ROPR) set. A novel list of q-ROFR aggregation information, detailed description of the fundamental characteristics of the developed aggregation operators and the q-ROFR entropy measure that determine the unknown weight information of decision makers as well as the criteria weights are specified. Further an algorithmis given to tackle the uncertain scenario in emergency to give reliable and reasonable emergency decisions. By using proposed list of q-ROFR aggregation information all emergency alternatives are ranked to get the optimal one. Besides this, the q-ROFR entropy measure method is used to determine criteria and experts' weights objectively in the EDMprocess. Finally, through an illustrative example of COVID-19 analysis is compared with existingEDM methods. The results verify the effectiveness and practicability of the proposed methodology. [ABSTRACT FROM AUTHOR]

Spherical fuzzy set (SFS) as one of several non-standard fuzzy sets, it introduces a number triplet (a,b,c) that satisfies the requirement a² + b² þ c² ≤ 1 to express membership grades. Due to the expression, SFS has a more extensive description space when describing fuzzy information, which attracts more attention in scientific research and engineering practice. Just for this reason, how to describe the fuzzy information more reasonably and perfectly is the hot that scholars pay close attention to. In view of this hot, in this paper, the notion of spherical hesitant fuzzy set is introduced as a generalization of spherical fuzzy sets. Some basic operations using sine trigonometric function are presented for spherical hesitant fuzzy sets. We define spherical hesitant fuzzy weighted average and spherical hesitant fuzzy weighted geometric aggregation operators. Based on these new aggregation operators, we propose a method for multi-criteria decision making (MCDM) in the spherical hesitant fuzzy information. Besides, a numerical real-life application about solid waste collection system selection is provided to demonstrate the validity of the proposed approaches along with relevant discussions, the merits of proposed approaches are also analyzed by validity test. [ABSTRACT FROM AUTHOR]

The emergency response to the health care management in the hospital do not have enough systems for providing medical service to the COVID19 patients (e.g., scheduled or nonemergency). Therefore, in this paper, we developed an emergency decision support model for consideration of patients care and admission scheduling (PCAS). The complex decision support model assigns a set of patients into a number of restricted resources like rooms, time slots, and beds depending on satisfying a number of predefined constraints such as disease severity, waiting time, and disease types. This is a crucial issue with multi‐criteria decision making (MCDM). In this paper, we first begin an assessment into the admission and care to tackle this issue and collect four factors effecting the admission and care of COVID‐19 patients that form a system of criteria. While there is a lot of vague and uncertain data that can be effectively depicted for these indicators by the spherical hesitant fuzzy set, then, we implement a strong MCDM method based on list of aggregation operators to address the patients' hospital admission and care. Last of all, a numerical real‐life application about PCAS is provided to demonstrate the validity of the proposed approaches along with relevant discussions, the merits of proposed approaches are also analyzed by validity test. The proposed methodology has been shown to help hospitals manage the admissions and care of COVID‐19 patients in a flexible manner. [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]

In multiattribute group decision‐making (MAGDM), experts often articulate their preference information to support decision‐making by applying the multigranular linguistic model. Thus, the present work aims to introduce a novel MAGDM model to manage multigranular generalized orthopair 2‐tuple linguistic information (GO2TLI). To begin with, a generalized orthopair 2‐tuple linguistic model is put forward with the attempt of taking advantages of both q‐rung orthopair fuzzy set (q‐ROFS) and the 2‐tuple linguistic model, while a transformation approach is supplied to tackle the consistency of multigranular GO2TLI. In addition, the Archimedean Copula as well as the Co‐Copula operators are extended to handle GO2TLI along with their operational laws, to comprehensively model the relationship among attributes and experts. The Banzhaf Choquet‐Copula aggregation operators on the generalized orthopair 2‐tuple linguistic (GO2TLBCCA) are introduced, also some of its properties discussed. Third, the algorithms for regulating and determining the fuzzy measure (FM) of attributes and experts sets are proposed, followed by the corresponding decision‐making approaches based upon the proposed GO2TLBCCA. The proposed MAGDM model can not only accommodate effectively the FMs of attribute (and expert) sets which are given subjectively, but also effectively address some multigranular GO2TLI as well as the partially unknown or completely unknown weights of attribute and expert sets. Finally, a case study is provided to demonstrate the validity of the proposed approach along with relevant discussions, the merits of the proposed approach are also analyzed by comparing with some extant decision methods. [ABSTRACT FROM AUTHOR]

The basic ideas of rough sets and intuitionistic fuzzy sets (IFSs) are precise statistical instruments that can handle vague knowledge easily. The EDAS (evaluation based on distance from average solution) approach plays an important role in decision-making issues, particularly when multicriteria group decision-making (MCGDM) issues have more competing criteria. The purpose of this paper is to introduce the intuitionistic fuzzy rough Frank EDAS (IFRF-EDAS) methodology based on IF rough averaging and geometric aggregation operators. We proposed various aggregation operators such as IF rough Frank weighted averaging (IFRFWA), IF rough Frank ordered weighted averaging (IFRFOWA), IF rough Frank hybrid averaging (IFRFHA), IF rough Frank weighted geometric (IFRFWG), IF rough Frank ordered weighted geometric (IFRFOWG), and IF rough Frank hybrid geometric (IFRFHG) on the basis of Frank t-norm and Frank t-conorm. Information is given for the basic favorable features of the analyzed operator. For the suggested operators, a new score and precision functions are described. Then, using the suggested method, the IFRF-EDAS method for MCGDM and its stepwise methodology are shown. After this, a numerical example is given for the established model, and a comparative analysis is generally articulated for the investigated models with some previous techniques, showing that the investigated models are much more efficient and useful than the previous techniques. [ABSTRACT FROM AUTHOR]

In this study, we highlight the errors in Sections 2.3, 2.4, 3, and 4 in the article by Fahmi et al. (J Ambient Intell Human Comput (2020). https://doi.org/10.1007/s12652-020-02272-9) by counter definitions and theorems. We find that the definition of cubic Pythagorean fuzzy set (CPFS) (Definition 2.3.1) and operational laws (Definition 2.3.2) violates the rules to consider the membership and nonmembership functions, and then, we redefined the corrected definition and their operations for CPFS. Furthermore, we redefine the concept of cubic Pythagorean linguistic fuzzy set (CPLFS) and their basic operational laws. In addition, we find that Sections 3 and 4 (consist of a list of Maclaurin symmetric mean (MSM) and dual MSM aggregation operators) are invalid, and then, we redefined the list of updated MSM and dual MSM aggregation operators in correct way. Finally, we established the numerical application of the proposed improved algorithm using cubic Pythagorean linguistic fuzzy information to show the applicability and effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

Robotization is necessary to keep up with the constant changes in production, which calls for a staff with robotics expertise. A manufacturing business must also have the ability to swiftly change its production method. But today the procedure is drawn-out and complicated. In this study, inverse kinematics functionality and a machine learning model have been used to simulate an industrial robot's movement in a digital environment. By using machine learning, less time and money must be invested in developing the procedure and determining the robot's route. In this article, feed-forward double hierarchy linguistic neural networks with estimation information for double hierarchy linguistic term sets are proposed. First defined were the Yager operational rules and Yager aggregation operators for the double hierarchy linguistic terms set. Following that, we'll discuss fuzzy neurons, feed-forward neural networks, simple neural networks, hybrid neural networks, and the sigmoid function. After that, explain feed-forward, double-hierarchy linguistic neural networks, including how their output is calculated. The weight vector of expert's information is calculated by using the entropy measure with the help of Yager aggregation operators. Finally, we use the Yager t-norms to determine the output date of feed-forward double hierarchy linguistic neural networks and also find the output data. Linguistic neural network with Yager T-norms apply to the Robot selection for manufacturing bussing. The proposed approach of linguistic neural network are compared with Extended TOPSIS methods and GRA method for ranking. [ABSTRACT FROM AUTHOR]

With respect to multiple criteria group decision-making (MCGDM) problems in which both the criteria weights and the expert weights take the form of crisp numbers and attribute values take the form of interval-valued picture fuzzy uncertain linguistic numbers, some new group decision-making analysis methods are developed. Firstly, some operational laws, expected value, and accuracy function of interval-valued picture fuzzy uncertain linguistic numbers are introduced. Then, an interval-valued picture fuzzy uncertain linguistic averaging and geometric aggregation operators are developed. Furthermore, some desirable properties of the developed operators, such as commutativity, idempotency, and monotonicity, have been studied. Based on these operators, an approach to multiple criteria group decision-making with interval-valued picture fuzzy uncertain linguistic information has been proposed. Finally, a practical example of 3PL supplier selection in logistics service value concretion is taken to test the defined method and to expose the effectiveness of the defined model. [ABSTRACT FROM AUTHOR]

Interval-valued picture fuzzy linguistic variable concept is introduced in this article, in which we consider principal component and proposed a generalized interval-valued picture fuzzy linguistic induced hybrid aggregation (GIVPLIHA) operator with entropic order-inducing variable and TOPSIS method. Then, we discussed some basic properties of the GIVPLIHA operator. We also discussed an algorithm for linguistic group decision-making based on GIVPLIHA operator and TOPSIS technique. To prove the validity and applicability of the developed method, finally, we solved a decision-making problem of a company to make a policy for the selection of the best investment strategy. 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 fuzzy aggregation information plays an important role in the group decision support system under the interval-valued hesitant fuzzy information and interval-valued probabilistic hesitant fuzzy information. Therefore, in this paper, we develop a new approach of the interval-valued hesitant fuzzy Frank aggregation (IVHFFA) and interval-valued probabilistic hesitant fuzzy aggregation (IVPHFFA) operators. First, we define some operational laws of IVHEs and IVPHFEs by using Frank t-norm and t-conorm. Furthermore, we develop a series of IVHFFA and IVPHFFA operators based on these operational laws under the IVHF and IVPHF information. Also, discuss some fundamental properties and relations of the proposed aggregation operators for IVHF and IVPHF information. In order to implement the proposed aggregation operators of IVHF and IVPHF information in group decision-making problem, we construct general algorithms for multi-attribute group decision-making problem based on the proposed IVHFFA and IVPHFFA. Finally, from the comparative and sensitivity analysis, the proposed fuzzy decision-making model is more effective and reliable as compared with existing method. [ABSTRACT FROM AUTHOR]

Significant emergency measures should be taken until an emergency event occurs. It is understood that the emergency is characterized by limited time and information, harmfulness and uncertainty, and decision‐makers are always critically bound by uncertainty and risk. This paper introduces many novel approaches to addressing the emergency situation of COVID‐19 under spherical fuzzy environment. Fundamentally, the paper includes six main sections to achieve appropriate and accurate measures to address the situation of emergency decision‐making. As the spherical fuzzy set (FS) is a generalized framework of fuzzy structure to handle more uncertainty and ambiguity in decision‐making problems (DMPs). First, we discuss basic algebraic operational laws (AOLs) under spherical FS. In addition, elaborate on the deficiency of existing AOLs and present three cases to address the validity of the proposed novel AOLs under spherical fuzzy settings. Second, we present a list of Einstein aggregation operators (AgOp) based on the Einstein norm to aggregate uncertain information in DMPs. Thirdly, we are introducing two techniques to demonstrate the unknown weight of the criteria. Fourthly, we develop extended TOPSIS and Gray relational analysis approaches based on AgOp with unknown weight information of the criteria. In fifth, we design three algorithms to address the uncertainty and ambiguity information in emergency DMPs. Finally, the numerical case study of the novel carnivorous (COVID‐19) situation is provided as an application for emergency decision‐making based on the proposed three algorithms. Results explore the effectiveness of our proposed methodologies and provide accurate emergency measures to address the global uncertainty of COVID‐19. [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]

In this paper, we define aggregation operators for trapezoidal cubic linguistic fuzzy sets which includes generalized cubic linguistic fuzzy averaging (geometric) operator, generalized trapezoidal cubic linguistic fuzzy weighted averaging (GTrCLFWA) operator, generalized trapezoidal cubic linguistic fuzzy weighted geometric (GTrCFWG) operator, generalized trapezoidal cubic linguistic fuzzy ordered weighted average (GTrCLFOWA) operator, generalized trapezoidal cubic linguistic fuzzy ordered weighted geometric (GTrCLFOWG) operator, generalized trapezoidal cubic linguistic fuzzy hybrid averaging (GTrCLFHA) operator and generalized trapezoidal cubic linguistic fuzzy hybrid geometric (GTrCLFHG) operator. Furthermore, we relate these aggregation operators to develop an approach to multiple attribute group decision-making with trapezoidal cubic linguistic fuzzy information. Finally, a numerical example is providing to demonstrate the submission of the established approach. [ABSTRACT FROM AUTHOR]

Trapezoidal cubic fuzzy numbers (TzCFNs) are an extraordinary cubic fuzzy set on a real number set. TzCFNs are useful for dealing with well-known quantities in decision data and decision making problems themselves. This paper is about multi-attribute group decision making problems in which the attribute values are stated with TzCFNs, which are solved by developing a new decision method based on power average operators of TzCFNs. The new operation laws for TzCFNs are given. Hereby, the power average operator of real numbers is extended to four kinds of power average operators of TzCFNs, involving the power average operator of TzCFNs, the weighted power average operator of TzCFNs, the power ordered weighted average operator of TzCFNs, and the power hybrid average operator of TzCFNs. In the proposed group decision method, the individual overall evaluation values of alternatives are generated by using the power average operator of TzCFNs. Applying the hybrid average operator of TzCFNs, the specific general evaluation standards of alternatives are then combined into the collective ones, which are used to rank the alternatives. The example analysis shows the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy set is one of the successful extensions of the intuitionistic fuzzy set for handling uncertainties in information. Under this environment, in this paper, we introduce the notion of Pythagorean fuzzy Einstein hybrid averaging (PFEHA) aggregation operator along with some of its properties, namely idempotency, boundedness, and monotonicity. PFEHA aggregation operator is the generalization of Pythagorean fuzzy Einstein weighted averaging aggregation operator and Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. The operator proposed in this paper provides more accurate and precise results as compared to the existing operators. Therefore, this method plays a vital role in real-world problems. Finally, we applied the proposed operator and method to multiple-attribute group decision making. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of the Pythagorean hesitant fuzzy set (PHFS), which is the generalization of the intuitionistic hesitant fuzzy set under the restriction that the square sum of its membership degrees is ≤1. In decision making with PHFSs, aggregation operators play a key role because they can be used to synthesize multidimensional evaluation values represented as Pythagorean hesitant fuzzy values into collective values. Under PHFS environments, Pythagorean hesitant fuzzy ordered weighted averaging and Pythagorean fuzzy ordered weighted geometric operators are used to aggregate the Pythagorean hesitant fuzzy values. The main advantage of these operators is that they provide more accurate and valuable results. Furthermore, these operators are applied to decision-making problems in which experts provide their preferences in the Pythagorean hesitant fuzzy environment to show the validity, practicality, and effectiveness of the new approach. Finally, we compare the proposed approach to the existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of Einstein aggregation operators, such as the interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operator and the interval-valued Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. We also discuss some desirable properties, such as idempotency, boundedness, commutativity, and monotonicity. The main advantage of using the proposed operators is that these operators give a more complete view of the problem to the decision makers. These operators provide more accurate and precise results as compared the existing method. Finally, we apply these operators to deal with multiple-attribute group decision making under interval-valued Pythagorean fuzzy information. For this, we construct an algorithm for multiple-attribute group decision making. Lastly, we also construct a numerical example for multiple-attribute group decision making. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose the 2-tuple spherical fuzzy linguistic aggregation operators and a decision-making approach to deal with uncertainties in the form of 2-tuple spherical fuzzy linguistic sets. 2-tuple spherical fuzzy linguistic operators have more flexibility than general fuzzy set. We proposed a numbers of aggregation operators, namely 2-tuple spherical fuzzy linguistic weighted average, 2-tuple spherical fuzzy linguistic ordered weighted average, 2-tuple spherical fuzzy linguistic hybrid average, 2-tuple spherical fuzzy linguistic weighted geometric, 2-tuple spherical fuzzy linguistic ordered geometric, and 2-tuple spherical fuzzy linguistic hybrid geometric operators. The distinguishing feature of these proposed operators is studied. At that point, we have used these operators to design a model to deal with multiple attribute decision-making issues under the 2-tuple spherical fuzzy linguistic information. Then, a practical application for best company selection for feeds is given to prove the introduced technique and to show its practicability and effectiveness. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantage of our method. Results indicate that the proposed method is suitable and effective for decision making problems. [ABSTRACT FROM AUTHOR]

The harmful waste products, beverages, chemical agents that are discharged or emitted by industrial processes are categorized as industrial waste (IW). IW is one of the most severe problems facing governments around the world due to its environmental effect and severity. So the aim of this paper is to develop a method for selecting industrial waste management technique (IWMT) for industry. Dombi Norms were commonly referred to as Dombi operations, but their applications might be better expressed if they are presented with a new level of flexibility within the general parameter. Dombi operations have not yet been applied in non-linear Diophantine fuzzy sets (N-LDFSs) in a suitable form. Therefore we apply the Dombi operators on complex N-LDFS (CN-LDFS) and develop a generalized area of research in decision making problems (DMPs). The majority of decision-making challenges in the actual world contain a wide range of elements that must be taken into account. Making decision under such circumstances can frequently be challenging. To deal with such complicated issues, we require multi-attribute group decision-making (MAGDM) techniques. The aims to discuss MAGDM issues, this paper will introduce a new COmbinative Distance-based ASsessment (CODAS) methodology. In this paper, we put forward three novel aggregation operators (AOs): complex non-linear Diophantine fuzzy Dombi weighted averaging (CN-LDFDWA), complex non-linear Diophantine fuzzy Dombi order weighted averaging (CN-LDFDOWA), and complex non-linear Diophantine fuzzy Dombi hybrid weighted averaging (CN-LDFDHWA). These operators are used in the operational parameter to help a successful solution of the problem. Due to the growing energy and material shortages, as well as to comply with environmental laws and regulations and to take advantage of disposal economics in the current context, industrial waste (IW) should be taken into consideration as one of the potential resources in the steel industry. Further, the proposed decision support model applied to solve a case study regarding to IWMT for Pakistan steel mill corporation (PSMC) under complex N-LDF Dombi operators. The proposed method is more effective and reliable for decision making (DM) model, as compared to the existing method. • We developed aggregation operators (AOs) for CN-LDF Dombi Norms to solve MAGDM issue. • We developed CN-LDFDWA AOs based on CODAS method with all unknown information. • An example regarding to the selection of best IW technique for PSMC is provided. • Comparison provided the feasibility of our work and results are discussed based on ranking. [ABSTRACT FROM AUTHOR]

The concept of interval-valued Pythagorean fuzzy (IVPF) sets is capable of handling imprecise and ambiguous information and managing complex uncertainty in real-world applications. The focus of our this paper is to introduce some generalized operators, such as the generalized interval-valued Pythagorean fuzzy Einstein weighted averaging (abbreviated as GIVPFEWA) operator, the generalized interval-valued Pythagorean fuzzy Einstein ordered weighted averaging (abbreviated as GIVPFEOWA) operator, and the generalized interval-valued Pythagorean fuzzy Einstein hybrid averaging (abbreviated as GIVPFEHA) operator along with their some general properties, such as idempotency, commutativity, monotonicity and boundedness. Furthermore, the method for multiple attribute group decision making problems based on these operators was developed, and the operational processes were illustrated in detail. The main advantage of using the proposed methods and operators is that these operators and methods give a more complete view of the problem to the decision makers. These methods provide more general, more accurate and precise results as compared to the existing methods. Therefore these methods play a vital role in real world problems. Finally the proposed operators have been applied to decision-making problems to show the validity, practicality and effectiveness of the new approach. A systematic comparison between the existing work and the proposed work also has been given. [ABSTRACT FROM AUTHOR]

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]