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Due to the complexity and uncertainty of decision-making, probabilistic linguistic term sets (PLTSs) are currently important tools for qualitative evaluation of decision-makers. The asymmetry of evaluation information can easily lead to the loss of subjective preference information for decision-makers, and the existing operation of decision-maker evaluation information fusion operators is difficult to solve this problem. To solve such problems, this paper proposes some new operational methods for PLTSs based on Dombi T-conorm and T-norm. Considering the interrelationships between the input independent variables of PLTSs, the probabilistic linguistic weighted Dombi Bonferroni mean Power average (PLWDBMPA) operators are extended and the properties of these aggregation operators are proposed. Secondly, the PLWDBMPA operator is used to fuse the evaluation information of decision-makers, avoiding the loss of decision information as much as possible. This paper uses social media platforms and web crawler technology to obtain online comments from users on decision-making to obtain the public's attitude towards decision events. TF-IDF and Word2Vec are used to calculate the weight of alternatives on each attribute. Under traditional group decision-making methods and integrating the wisdom of the public, a novel multi-attribute group decision-making method based on TODIM method is proposed. Finally, the case study of Turkey earthquake shelter selection proves this method is scientific and effective. Meanwhile, the superiority of this method was further verified through comparisons with the PL-TOPSIS, PLWA, SPOTIS and PROMETHEE method. [ABSTRACT FROM AUTHOR]

Circular q-rung orthopair fuzzy sets (FSs) were recently considered as an extension of q-rung orthopair FSs (q-ROFSs), circular intuitionistic FSs (Cir-IFSs), and circular Pythagorean FSs (Cir-PFSs). However, they are only considered for some simple algebraic properties. In this paper, we advance the work on circular q-ROFSs (Cirq-ROFSs) in Dombi aggregation operators (AOs) with more mathematical properties of algebraic laws. These include the circular q-rung orthopair fuzzy (Cirq-ROF) Dombi weighted averaging (Cirq-ROFDWA), Cirq-ROF Dombi ordered weighted averaging (Cirq-ROFDOWA), Cirq-ROF Dombi weighted geometric (Cirq-ROFDWG), and Cirq-ROF Dombi ordered weighted geometric (Cirq-ROFDOWG) operators. Additionally, we present the properties of idempotency, monotonicity, and boundedness for the proposed operators. In the context of artificial intelligence, symmetry analysis plays a significant and efficient role that can refer to several aspects. Thus, to compute the major aspect, we identify the multi-attribute decision-making (MADM) technique based on the proposed operators for Cirq-ROF numbers (Cirq-ROFNs) to enhance the worth of the evaluated operators. Finally, we use some existing techniques for comparison to our results to show the validity and supremacy of the proposed method. [ABSTRACT FROM AUTHOR]

The q-rung orthopair fuzzy (q-ROF) set is an efficient tool for dealing with uncertain and inaccurate data in real-world multi-attribute decision-making (MADM). In MADM, aggregation operators play a significant role. The majority of well-known aggregation operators are formed using algebraic, Einstein, Hamacher, Frank, and Yager t-conorms and t-norms. These existing t-conorms and t-norms are some special cases of Archimedean t-conorms (ATCNs) and Archimedean t-norms (ATNs). Therefore, this article aims to extend the ATCN and ATN operations under the q-ROF environment. In this paper, firstly, we present some new operations for q-ROF sets based on ATCN and ATN. After that, we explore a few desirable characteristics of the suggested operational laws. Then, using these operational laws, we develop q-ROF Archimedean weighted averaging (geometric) operators, q-ROF Archimedean order weighted averaging (geometric) operators, and q-ROF Archimedean hybrid averaging (geometric) operators. Next, we develop a model based on the proposed aggregation operators to handle MADM issues. Finally, we elaborate on a numerical problem about site selection for software operating units to highlight the adaptability and dependability of the developed model. [ABSTRACT FROM AUTHOR]

The Complex Pythagorean fuzzy set (CPyFS) is an efficient tool to handle two-dimensional periodic uncertain information, which has various applications in fuzzy modeling and decision making. It is known that the aggregation operators influence decision-making processes. Algebraic aggregation operators are the important and widely used operators in decision making techniques that deal with uncertain problems. This paper investigates some complex Pythagorean fuzzy geometric aggregation operators, such as complex Pythagorean fuzzy weighted geometric (CPyFWG), complex Pythagorean fuzzy ordered weighted geometric (CPyFOWG), complex Pythagorean fuzzy hybrid geometric (CPyFHG), induced complex Pythagorean fuzzy ordered weighted geometric (I-CPyFOWG), and induced complex Pythagorean fuzzy hybrid geometric (I-CPyFHG), and their structure properties, such as idempotency, boundedness, and monotonicity. In addition, we compare the proposed model with their existing models, such as complex fuzzy set and complex intuitionistic fuzzy set. We analyze an example involving the selection of an acceptable location for hospitals in order to demonstrate the effectiveness, appropriateness, and efficiency of the novel aggregation operators. [ABSTRACT FROM AUTHOR]

Scientific progression has allowed researchers to develop novel and innovative ways to deal with uncertainty in data, allowing for the development of more precise and accurate data representation models. This paper aims to extend an already reported concept of Cubic Pythagorean fuzzy set to Cubic Pythagorean Fuzzy Soft Set (C P F S s) as it incorporates both interval-valued Pythagorean fuzzy sets (IVPFS) and Pythagorean fuzzy sets (PFS) at the same time, providing a more targeted approach to deal with uncertainty. This hybrid structure can better handle data in comparison to the ones in the literature by having the characteristics of PFS and soft sets, leading to a more targeted approach to handle attributes in decision-making studies. In this study, we defined various internals and externals of C P F S s , set operators, aggregation operators, and developed an algorithm based on distance measures for ( C P F S s ), which are applied in a disease diagnostic decision-making problem. [ABSTRACT FROM AUTHOR]

In multi-attribute group decision-making (MAGDM) problems, prioritization is sometimes important. Several techniques and methods have been introduced in fuzzy systems to use prioritization. The main purpose of this paper is to propose prioritized aggregation operators (AOs) for intuitionistic fuzzy (IF) information. These AOs are symmetric in nature and are based on the novel Aczel–Alsina t-norm and t-conorm. Herein, we propose IF-prioritized Aczel–Alsina averaging (IFPAAA) and IF-prioritized Aczel–Alsina geometric (IFPAAG) operators. It is shown that these AOs satisfy the basic features of aggregation. Some additional results for these AOs are also investigated. These proposed operators can capture the prioritization phenomenon among the aggregated arguments, and the weights for prioritization are obtained from expert information. Finally, the proposed AOs are used in an MAGDM problem where a doctor is selected for a hospital. A comparison of the proposed prioritized AOs is also established with other well-known AOs to show the significance of the IFPAAA and IFPAAG operators. [ABSTRACT FROM AUTHOR]

Managing ambiguous and asymmetric types of information is a very challenging task under the consideration of classical data. Furthermore, Aczel-Alsina aggregation operators are the new developments in fuzzy sets theory. However, when decision-makers need to use these structures in fuzzy rough structures, these operators fail to deal with such types of values, as fuzzy rough structures use lower and upper approximation spaces. Thus, an encasement of an intuitionistic fuzzy set has a chance of data loss, whereas an intuitionistic fuzzy rough set can resolve the problem of data loss. Motivated by the notion of intuitionistic fuzzy rough sets and new aggregation operators i.e., intuitionistic fuzzy Aczel-Alsina operators, this paper firstly initiates some basic Aczel-Alsina operational rules for intuitionistic fuzzy rough numbers. Secondly, based on these newly defined operational rules, we have developed some new aggregation operators, such as intuitionistic fuzzy rough Aczel-Alsina weighted average (IFRAAWA), intuitionistic fuzzy rough Aczel-Alsina ordered weighted average (IFRAAOWA), and intuitionistic fuzzy rough Aczel-Alsina hybrid average (IFRAAHA) aggregation operators. Moreover, the properties of these aggregation operators have been initiated. These operators can help in evaluating awkward and asymmetric information in real-life problems. The use of aggregation operators in medical diagnosis and MADM is an efficient method that can help in healthcare and decision-making applications. To present an effective use of these developed operators in medical diagnosis and the selection of the best next-generation firewall, we have established an algorithm along with a numerical example to provide authenticity and clarity to the established work. Furthermore, a comparative analysis of the introduced work shows the superiority of the introduced approach. [ABSTRACT FROM AUTHOR]

Aggregation operators have become an essential tool in many applications. The functional equations related to aggregation operators play an important role in fuzzy sets and fuzzy logic theory. The modular equation is strongly connected with the distributivity equation and can be considered as a constrained associative equation. In this paper, we consider the submodular inequality, which can be viewed as a generalization of the modular equation. First, we discuss the submodular inequality of two general aggregation operators under duality and isomorphism. Moreover, one result of the submodular inequality is presented for the ordinal sum aggregation operators. In the cases of triangular norms and triangular conorms, we present the solutions and validate the symmetry in the related results for some classes of aggregation operators. [ABSTRACT FROM AUTHOR]

Aggregation operators perform a valuable and significant role in various decision-making processes. Averaging and geometric aggregation operators are both used for capturing the interrelationships of the aggregated preferences, even if the preferences are independent. The purpose of this paper is to analyze the theory of complex linguistic fuzzy (CLF) sets and their important laws, such as algebraic laws, score values, and accuracy values, and to describe the relationship between the score and accuracy values with the help of their properties. Additionally, based on the proposed CLF information, we introduce the theory of CLF weighted averaging (CLFWA), CLF ordered weighted averaging (CLFOWA), CLF hybrid averaging (CLFHA), CLF weighted geometric (CLFWG), CLF ordered weighted geometric (CLFOWG), and CLF hybrid geometric (CLFHG) operators. The fundamental properties and some valuable results of these operators are evaluated, and their particular cases are described. Based on the presented operators, a technique for evaluating the "multi-attribute decision-making" (MADM) problems in the consideration of CLF sets is derived. The superiority of the derived technique is illustrated via a practical example, a set of experiments, and significant and qualitative comparisons. The illustration results indicate that the derived technique can be feasible and superior in evaluating CLF information. Further, it can be used for determining the interrelationships of attributes and the criteria of experts. Moreover, it is valuable and capable of evaluating the MADM problems using CLF numbers. [ABSTRACT FROM AUTHOR]

This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability and decision theory methods. Multi-attribute decision-making (MADM) technique is a very effective and well-known tool to investigate fuzzy information more effectively. However, the selection of houses cannot be carried out by utilizing symmetry information, because enterprises does not have complete information, so asymmetric information should be used when selecting enterprises. Hamy mean (HM) operator is a feasible tool to handle strategic decision-making problems because it can capture the order between the finite input terms. Additionally, the complex interval-valued q-rung orthopair fuzzy (CIVq-ROF) setting is a broadly flexible and massively dominant technique to operate problematic and awkward data in actual life problems. The major contribution of this analysis is how to aggregate the collection of alternatives into a singleton set, for this we analyzed the technique of CIVq-ROF Hamy mean (CIVq-ROFHM) operator and CIVq-ROF weighted Hamy mean (Cq-ROFWHM) operator and some well-known results are deliberated. Keeping the advantages of the parameters in HM operators, we discussed the specific cases of the invented operators. To investigate the decision-making problems based on CIVq-ROF information, we suggested the following multi-attribute decision-making (MADM) technique to determine the beneficial term from the finite group of alternatives with the help of evaluating several examples. This manuscript showed how to make decisions when there is asymmetric information about enterprises. Finally, based on the evaluating examples, we try to discover the sensitive analysis and supremacy of the invented operators to find the flexibility and dominancy of the diagnosed approaches. [ABSTRACT FROM AUTHOR]

This paper aims at developing new methods for multi-attribute decision making (MADM) under a single-valued neutrosophic hesitant fuzzy environment, in which each element has sets of possible values designed by truth, indeterminacy, and falsity membership hesitant functions. First, taking advantage of the Choquet integral and that it can reflect more correlations of attributes in MADM, two aggregation operators are defined based on the Choquet integral, specifically, the single-valued neutrosophic hesitant fuzzy Choquet ordered averaging (SVNHFCOA) operator and single-valued neutrosophic hesitant fuzzy Choquet ordered geometric (SVNHFCOG) operator, and their properties are also discussed in detail. Then, novel MADM approaches based on the SVNHFCOA and SVNHFCOG operators are established to process single-valued neutrosophic hesitant fuzzy information. Finally, this work provides a numerical example of investment alternatives to validate the application and effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

In order to improve the ability of airspace management, a multi-attribute decision-making tool based on q-rung orthopair probability hesitant fuzzy GRA-TOPSIS is proposed to solve the problem of airspace operation effectiveness evaluation; this is in view of the fact that there are few airspace operation effectiveness evaluation methods in general aviation airports. Firstly, taking general aviation airports as the research object, a complete airspace operation effectiveness evaluation system is newly established, its evaluation indicators are introduced, and its multi-attribute decision-making ideas are explained. Then, based on the q-rung orthopair probability hesitant fuzzy set, a new distance measure and information aggregation operator are defined, which can better deal with symmetry information. Secondly, we build a deviation maximization model to calculate the attribute weights of indicator elements in the decision-making process. Then, we combine the GRA method and TOPSIS method to rank the airspace operation effectiveness evaluation schemes. Finally, combined with calculation examples and comparative analysis, the reliability and rationality of the method proposed in this paper are verified, and the symmetry relationship between the evaluation results and the actual situation is better reflected. Experiments show that the method proposed in this paper can obtain more accurate airspace operation effectiveness evaluation results, and can provide reference for related research. [ABSTRACT FROM AUTHOR]

The aggregation operator is a potential tool to fuse the information derived from multisources, which has been applied in group decision, combination classification and scheduling clusters successfully. To better characterize complex decision situations and capture complex opinions of decision-makers (DMs), aggregation operators are required to be explored from different viewpoints. In view of information fusion of hesitant 2-tuple linguistic variables, this paper establishes four new aggregation operators, which are called the hesitant 2-tuple linguistic prioritized weighted averaging (H2TLPWA) aggregation operator, hesitant 2-tuple linguistic prioritized weighted geometric (H2TLPWG) aggregation operator, hesitant 2-tuple linguistic correlated averaging (H2TLCA) aggregation operator, and hesitant 2-tuple linguistic correlated geometric (H2TLCG) aggregation operator, respectively. The H2TLPWA aggregation operator and H2TLPWG aggregation operator can characterize the prioritization relationship of the aggregated arguments. The H2TLCA aggregation operator and H2TLCG aggregation operator can describe dependencies between criteria in decision-making problem solving. Moreover all aggregation operation operators have the properties of idempotency, boundedness and monotonicity, and the H2TLCA aggregation operator and H2TLCG aggregation operator are also verified to be symmetric functions. In addition, the H2TLPWA aggregation operator and H2TLCA aggregation operator are employed to settle multicriteria decision-making problems with hesitant 2-tuple linguistic terms. By virtue of predefining discrete initial linguistic labels with symmetrical distribution, the detailed steps of the decision-making process with an example are given to illustrate their practicality and effectiveness. [ABSTRACT FROM AUTHOR]

Maritime shipping is a crucial method of transporting goods internationally and is vital in supporting global trade. However, due to its global scope, the international shipping market is susceptible to political and economic disturbances. The recent escalation in the Israeli–Palestinian conflict has severely impacted the international shipping market, particularly in the tense Red Sea region. Previous research has neglected the significance of evaluating international shipping companies, particularly their origins, within their evaluation frameworks. A fuzzy multi-attribute decision-making (MADM) approach is necessary to address the complexity of evaluating shipping companies with unclear criteria and uncertain expert opinions. Symmetry is crucial in various mathematical fields, with recent applications in hesitant fuzzy sets (HFSs) and neutrosophic sets (NSs), which are frequently employed to solve complex MADM problems. The consideration of symmetry in decision-making processes can enhance the robustness and fairness of evaluations, ensuring a balanced and unbiased approach. The neutrosophic–hesitant fuzzy set (NHFS) considers both the uncertainty of membership degrees of elements (hesitancy in HFSs) and the performance of membership degrees in the true, false, and neutral aspects (the ternary relation in NSs). NHFSs can be seen as a generalization of HFSs and NSs, providing a flexible mathematical framework to more effectively describe and analyze the uncertainties, hesitancies, and fuzziness involved in MADM problems. This study presents single-valued neutrosophic power Hamy mean (SVNPHM) operators and single-valued neutrosophic weighted power Hamy mean (SVNWPHM) operators, which are derived from power aggregation operators (AOs) and the Hamy mean (HM), within the framework of single-valued neutrosophic sets (SVNS). Some properties were investigated via these operators. Furthermore, SVNWPHM operators were employed to address single-valued neutrosophic MADM issues. The proposed methodology was validated by conducting a case study on international shipping provider selection, showcasing the methodology's relevance and efficiency. [ABSTRACT FROM AUTHOR]

In order to further investigate the level of online medical services in China and improve the medical experience of patients, this study aims to establish an online review-driven picture fuzzy multi-criteria group decision-making (MCGDM) approach for the online medical service evaluation of doctors. First, based on the Aczel–Alsina t-norm and t-conorm, the normal picture fuzzy Aczel–Alsina operations involving a variable parameter are defined to make the corresponding operations more flexible than other operations. Second, two picture fuzzy Aczel–Alsina aggregation operators are developed, and the corresponding properties are discussed as well. Third, combined with the online review information of China's medical platform Haodaifu, the online review-driven evaluation attributes and their corresponding weights are obtained, which can make the evaluation model more objective. Fourth, an extended normal picture fuzzy complex proportional assessment (COPRAS) decision-making method for the service quality evaluation of online medical services is proposed. Finally, an empirical example is presented to verify the feasibility and validity of the proposed method. A sensitivity analysis and a comparison analysis are also conducted to demonstrate the effectiveness and flexibility of the proposed approach. [ABSTRACT FROM AUTHOR]

Initially, fuzzy sets and intuitionistic fuzzy sets were used to address real-world problems with imprecise data. Eventually, the notion of the hesitant fuzzy set was formulated to handle decision makers' reluctance to accept asymmetric information. However, in certain scenarios, asymmetric information is gathered in terms of a possible range of acceptance and nonacceptance by players rather than specific values. Furthermore, decision makers exhibit some hesitancy regarding this information. In such a situation, all the aforementioned expansions of fuzzy sets are unable to accurately represent the scenario. The purpose of this article is to present asymmetric information situations in which the range of choices takes into account the hesitancy of players in accepting or not accepting information. To illustrate these problems, we develop matrix games that consider the payoffs of interval-valued intuitionistic hesitant fuzzy elements (IIHFEs). Dealing with these types of fuzzy programming problems requires a significant amount of effort. To solve these matrix games, we formulate two interval-valued intuitionistic hesitant fuzzy programming problems. Preserving the hesitant nature of the payoffs to determine the optimal strategies, these two problems are transformed into two nonlinear programming problems. This transformation involves using mathematical operations for IIHFEs. Here, we construct a novel aggregation operator of IIHFEs, viz., min-max operators of IIHFEs. This operator is suitable for applying the developed methodology. The cogency and applicability of the proposed methodology are verified through a numerical example based on the situation of conflict between hackers and defenders to prevent damage to cybersecurity. To validate the superiority of the proposed model along with the computed results, we provide comparisons with the existing models. [ABSTRACT FROM AUTHOR]

In order to solve multiple-attribute group decision-making (MAGDM) problems under a trapezoid intuitionistic fuzzy linguistic (TIFL) environment and the relationships between multiple input parameters needed, in this paper, we extend the Maclaurin symmetric mean (MSM) operators to TIFL numbers (TIFLNs). Some new aggregation operators are proposed, including the trapezoid intuitionistic fuzzy linguistic Maclaurin symmetric mean (TIFLMSM) operator, trapezoid intuitionistic fuzzy linguistic generalized Maclaurin symmetric mean (TIFLGMSM) operator, trapezoid intuitionistic fuzzy linguistic weighted Maclaurin symmetric mean (TIFLWMSM) operator and trapezoid intuitionistic fuzzy linguistic weighted generalized Maclaurin symmetric mean (TIFLWGMSM) operator. Next, based on the TIFLWMSM and TIFLWGMSM operators, two methods are presented to deal with MAGDM problems. Finally, there is a numerical example to verify the effectiveness and feasibility of the proposed approaches. [ABSTRACT FROM AUTHOR]

This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability and decision theory methods. Multiple-criteria decision making (MCDM) is a very effective and well-known tool to investigate fuzzy information more effectively. However, the selection of houses cannot be done by utilizing symmetry information, because enterprises do not have complete information, so asymmetric information should be used when selecting enterprises. In this paper, the notion of soft set (S f t S) and interval-valued T-spherical fuzzy set (IVT-SFS) are combined to produce a new and more effective notion called interval-valued T-spherical fuzzy soft set   (I V T − S F S f t S) . It is a more general concept and provides more space and options to decision makers (DMs) for making their decision in the field of fuzzy set theory. Moreover, some average aggregation operators like interval-valued T-spherical fuzzy soft weighted average (I V T − S F S f t W A) operator, interval-valued T-spherical fuzzy soft ordered weighted average (I V T − S F S f t O W A) operator, and interval-valued T-spherical fuzzy soft hybrid average (I V T − S F S f t H A) operators are explored. Furthermore, the properties of these operators are discussed in detail. An algorithm is developed and an application example is proposed to show the validity of the present work. This manuscript shows how to make a decision when there is asymmetric information about an enterprise. Further, in comparative analysis, the established work is compared with another existing method to show the advantages of the present work. [ABSTRACT FROM AUTHOR]

The picture fuzzy set is a generation of an intuitionistic fuzzy set. The aggregation operators are important tools in the process of information aggregation. Some aggregation operators for picture fuzzy sets have been proposed in previous papers, but some of them are defective for picture fuzzy multi-attribute decision making. In this paper, we introduce a transformation method for a picture fuzzy number and trapezoidal fuzzy number. Based on this method, we proposed a picture fuzzy multiplication operation and a picture fuzzy power operation. Moreover, we develop the picture fuzzy weighted geometric ( P F W G ) aggregation operator, the picture fuzzy ordered weighted geometric ( P F O W G ) aggregation operator and the picture fuzzy hybrid geometric ( P F H G ) aggregation operator. The related properties are also studied. Finally, we apply the proposed aggregation operators to multi-attribute decision making and pattern recognition. [ABSTRACT FROM AUTHOR]

An interval-valued q-rung orthopair fuzzy set ( I V q r O F S ) is a robust and esteemed model in managing imprecise information, utilizing a controllable parameter q ≥ 1 . Expanding its applicability, we propose a refinement to it, termed the interval-valued p,q-rung orthopair fuzzy set, denoted I V p , q r O F S . This advancement enables the handling of scenarios where varied assessment levels for membership and non-membership grades are necessary, a challenge unaddressed by existing extensions of interval-valued intuitionistic fuzzy sets. We establish the fundamental mathematical operations for the I V p , q r O F S and explore their key properties. To compare interval-valued p,q-rung orthopair fuzzy ( I V p , q r O F ) numbers, a novel score function is put forward and compared to the known I V q r O F S -based score functions to determine its viability. Moreover, we present I V p , q r O F aggregation operators (AOs), accompanied by rigorous proof of their essential characteristics, including boundedness, monotonicity, and symmetry. This study introduces the interaction of I V p , q r O F criteria through the inter-criteria correlation (CRITIC) approach. This method determines criteria weights based on the proposed distance measurements and the score function. The CRITIC method is integrated with the exponential TODIM approach (exp-TODIM), resulting in an innovative decision-making framework that is less susceptible to parameter fluctuations and showcases a high stability. An illustrative example of selecting a suitable supplier is provided to demonstrate the practical application of the developed exp-TODIM approach. Finally, a sensitivity analysis is conducted to exhibit the method's stability, and a comparative analysis is performed to elucidate its strengths and advantages. [ABSTRACT FROM AUTHOR]

This paper focuses on multi-attribute group decision-making (MAGDM) course in which attributes are evaluated in terms of interval-valued intuitionistic fuzzy (IVIF) information. More explicitly, this paper introduces new aggregation operators for IVIF information and further proposes a new IVIF MAGDM method. The power average (PA) operator and the Muirhead mean (MM) are two powerful and effective information aggregation technologies. The most attractive advantage of the PA operator is its power to combat the adverse effects of ultra-evaluation values on the information aggregation results. The prominent characteristic of the MM operator is that it is flexible to capture the interrelationship among any numbers of arguments, making it more powerful than Bonferroni mean (BM), Heronian mean (HM), and Maclaurin symmetric mean (MSM). To absorb the virtues of both PA and MM, it is necessary to combine them to aggregate IVIF information and propose IVIF power Muirhead mean (IVIFPMM) operator and the IVIF weighted power Muirhead mean (IVIFWPMM) operator. We investigate their properties to show the strongness and flexibility. Furthermore, a novel approach to MAGDM problems with IVIF decision-making information is introduced. Finally, a numerical example is provided to show the performance of the proposed method. [ABSTRACT FROM AUTHOR]

Keeping in mind the importance and well growing Pythagorean fuzzy sets, in this paper, some novel operators for Pythagorean fuzzy sets and their properties are demonstrated. In this paper, we develop a comprehensive model to tackle decision-making problems where strong points of view are in the favour and against the some projects, entities or plans. Therefore, a new approach, based on Pythagorean fuzzy set models by means of Pythagorean fuzzy Dombi aggregation operators is proposed. An approach to deal with decision-making problems using Pythagorean Dombi averaging and Dombi geometric aggregation operators is established. This model has a stronger capability than existing averaging, geometric, Einstein, logarithmic averaging and logarithmic geometric aggregation operators for Pythagorean fuzzy information. Finally, the proposed method is demonstrated through an example of how the proposed method helps us and is effective in decision-making problems. [ABSTRACT FROM AUTHOR]

Recently, neutrosophic sets are found to be more general and useful to express incomplete, indeterminate and inconsistent information. The purpose of this paper is to introduce new aggregation operators based on logarithmic operations and to develop a multi-criteria decision-making approach to study the interaction between the input argument under the single valued neutrosophic (SVN) environment. The main advantage of the proposed operator is that it can deal with the situations of the positive interaction, negative interaction or non-interaction among the criteria, during decision-making process. In this paper, we also defined some logarithmic operational rules on SVN sets, then we propose the single valued neutrosophic hybrid aggregation operators as a tool for multi-criteria decision-making (MCDM) under the neutrosophic environment and discussd some properties. Finally, the detailed decision-making steps for the single valued neutrosophic MCDM 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 decision process to evaluate their best alternative. [ABSTRACT FROM AUTHOR]

The Maclaurin symmetric mean (MSM) operator has a good aggregation effect. It can capture the relationships between multiple input parameters, and the neutrosophic uncertain linguistic numbers can well represent some indeterminate and incomplete information. In this paper, we combine the MSM operator with the singled-valued neutrosophic uncertain linguistic set and propose some MSM operators based on single-valued neutrosophic uncertain linguistic environment, such as single-valued neutrosophic uncertain linguistic Maclaurin symmetric mean(SVNULMSM) operator and single-valued neutrosophic uncertain linguistic generalized Maclaurin symmetric mean(SVNULGMSM) operator. First of all, according to the neutrosophic set and uncertain linguistic numbers, we propose the single-valued neutrosophic uncertain linguistic numbers and give some operating rules. Furthermore, considering the influence of attribute weight on the results, we introduce the weighted SVNULMSM operator and weighted SVNULGMSM operator. Then, we propose a method to deal with MSDM problems and give the specific steps to solve the problem. Finally, an investment example is used to verify the effectiveness of our method, and the superiority of the method is proved by comparing with other methods. [ABSTRACT FROM AUTHOR]

A significant addition to fuzzy set theory for expressing uncertain data is an n,m-th power root fuzzy set. Compared to the nth power root, Fermatean, Pythagorean, and intuitionistic fuzzy sets, n,m-th power root fuzzy sets can cover more uncertain situations due to their greater range of displayed membership grades. When discussing the symmetry between two or more objects, the innovative concept of an n,m-th power root fuzzy set over dual universes is more flexible than the current notion of an intuitionistic fuzzy set, a Pythagorean fuzzy set, and a nth power root fuzzy set. In this study, we demonstrate a number of additional operations on n,m-th power root fuzzy sets along with a number of their special aspects. Additionally, to deal with choice information, we create a novel weighted aggregated operator called the n,m-th power root fuzzy weighted power average (FWPA m n ) across n,m-th power root fuzzy sets and demonstrate some of its fundamental features. To rank n,m-th power root fuzzy sets, we also define the score and accuracy functions. Moreover, we use this operator to identify the countries with the best standards of living and show how we can select the best option by contrasting aggregate results using score values. Finally, we contrast the results of the FWPA m n  operator with the square-root fuzzy weighted power average (SR-FWPA), the nth power root fuzzy weighted power average (nPR-FWPA), the Fermatean fuzzy weighted power average (FFWPA), and the n,m-rung orthopair fuzzy weighted power average (n,m-ROFWPA) operators. [ABSTRACT FROM AUTHOR]

Human activity recognition (HAR) is the process of interpreting human activities with the help of electronic devices such as computer and machine version technology. Humans can be explained or clarified as gestures, behavior, and activities that are recorded by sensors. In this manuscript, we concentrate on studying the problem of HAR; for this, we use the proposed theory of Aczel and Alsina, such as Aczel–Alsina (AA) norms, and the derived theory of Choquet, such as the Choquet integral in the presence of Atanassov interval-valued intuitionistic fuzzy (AIVIF) set theory for evaluating the novel concept of AIVIF Choquet integral AA averaging (AIVIFC-IAAA), AIVIF Choquet integral AA ordered averaging (AIVIFC-IAAOA), AIVIF Choquet integral AA hybrid averaging (AIVIFC-IAAHA), AIVIF Choquet integral AA geometric (AIVIFC-IAAG), AIVIF Choquet integral AA ordered geometric (AIVIFC-IAAOG), and AIVIF Choquet integral AA hybrid geometric (AIVIFC-IAAHG) operators. Many essential characteristics of the presented techniques are shown, and we also identify their properties with some results. Additionally, we take advantage of the above techniques to produce a technique to evaluate the HAR multiattribute decision-making complications. We derive a functional model for HAR problems to justify the evaluated approaches and to demonstrate their supremacy and practicality. Finally, we conduct a comparison between the proposed and prevailing techniques for the legitimacy of the invented methodologies. [ABSTRACT FROM AUTHOR]

In actual multiple attribute decision making, people often use language to evaluate attributes of the object, and sometimes there are associations between the attributes. Therefore, the study of multiple attribute decision making with language as attributes and associations between attributes is of great theoretical significance and practical value. The Heronian mean is not only an operator which reflects the associations between attributes, but also has excellent properties, including idempotency, monotonicity, boundedness, parameter symmetry, and alternate symmetry. In this paper, firstly a new linguistic generalized weighted Heronian mean (LGWHM) was provided, and its properties including idempotency, monotonicity, boundedness, and limit were studied. Then, a new three-parameter linguistic generalized weighted Heronian mean (TPLGWHM) and its idempotency, monotonicity, and boundedness properties were proposed. Finally, multi-attribute decision making methods based on the new linguistic generalized weighted Heronian mean were given, and an example was analyzed and compared with other methods. [ABSTRACT FROM AUTHOR]

In recent years, typhoon disasters have occurred frequently and the economic losses caused by them have received increasing attention. This study focuses on the evaluation of typhoon disasters based on the interval neutrosophic set theory. An interval neutrosophic set (INS) is a subclass of a neutrosophic set (NS). However, the existing exponential operations and their aggregation methods are primarily for the intuitionistic fuzzy set. So, this paper mainly focus on the research of the exponential operational laws of interval neutrosophic numbers (INNs) in which the bases are positive real numbers and the exponents are interval neutrosophic numbers. Several properties based on the exponential operational law are discussed in detail. Then, the interval neutrosophic weighted exponential aggregation (INWEA) operator is used to aggregate assessment information to obtain the comprehensive risk assessment. Finally, a multiple attribute decision making (MADM) approach based on the INWEA operator is introduced and applied to the evaluation of typhoon disasters in Fujian Province, China. Results show that the proposed new approach is feasible and effective in practical applications. [ABSTRACT FROM AUTHOR]

The Dombi operations of T-norm and T-conorm introduced by Dombi can have the advantage of good flexibility with the operational parameter. In existing studies, however, the Dombi operations have so far not yet been used for neutrosophic sets. To propose new aggregation operators for neutrosophic sets by the extension of the Dombi operations, this paper firstly presents the Dombi operations of single-valued neutrosophic numbers (SVNNs) based on the operations of the Dombi T-norm and T-conorm, and then proposes the single-valued neutrosophic Dombi weighted arithmetic average (SVNDWAA) operator and the single-valued neutrosophic Dombi weighted geometric average (SVNDWGA) operator to deal with the aggregation of SVNNs and investigates their properties. Because the SVNDWAA and SVNDWGA operators have the advantage of good flexibility with the operational parameter, we develop a multiple attribute decision-making (MADM) method based on the SVNWAA or SVNWGA operator under a SVNN environment. Finally, an illustrative example about the selection problem of investment alternatives is given to demonstrate the application and feasibility of the developed approach. [ABSTRACT FROM AUTHOR]

The intuitionistic hesitant fuzzy set (IHFS) is an enriched version of hesitant fuzzy sets (HFSs) that can cover both fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). By assigning membership and non-membership grades as subsets of [0, 1], the IHFS can model and handle situations more proficiently. Another related theory is the theory of set pair analysis (SPA), which considers both certainties and uncertainties as a cohesive system and represents them from three aspects: identity, discrepancy, and contrary. In this article, we explore the suitability of combining the IHFS and SPA theories in multi-attribute decision making (MADM) and present the hybrid model named intuitionistic hesitant fuzzy connection number set (IHCS). To facilitate the design of a novel MADM algorithm, we first develop several averaging and geometric aggregation operators on IHCS. Finally, we highlight the benefits of our proposed work, including a comparative examination of the recommended models with a few current models to demonstrate the practicality of an ideal decision in practice. Additionally, we provide a graphical interpretation of the devised attempt to exhibit the consistency and efficiency of our approach. [ABSTRACT FROM AUTHOR]

The success of any endeavor or process is heavily contingent on the ability to reconcile and satisfy balance requirements, which are often characterized by symmetry considerations. In practical applications, the primary goal of decision-making processes is to efficiently manage the symmetry or asymmetry that exists within different sources of information. In order to address this challenge, the primary aim of this study is to introduce novel Dombi operation concepts that are formulated within the framework of interval-valued Pythagorean fuzzy aggregation operators. In this study, an updated score function is presented to resolve the deficiency of the current score function in an interval-valued Pythagorean fuzzy environment. The concept of Dombi operations is used to introduce some interval-valued Pythagorean fuzzy aggregation operators, including the interval-valued Pythagorean fuzzy Dombi weighted arithmetic (IVPFDWA) operator, the interval-valued Pythagorean fuzzy Dombi ordered weighted arithmetic (IVPFDOWA) operator, the interval-valued Pythagorean fuzzy Dombi weighted geometric (IVPFDWG) operator, and the interval-valued Pythagorean fuzzy Dombi ordered weighted geometric (IVPFDOWG) operator. Moreover, the study investigates many important properties of these operators that provide new semantic meaning to the evaluation. In addition, the suggested score function and newly derived interval-valued Pythagorean fuzzy Dombi aggregation (IVPFDA) operators are successfully employed to select a subject expert in a certain institution. The proposed approach is demonstrated to be successful through empirical validation. Lastly, a comparative study is conducted to demonstrate the validity and applicability of the suggested approaches in comparison with current techniques. This research contributes to the ongoing efforts to advance the field of evaluation and decision-making by providing novel and effective tools and techniques. [ABSTRACT FROM AUTHOR]

Complex picture fuzzy sets are the updated version of the complex intuitionistic fuzzy sets. A complex picture fuzzy set covers three major grades such as membership, abstinence, and falsity with a prominent characteristic in which the sum of the triplet will be contained in the unit interval. In this scenario, we derive the power aggregation operators based on the Aczel–Alsina operational laws for managing the complex picture of fuzzy values. These complex picture fuzzy power aggregation operators are complex picture fuzzy Aczel–Alsina power averaging, complex picture fuzzy Aczel–Alsina weighted power averaging, complex picture fuzzy Aczel–Alsina power geometric, and complex picture fuzzy Aczel–Alsina weighted power geometric operators. We also investigate their theoretical properties. To justify these complex picture fuzzy power aggregation operators, we illustrate a procedure of a decision-making technique in the presence of complex picture fuzzy values and derive an algorithm to evaluate some multi-attribute decision-making problems. Finally, a practical example is examined to illustrate the decision-making procedure under the consideration of derived operators, and their performance is compared with that of various operators to show the supremacy and validity of the proposed approaches. [ABSTRACT FROM AUTHOR]

In this research, we first offer unique notions of averaging and geometric aggregation operators with confidence level by employing a probabilistic neutrosophic hesitant fuzzy rough framework. Then, we look into other descriptions of the suggested operators, such as idempotency, boundedness, and monotonicity. Additionally, for the derived operators, we establish the score and accuracy functions. We also provide a novel approach to assessing the selection procedure for smart medical devices (SMDs). The selection criteria for SMDs are quite complex, which is the most noteworthy feature of this investigation. It is suggested that these processes be simulated using a method utilizing a hesitant fuzzy set, a rough set, and a probabilistic single-valued neutrosophics set. The proposed approach is employed in the decision-making process, while taking into consideration the decision-makers' (DMs') level of confidence in the data they have obtained in order to deal with ambiguity, incomplete data, and uncertainty in lower and upper approximations. The major goal was to outline the issue's complexities in order to pique interest among experts in the health care sector and encourage them to evaluate SMDs using various evaluation standards. The analysis of the technique's outcomes demonstrated that the rankings and the results themselves were adequate and trustworthy. The effectiveness of our suggested improvements is also demonstrated through a symmetrical analysis. The symmetry behavior shows that the current techniques address more complex and advanced data. [ABSTRACT FROM AUTHOR]

Assessment specialists (experts) are sometimes expected to provide two types of information: knowledge of rating domains and the performance of rating objects (called confidence levels). Unfortunately, the results of previous information aggregation studies cannot be properly used to combine the two categories of data covered above. Additionally, a significant range of symmetric/asymmetric events and structures are frequently included in the implementation process or practical use of fuzzy systems. The primary goal of the current study was to use cubic Fermatean fuzzy set features to address such situations. To deal with the ambiguous information of the aggregated arguments, we defined information aggregation operators with confidence degrees. Two of the aggregation operators we initially proposed were the confidence cubic Fermatean fuzzy weighted averaging (CCFFWA) operator and the confidence cubic Fermatean fuzzy weighted geometric (CCFFWG) operator. They were used as a framework to create an MCDM process, which was supported by an example to show how effective and applicable it is. The comparison of computed results was carried out with the help of existing approaches. [ABSTRACT FROM AUTHOR]

In this research, we provide tools to overcome the information loss limitation resulting from the requirement to estimate the results in the discrete initial expression domain. Through the use of 2-tuples, which are made up of a linguistic term and a numerical value calculated between [ 0.5 , 0.5) , the linguistic information will be expressed. This model supports continuous representation of the linguistic data within its scope, permitting it to express any information counting received through an aggregation procedure. This study provides a novel approach to develop a linguistic multi-attribute group decision-making (MAGDM) approach with complex fractional orthotriple fuzzy 2-tuple linguistic (CFOF2TL) assessment details. Initially, the concept of a complex fractional orthotriple fuzzy 2-tuple linguistic set (CFO2TLS) is proposed to convey uncertain and fuzzy information. In the meantime, simple aggregation operators, such as CFOF2TL weighted average and geometric operators, are defined. In addition, the CFOF2TL Maclaurin's symmetric mean (CFOF2TLMSM) operators and their weighted shapes are presented, and their attractive characteristics are also discussed. A new MAGDM approach is built using the developed aggregation operators to address managing economic crises under COVID-19 with the CFOF2TL information. As a result, the effectiveness and robustness of the developed method are accompanied by an empirical example, and a comparative study is carried out by contrasting it with previous approaches. [ABSTRACT FROM AUTHOR]

Hesitant fuzzy evaluation strategy related to the interval-valued membership and nonmembership degrees should be an appropriate choice due to the lack of experience, ability and knowledge of some decision experts. In addition, it is important to reasonably model the interrelationship of these experts. In this work, firstly, the generalized interval-valued q-rung orthopair hesitant fuzzy sets (GIVqROHFSs) are defined, and some operational rules with respect to GIVqROF numbers are discussed. Secondly, two types of operators, which are denoted as GIVqROHFCA and GIVqROHFCGM, are developed. Thirdly, the desired properties and relationships of two operators are studied. Furthermore, a new multiple attributes group decision making (MAGDM) approach is proposed. Finally, three experiments are completed to illustrate the rationality of the developed method and the monotonicity of this approach concerning the parameter in the GIVqROHFCGM operator and the GIVqROHFCA operator which meets symmetrical characteristics, and shows the superiority and reliability of this new method in solving the GIVqROHF problems. The main advantages of this work include three points: (1) extending hesitant fuzzy sets to the interval-valued q-rung orthopair fuzzy case and proposing two types of aggregation operators for the GIVqROHF information; (2) considering the interaction among decision makers and among attributes in decision problems, and dealing with this interrelationship by fuzzy measure; (3) introducing the new decision method for the GIVqROHF environment and enriching the mathematical tools to solve multiple attributes decision-making problems. [ABSTRACT FROM AUTHOR]

Aggregation operators (AOs) are utilized to overcome the influence of uncertain and vague information in different fuzzy environments. A multi-attribute decision-making (MADM) technique plays a vital role in several fields of different environments such as networking analysis, risk assessment, cognitive science, recommender systems, signal processing, and many more domains in ambiguous circumstances. In this article, we elaborated the notion of Aczel–Alsina t-norm (TNM) and t-conorm (TCNM) under the system of complex Pythagorean fuzzy (CPyF) sets (CPyFSs). Some basic operational laws of Aczel–Alsina TNM and TCNM are established including Aczel–Alsina sum, product, scalar multiplication, and power operations based on CPyFSs. We established several AOs of CPyFSs such as CPyF Aczel–Alsina weighted average (CPyFAAWA), and CPyF Aczel–Alsina weighted geometric (CPyFAAWG) operators. The proposed CPyFAAWA and CPyFAAWG operators are symmetric in nature and satisfy the properties of idempotency, monotonicity, boundedness and commutativity. To solve an MADM technique, we established an illustrative example to select a suitable candidate for a vacant post in a multinational company. To see the advantages of our proposed AOs, we compared the results of existing AOs with the results of newly established AOs. [ABSTRACT FROM AUTHOR]

In this paper, the novel approach of complex T-spherical fuzzy sets (CTSFSs) and their operational laws are explored and also verified with the help of examples. CTSFS composes the grade of truth, abstinence, and falsity with a condition that the sum of q-power of the real part (also for imaginary part) of the truth, abstinence, and falsity grades cannot be exceeded from a unit interval. Additionally, to examine the interrelationships among the complex T-spherical fuzzy numbers (CTSFNs), we propose two aggregation operators, called complex T-spherical fuzzy weighted averaging (CTSFWA) and complex T-spherical fuzzy weighted geometric (CTSFWG) operators. A multi-attribute decision making (MADM) problem is resolved based on CTSFNs by using the proposed CTSFWA and CTSFWG operators. To examine the proficiency and reliability of the explored works, we use an example to make comparisons between the proposed operators and some existing operators. Based on the comparison results, the proposed CTSFWA and CTSFWG operators are well suited in the fuzzy environment with legitimacy and prevalence by contrasting other existing operators. [ABSTRACT FROM AUTHOR]

Aggregating data is the main line of any discipline dealing with fusion of information from the knowledge-based systems to decision-making. The purpose of aggregation methods is to convert a list of objects, all belonging to a given set, into a single representative object of the same set usually by an n-ary function, so-called aggregation operator. As the useful aggregation functions for modeling real-life problems are limited, the basic problem is to construct a proper aggregation operator, usually a symmetric one, for each situation. During the last decades, a number of construction methods for aggregation functions have been developed to build new classes based on the existing well-known operators. There are three main construction methods in common use: transformation, composition, and convex combination. This paper compares these methods with respect to the type of aggregating problems that can be handled by each of them. [ABSTRACT FROM AUTHOR]

In the modern world, the computation of vague data is a challenging job. Different theories are presented to deal with such situations. Amongst them, fuzzy set theory and its extensions produced remarkable results. Samrandache extended the theory to a new horizon with the neutrosophic set (NS), which was further extended to interval neutrosophic set (INS). Neutrosophic cubic set (NCS) is the generalized version of NS and INS. This characteristic makes it an exceptional choice to deal with vague and imprecise data. Aggregation operators are key features of decision-making theory. In recent times several aggregation operators were defined in NCS. The intent of this paper is to generalize these aggregation operators by presenting neutrosophic cubic generalized unified aggregation (NCGUA) and neutrosophic cubic quasi-generalized unified aggregation (NCQGUA) operators. The accuracy and precision are a vital tool to minimize the potential threat in decision making. Generally, in decision making methods, alternatives and criteria are considered to evaluate the better outcome. However, sometimes the decision making environment has more components to express the problem completely. These components are named as the state of nature corresponding to each criterion. This complex frame of work is dealt with by presenting the multi-expert decision-making method (MEDMM). [ABSTRACT FROM AUTHOR]

In recent decades, there has been a massive growth towards the prime interest of the hydrogen energy industry in automobile transportation fuel. Hydrogen is the most plentiful component and a perfect carrier of energy. Generally, evaluating a suitable hydrogen power plant site is a complex selection of multi-criteria decision-making (MCDM) problem concerning proper location assessment based on numerous essential criteria, the decision-makers expert opinion, and other qualitative/quantitative aspects. This paper presents the novel single-valued neutrosophic (SVN) multi-attribute decision-making method to help decision-makers choose the optimal hydrogen power plant site. At first, novel operating laws based on sine trigonometric function for single-valued neutrosophic sets (SVNSs) are introduced. The well-known sine trigonometry function preserves the periodicity and symmetric in nature about the origin, and therefore it satisfies the decision-maker preferences over the multi-time phase parameters. In conjunction with these properties and laws, we define several new aggregation operators (AOs), called SVN weighted averaging and geometric operators, to aggregate SVNSs. Subsequently, on the basis of the proposed AOs, we introduce decision-making technique for addressing multi-attribute decision-making (MADM) problems and provide a numerical illustration of the hydrogen power plant selection problem for validation. A detailed comparative analysis, including a sensitivity analysis, was carried out to improve the understanding and clarity of the proposed methodologies in view of the existing literature on MADM problems. [ABSTRACT FROM AUTHOR]

The neutrosophic cubic sets are an extension of the cubic sets to the neutrosophic sets. It contains three variables, which respectively represent the membership degree, non-membership degree and uncertainty of the element to the set. The score function is an important indicator in the multi-attribute decision-making problem. In this paper, we consider the possibility that an element belongs to a set and put forward the concept of possibility neutrosophic cubic sets. On this basis, we introduce some related concepts and give the binary operation of possibility neutrosophic cubic sets and use specific examples to supplement the corresponding definition. Meanwhile, a decision-making method based on the score function of possibility neutrosophic cubic sets is proposed and a numerical example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Focusing on ill-structured multiple attribute decision-making (MADM) problems, including decision hesitancy and attribute prioritization relationships, this paper investigates appropriate approaches for decision making. Firstly, we introduce the probabilistic hybrid linguistic term set (P-HLTS) for capturing probabilistic preferences about possible linguistic labels belonging to a wide range of hesitant linguistic term sets. Entropy and distance measurements for P-HLTS are developed without arbitrary complementing operations. To facilitate decision making with attribute prioritization relationships, we present a probabilistic uncertain balanced linguistic-prioritized weighted average (PUBL-PWA) operator and the probabilistic uncertain balanced linguistic-induced prioritized ordered weighted average (PUBL-IPOWA) operator. In terms of the strength of the above tools, we further construct two multiple attribute group decision-making (MAGDM) approaches under P-HLTS environments, namely, an approach for decision-making situations where attribute prioritization relationships are known in advance and the relative importance of decision makers (DMs) or decision-making units (DMUs) is not required for consideration, and second approach for decision-making situations where both attribute prioritization relationships and the weighted vectors of DMs or DMUs are explicitly unknown. In general, our proposed approaches are more flexible and practical when considering heterogeneous opinions, avoiding information distortion brought about by complementing operation-based distance measures. Furthermore, illustrative application studies are conducted to verify our developed approaches. [ABSTRACT FROM AUTHOR]

In this paper, we introduce certain aggregation operators, namely, the m-polar fuzzy (mF) Hamacher weighted average operator, mF Hamacher ordered weighted average (mFHOWA) operator, mF Hamacher hybrid average (mFHHA) operator, mF Hamacher weighted geometric (mFHWG) operator, mF Hamacher weighted ordered geometric operator, and mF Hamacher hybrid geometric (mFHHG) operator. We discuss some properties of these operators, inclusive of their ability to implement both symmetric and asymmetric treatments of the items. We develop an algorithmic model to solve multi-attribute decision-making (MADM) problems in mF environment using mF Hamacher weighted average operator (mFHWA) and mFHWG operators. They can compensate for the possible asymmetric roles of the attributes that describe the problem. In the end, to prove the validity and feasibility of the proposed work, we give applications for selecting the most affected country regarding human trafficking, selecting health care waste treatment methods and selecting the best company for investment. We also solve practical MADM problems by using ELECTRE-I method, and give a comparative analysis. [ABSTRACT FROM AUTHOR]

The theory investigated in this analysis is substantially more suitable for evaluating the dilemmas in real life to manage complicated, risk-illustrating, and asymmetric information. The complex Pythagorean fuzzy set is expanded upon by the complex q-rung orthopair fuzzy set (Cq-ROFS). They stand out by having a qth power of the real part of the complex-valued membership degree and a qth power of the real part and imaginary part of the complex-valued non-membership degree that is equal to or less than 1. We define the comparison method for two complex q-rung orthopair fuzzy numbers as well as the score and accuracy functions (Cq-ROFNs). Some averaging and geometric aggregation operators are examined using the Cq-ROFSs operational rules. Additionally, their main characteristics have been fully illustrated. Based on the suggested operators, we give a novel approach to solve the multi-attribute group decision-making issues that arise in environmental contexts. Making the best choice when there are asymmetric types of information offered by different specialists is the major goal of this work. Finally, we used real data to choose an ideal extinguisher from a variety of options in order to show the effectiveness of our decision-making technique. The effectiveness of the experimental outcomes compared to earlier research efforts is then shown by comparing them to other methods. [ABSTRACT FROM AUTHOR]

Due to the fact that there is no symmetry in the division of cancer cells, it is important to consider this asymmetrical behavior. Because of this heterogeneity during any therapy, not every cancer cell that is killed only is abolished, which is sensitive to the particular treatment chosen. Mathematical models that describe these pathways are critical for predicting cancer cell proliferation behavior. The literature on the mathematical modeling of cancer onset, growth, and metastasis is extensive. Both deterministic and stochastic factors were used to develop mathematical models to mimic the development rate of cancer cells. We focus on the cell's heterogeneity in our model so that the cells generally responsible for spreading cancer, which are called stem cells, can be killed. Aggregation operators (AOs) play an important role in decision making, especially when there are several competing factors. A key issue in the case of uncertain data is to develop appropriate solutions for the aggregation process. We presented two novel Einstein AOs: q-rung picture fuzzy dynamic Einstein weighted averaging (q-RPFDEWA) operator and q-rung picture fuzzy dynamic Einstein weighted geometric (q-RPFDEWG) operator. Several enticing aspects of these AOs are thoroughly discussed. Furthermore, we provide a method for dealing with multi-period decision-making (MPDM) issues by applying optimal solutions. A numerical example is presented to explain how the recommended technique can be used in cancer therapy assessment. Authenticity analysis is also presented to demonstrate the efficacy of the proposed technique. The suggested AOs and decision-making methodologies are generally applicable in real-world multi-stage and dynamic decision analysis. [ABSTRACT FROM AUTHOR]

Using the strength of a single-valued neutrosophic set (SVNS) with the flexibility of a hesitant fuzzy set (HFS) yields a robust model named the single-valued neutrosophic hesitant fuzzy set (SVNHFS). Due to the ability to utilize three independent indexes (truthness, indeterminacy, and falsity), an SVNHFS is an efficient model for optimization and computational intelligence (CI) as well as an intelligent decision support system (IDSS). Taking advantage of the flexibility of operational parameters in Dombi's t-norm and t-conorm operations, new aggregation operators (AOs) are proposed, which are named the SVN fuzzy Dombi weighted averaging (SVNHFDWA) operator, SVN hesitant fuzzy Dombi ordered weighted averaging (SVNHFDOWA) operator, SVN hesitant fuzzy Dombi hybrid averaging (SVNHFDHWA) operator, SVN hesitant fuzzy Dombi weighted geometric (SVNHFDWG) operator, SVN hesitant fuzzy Dombi ordered weighted geometric (SVNHFDOWG) operator as well as SVN hesitant fuzzy Dombi hybrid weighted geometric (SVNHFDHWG) operator. The efficiency of these AOs is investigated in order to determine the best option using SVN hesitant fuzzy numbers (SVNHFNs) in an IDSS. Additionally, a practical application of SVNHFDWA and SVNHFDWG is also presented to examine symmetrical analysis in the selection of wireless charging station for vehicles. [ABSTRACT FROM AUTHOR]

The concept of m-polar spherical fuzzy sets (mPSFS) is a combination of m-polar fuzzy sets (mPFS) and spherical fuzzy sets (SFS). An mPSFS is an optimal strategy for addressing multipolarity and fuzziness in terms of ordered triples of positive membership grades (PMGs), negative membership grades (NMGs), and neutral grades (NGs). In this study, the innovative concept of m-polar spherical fuzzy topology (mPSF-topology) is proposed for data analysis and information aggregation. We look into the characteristics and results of mPSF-topology with the help of several examples. Topological structures on mPSFSs help with both the development of new artificial intelligence (AI) tools for different domain strategies and the study of different kinds of uncertainty in everyday life problems. These strategies make it possible to recognise and look into a situation early on, which helps professionals to reduce certain risks. In order to address various group decision-making issues in the m-polar spherical fuzzy domain, one suggestion has been to apply an extended linear assignment model (LAM) along with the SIR method known as superiority and inferiority ranking methodology in order to analyze road accident issues and dispute resolution. In addition, we examine the symmetry of optimal decision and perform a comparative study between the research carried out using the suggested methodology and several existing methods. [ABSTRACT FROM AUTHOR]

It is well known that there are some unfavorable shortcomings in the ordinary operational rules (OORs) of intuitionistic fuzzy number (IFN), and there exists a close and forceful connection between the intuitionistic fuzzy set (IFS) and Dempster-Shafer Theory (DST). We can utilize this relationship to present a transparent and fruitful semantic framework for IFS in terms of DST. In the framework of DST, an IFN can be converted into a basic probability assignment (BPA) and operations on IFNs can be represented as operations on a belief interval (BI), which can break away from the revealed shortcomings of the OORs of the IFN. Although there are many operators to aggregate the IFN, the operator to aggregate the BPA is rare. The Maclaurin symmetric mean (MSM) operator has the advantage of considering interrelationships among any number of attributes. The power average (PA) operator can reduce the influences of extreme evaluation values. In addition, for measuring the difference between IFNs, we replace the Hamming distance and Euclidean distance with the Jousselme distance (JD). In this paper, we develop an intuitionistic fuzzy power MSM (IFPMSMDST) operator and an intuitionistic fuzzy weighted power MSM (IFPWMSMDST) operator in the framework of the DST and provide their favorable properties. Then, we propose a novel method based on the proposed operators to solve multi-attribute decision-making (MADM) problems without intermediate defuzzification when their attributes and weights are both IFNs. Finally, some examples are utilized to demonstrate that the proposed methods outperform the previous ones. [ABSTRACT FROM AUTHOR]

The q-rung orthopair fuzzy set (q-ROFS), which is the extension of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS), satisfies the sum of q-th power of membership degree and nonmembership degree is limited 1. Evidently, the q-ROFS can depict more fuzzy assessment information and consider decision-maker's (DM's) hesitance. Thus, the concept of a dual hesitant q-rung orthopair fuzzy set (DHq-ROFS) is developed in this paper. Then, based on Hamacher operation laws, weighting average (WA) operator and weighting geometric (WG) operator, some dual hesitant q-rung orthopair fuzzy Hamacher aggregation operators are developed, such as the dual hesitant q-rung orthopair fuzzy Hamacher weighting average (DHq-ROFHWA) operator, the dual hesitant q-rung orthopair fuzzy Hamacher weighting geometric (DHq-ROFHWG) operator, the dual hesitant q-rung orthopair fuzzy Hamacher ordered weighted average (DHq-ROFHOWA) operator, the dual hesitant q-rung orthopair fuzzy Hamacher ordered weighting geometric (DHq-ROFHOWG) operator, the dual hesitant q-rung orthopair fuzzy Hamacher hybrid average (DHq-ROFHHA) operator, and the dual hesitant q-rung orthopair fuzzy Hamacher hybrid geometric (DHq-ROFHHG) operator. The precious merits and some particular cases of above mentioned aggregation operators are briefly introduced. In the end, an actual application for scheme selection of construction project is provided to testify the proposed operators and deliver a comparative analysis. [ABSTRACT FROM AUTHOR]