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This study focuses on optimizing offshore drilling operations through Multi-Criteria Decision-Making (MCDM). It recognizes MCDM as a crucial framework for evaluating alternatives in the complex offshore drilling landscape. The objective is to identify the most suitable alternative among four approaches: Advanced Drilling Technologies, Drilling Process Optimization, Human Factors and Safety Enhancement, and Environmental Impact Mitigation. Evaluation criteria include Operational Efficiency, Safety Performance, Environmental Impact, and Cost-effectiveness. The research aims to contribute insights and recommendations for stakeholders in the offshore oil and gas industry. In the field of information aggregation and fusion, there is a growing interest among researchers in the domain of probabilistic linguistic expression sets, which are particularly effective in consolidating uncertain data. This article aims to explore various methodologies for information aggregation using probabilistic linguistic expressions. To achieve this goal, we have introduced procedural principles based on the Dombi (D) framework, specifically designed for managing probabilistic linguistic term elements (PLTEs). These principles are firmly grounded in both the product and sum of Dombi operations. As a result, we have developed a range of techniques for probabilistic linguistic aggregation, including entities such as the Probabilistic Linguistic Dombi Average (PLDA) and the Probabilistic Linguistic Dombi Geometric (PLDG). Additionally, we have created weighted aggregation operators (AOs) such as PLDWA and PLDWG, along with ordered AOs like PLDOWA and PLDOWG. By utilizing the D $\tau $ -norm and $\tau $ -conorm, we have designed versatile aggregation tools that support information reinforcement in both ascending and descending directions. Furthermore, we provide a comparative analysis between our proposed methodologies and the MARCOS approach. Additionally, we offer a detailed explanation of the distinctive attributes associated with these operators. Through the application of PLDA, PLDG, PLDWA, PLDWG, PLDOWA, and PLDOWG, we present strategies for effectively integrating probabilistic linguistic term sets (PLTs) into the realm of MCDM.

The paper aims are to impersonate some robust sine-hyperbolic operations laws to determine the group decision-making process under the fractional orthotriple linear Diophantine fuzzy set (FOLDFS) situation. The FOLDFS has a notable feature to trade with the dubious information with a broader membership representation space than the Spherical fuzzy set. Based on it, the present paper is classified into three phases. The first phase is to introduce new operational laws for FOLDFS using Dombi operational laws. The main idea behind the proposed operations is to incorporate the qualities of the sine hyperbolic function, namely periodicity and symmetric about the origin towards the decisions of the objects. Secondly, based on these laws, numerous operators (sine hyperbolic fractional orthotriple linear Diophantine fuzzy Dombi weighted averaging, sine hyperbolic fractional orthotriple linear Diophantine fuzzy Dombi ordered weighted averaging, sine hyperbolic fractional orthotriple linear Diophantine fuzzy Dombi hybrid averaging, sine hyperbolic fractional orthotriple linear Diophantine fuzzy Dombi weighted geometric, sine hyperbolic fractional orthotriple linear Diophantine fuzzy Dombi ordered weighted geometric, sine hyperbolic fractional orthotriple linear Diophantine fuzzy Dombi hybrid geometric) to aggregate the information are acquired along with their requisite properties and relations. Finally, an algorithm to interpret the multi-attribute group decision making problem is outlined based on the stated operators and manifest it with an illustrative example. A detailed comparative interpretation is achieved with some of the existing methods to reveal their influences.

Atanassov presented the dominant notion of intuitionistic fuzzy sets which brought revolution in different fields of science since their inception. The operations of t-norm and t-conorm introduced by Dombi were known as Dombi operations and Dombi operational parameter possesses natural flexibility with the resilience of variability. The advantage of Dombi operational parameter is very important to express the experts' attitude in decision-making. This study aims to propose intuitionistic fuzzy rough TOPSIS method based on Dombi operations. For this, first we propose some new operational laws based on Dombi operations to aggregate averaging and geometric aggregation operators under the hybrid study of intuitionistic fuzzy sets and rough sets. On the proposed concept, we present intuitionistic fuzzy rough Dombi weighted averaging, intuitionistic fuzzy rough Dombi ordered weighted averaging, and intuitionistic fuzzy rough Dombi hybrid averaging operators. Moreover, on the developed concept, we present intuitionistic fuzzy rough Dombi weighted geometric, intuitionistic fuzzy rough Dombi ordered weighted geometric, and intuitionistic fuzzy rough Dombi hybrid geometric operators. The basic related properties of the developed operators are presented in detailed. Then the algorithm for MCGDM based on TOPSIS method for intuitionistic fuzzy rough Dombi averaging and geometric operators is presented. By applying accumulated geometric operator, the intuitionistic fuzzy rough numbers are converted into the intuitionistic fuzzy numbers. The massive outbreak of the pandemic COVID-19 promoted the challenging scenario for the world organizations including scientists, laboratories, and researchers to conduct special clinical treatment strategies to prevent the people from COVID-19 pandemic. Additionally, an illustrative example is proposed to solve MCGDM problem to diagnose the most severe patient of COVID-19 by applying TOPSIS. Finally, a comparative analysis of the developed model is presented with some existing methods which show the applicability and superiority of the developed model. [ABSTRACT FROM AUTHOR]

In recent decades, robotics and automation technologies play an emerging role in the area of agriculture development. In the present communication, the concept of digital farming in terms of robotic agrifarming has been considered to be a multi-criteria decision-making problem under conflicting criteria and uncertain information availability. The notion of score/accuracy function of picture fuzzy soft number and picture fuzzy soft Dombi aggregation operators (weighted/ordered weighted average, hybrid/weighted geometric) have been introduced along with various operational laws and properties. Further, for the sake of providing a larger space to the decision makers and including the parametrization feature of the imprecise information, the traditional EDAS (Evaluation Based On Distance from average Solution) methodology has been modified and presented in the light of the proposed score/accuracy function and the introduced Dombi aggregation operators. In addition to this, an illustrative example related to digital farming has been studied in detail showing that the proposed methodology is highly helpful in finding the best alternative in order to have sustainable farming among various types of agrifarming. In order to understand the feasibility, loftiness and dependability of the proposed modified EDAS methodology, the comparative remarks and advantages have been listed for better understanding and readability with some existing MCDM approaches. [ABSTRACT FROM AUTHOR]

The operations proposed by Dombi based on t-norn (TN) and t-corom (TCN) are generally known as Dombi operations, which offer versatility in the working behavior of parameters. Over the last decade, group decision-making has been a very active research field. Especially, the development of new operational rules, aggregation operators, and multi-attribute group decision-making techniques based on these rules and operators have recently piqued the interest of scientists. Acknowledging the importance of t-spherical fuzzy sets and linguistic variable in this paper, firstly, we define the notion of linguistic T-spherical fuzzy set (Lt-SFS) where membership degree, abstinence degree and non-membership degree are presented in the form of linguistic variables. Dombi operations, score function, accuracy function for linguistic T-spherical fuzzy numbers (Lt-SFNs) are defined and some prominent properties of Dombi operations are then investigated. Furthermore, two aggregations operators based on Dombi operations namely, linguistic t-spherical fuzzy Dombi weighted averaging operator and linguistic t-spherical fuzzy Dombi weighted geometric operator are also developed. At that point, these Dombi operators are used to establish an extension of the technique for order of preference by similarity to ideal solution (TOPSIS) method, and a multi-attribute group decision-making approach is proposed to solve decision-making problems which is the key innovation of this paper. Finally, we apply the proposed technique for the selection of the best variety of maize and a comparison analysis is provided to demonstrate its applicability and feasibility. [ABSTRACT FROM AUTHOR]

The aim of the paper is to find most optimistic results from among uncertain information or vague data. We theoretically use the notion of neutrosophic cubic sets to create enhanced decision-making models for multi-criteria. The advantage of neutrosophic cubic sets is that it comprehends the knowledge of neutrosophic sets and interval valued neutrosophic sets. Aggregation operators are used to retrieve the core information from a collection of data. So, this research executes aggregation operators for neutrosophic cubic sets dynamically. In this paper we avail the aid of hamy mean and dombi operations to establish fuzzy dombi hamy mean aggregation operators for neutrosophic cubic sets. This paper also explains the algebraic sum and scalar multiplication operations. A decision making methodology has been generated to prove the necessity of the proposed operators. Finally an illustration is provided from a real life decision making situation.

In this paper, a new set of intuitionistic fuzzy aggregation operators have been introduced under the environment of intuitionistic fuzzy sets (IFSs). For this, firstly focused on some existing aggregation operators and then new operational rules known as Dombi operation have been pro- posed which make the advancement of flexibility behavior with the parameter. Based on Dombi operation laws, some new averaging and geometric aggregation operators namely, intuitionistic fuzzy Dombi weighted averaging, ordered weighted averaging and hybrid weighted averaging operator, classified as IFDWA, IFDOWA and IFDHWA operators respectively and intuitionistic fuzzy Dombi geometric, ordered weighted geometric and hybrid weighted geometric operators, labeled as IFDWG, IFDOWG and IFDHWG operators respectively have been proposed. Further, some properties such as idempotency, boundedness, monotonicity and commutative are investigated. Finally, a multi-attribute decision-making model has been developed for the proposed operators to select the best mutual fund for investment. The execution of the comparative study has been examined with the existing operators in this environment.

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]

This paper proposes a new effective tool to address complex multicriteria decision-making problems where all decision-making information is provided by decision makers in both the trapezoidal neutrosophic environment and the bipolar neutrosophic environment. Relatedly, the concepts and operating laws of the bipolar trapezoidal neutrosophic set are defined. Some priority aggregate operators for the aggregation of bipolar trapezoidal neutrosophic information are discussed. In addition, priority aggregation operators based on Dombi operations are developed: bipolar trapezoidal neutrosophic Dombi weighted averaging operator and bipolar trapezoidal neutrosophic Dombi weighted geometric operator. The desirable properties of these operators and the relationship between them are investigated. Two approaches are proposed to address multiple criteria for decision-making problems in the bipolar trapezoidal neutrosophic environment. The sensitivity of the proposed approaches is analyzed using examples, and a multiple comparison test is conducted to demonstrate their effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, Bonferroni mean (BM) and Dombi t‐conorms and t‐norms (Dt‐CN&t‐Ns) are combined under dual hesitant q‐rung orthopair fuzzy (DHq‐ROF) environment to produce DHq‐ROF‐Dombi BM, weighted Dombi BM, Dombi geometric BM, and Dombi weighted geometric BM aggregation operators (AOs). Using these operators, the decision making processes would become more flexible and also would possess the capabilities of capturing interrelationships among input arguments under imprecise decision making environments. Apart from those, a large number of AOs either already developed or not yet developed may also be derived from the proposed AOs. In the process of developing the AOs, some operational laws of DHq‐ROF numbers based on Dt‐CN&t‐Ns are defined first. Several important properties of the developed operators are discussed. The proposed AOs are used to frame a new methodology to solve multicriteria group decision making problems under DHq‐ROF contexts. Several illustrative examples are solved to demonstrate effectiveness and benefits of the developed method. Sensitivity analysis is performed to show the variations of ranking values with the change of different parameters in the decision making contexts. Finally, the introduced method is compared with several existing techniques to establish superiority and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The Dombi operators provide a flexible structure with its adjustable parameter because of Dombi generalized structure. On the other hand, priority aggregation operators play an important role in expressing the importance level of alternatives and attributes. In this study, novel Dombi prioritized aggregations are developed on q-rung orthopair fuzzy sets (q-ROFSs). The q-ROFSs include many fuzzy sets with dynamically changing q parameters. q-ROFSs include intuitionistic fuzzy sets, Pythagorean fuzzy sets and Fermatean fuzzy sets according to value of q parameter. In this study, Dombi prioritized aggregation of q-ROFSs is presented. The operators introduced are q-ROFSs Dombi prioritized weighted averaging operator (q-ROFSDPWA) and q-ROFSs Dombi prioritized weighted geometric operator (q-ROFSDPWG). We also investigate some of the properties of these operators. The proposed operators are used in MULTIMOORA method. The proposed methods with new aggregation operators are analyzed according to the q parameter of q-ROFSs and Dombi parameter on numerical example and also compared with other existing studies. It is seen that novel q-ROFSDPWA and q-ROFSDPWG aggregations give reasonable and stable results for multiple criteria decision making problem. [ABSTRACT FROM AUTHOR]

The aim of the paper is to find most optimistic results from among uncertain information or vague data. We theoretically use the notion of neutrosophic cubic sets to create enhanced decision-making models for multi-criteria. The advantage of neutrosophic cubic sets is that it comprehends the knowledge of neutrosophic sets and interval valued neutrosophic sets. Aggregation operators are used to retrieve the core information from a collection of data. So, this research executes aggregation operators for neutrosophic cubic sets dynamically. In this paper we avail the aid of hamy mean and dombi operations to establish fuzzy dombi hamy mean aggregation operators for neutrosophic cubic sets. This paper also explains the algebraic sum and scalar multiplication operations. A decision making methodology has been generated to prove the necessity of the proposed operators. Finally an illustration is provided from a real life decision making situation. [ABSTRACT FROM AUTHOR]

In this paper, a new set of intuitionistic fuzzy aggregation operators have been introduced under the environment of intuitionistic fuzzy sets (IFSs). For this, firstly focused on some existing aggregation operators and then new operational rules known as Dombi operation have been pro- posed which make the advancement of flexibility behavior with the parameter. Based on Dombi operation laws, some new averaging and geometric aggregation operators namely, intuitionistic fuzzy Dombi weighted averaging, ordered weighted averaging and hybrid weighted averaging operator, classified as IFDWA, IFDOWA and IFDHWA operators respectively and intuitionistic fuzzy Dombi geometric, ordered weighted geometric and hybrid weighted geometric operators, labeled as IFDWG, IFDOWG and IFDHWG operators respectively have been proposed. Further, some properties such as idempotency, boundedness, monotonicity and commutative are inves- tigated. Finally, a multi-attribute decision-making model has been developed for the proposed operators to select the best mutual fund for investment. The execution of the comparative study has been examined with the existing operators in this environment. [ABSTRACT FROM AUTHOR]

Algebraic operations are used effectively in decision-making problems. Especially, Dombi, Hamacher and Einstein algebraic operators are used frequently in the decision-making field. On the other hand, it is known that aggregation operators affect the decision-making process in decision-making problems. In this paper, we used Dombi operations to develop some Fermatean fuzzy aggregation operators. Arithmetic and geometric analysis of each aggregation method were performed. We defined the following operators: Fermatean fuzzy Dombi weighted average operator, Fermatean fuzzy Dombi weighted geometric operator, Fermatean fuzzy Dombi ordered weighted average operator, Fermatean fuzzy Dombi ordered weighted geometric operator, Fermatean fuzzy Dombi hybrid weighted average operator, Fermatean fuzzy Dombi hybrid weighted geometric operator. Also, an analysis was performed for the beta value of the Dombi parameter. Properties of proposed operators were presented, and operators were defined on Fermatean fuzzy sets. Finally, proposed operators were compared with the existing aggregation operators. To understand the impact of the proposed operators on the decision-making process, Fermatean fuzzy TOPSIS was established. [ABSTRACT FROM AUTHOR]

In this article, used Dombi t-norm (TN) and t-conorm (TCN) which can generate more complex and more flexible operation rules by adjusting a parameter to combine with prioritized aggregation operators (AOs) in bipolar fuzzy (BF) environment. In this study, introduced bipolar fuzzy Dombi prioritized AOs, namely bipolar fuzzy Dombi prioritized averaging operator, bipolar fuzzy Dombi geometric operator, bipolar fuzzy Dombi prioritized weighted averaging operator and bipolar fuzzy Dombi prioritized weighted geometric operator as these operators along with proofs to aggregate various preferences of the decision makers. In this purpose, we designed a multiple attribute decision-making technique for the proposed study. Finally, an illustrative example is given to demonstrate proposed approach under BF environment and a sensitivity analysis is considered for the working parameter on the ordering of the alternatives. A comparative study is provided for the choice best decision of the proposed approach with the existing problems. Finally, it is concluded that the proposed approach gives a more practical nature to aggregate the information process during the data analysis, and hence they take an alternative way for solving decision-making problems. [ABSTRACT FROM AUTHOR]

The choice of green suppliers involves a large amount of inaccurate, incomplete, and inconsistent information, and the single-valued triangular Neutrosophic number that is an extension of the single-valued Neutrosophic number can effectively handle such problems. Considering the advantages of the single-valued triangular Neutrosophic number, this paper proposes a new aggregate operator to solve the problem of multi-criteria decision making. The new aggregate operator takes into account the priority relationship and the interrelationship between the criteria. To make the new aggregate operator more flexible, this paper introduces the Dombi operations. This paper combines the Dombi operations with the prioritized average operator and the Bonferroni mean operator to propose the single-valued triangular Neutrosophic Dombi prioritized normalized Bonferroni mean (SVTNDPNBM) operator. Finally, the SVTNDPNBM operator is applied to the problem of the green supplier selection, which proves its feasibility and stability.

The operations of t‐norm (TN) and t‐conorm (TCN), developed by Dombi, are generally known as Dombi operations, which have an advantage of flexibility within the working behavior of parameter. In this paper, we use Dombi operations to construct a few Q‐rung orthopair fuzzy Dombi aggregation operators: Q‐rung orthopair fuzzy Dombi weighted average operator, Q‐rung orthopair fuzzy Dombi order weighted average operator, Q‐rung orthopair fuzzy Dombi hybrid weighted average operator, Q‐rung orthopair fuzzy Dombi weighted geometric operator, Q‐rung orthopair fuzzy Dombi order weighted geometric operator, and Q‐rung orthopair fuzzy Dombi hybrid weighted geometric operator. The different features of these proposed operators are reviewed. At that point, we have used these operators to build up a model to solve the multiple‐attribute decision making issues under Q‐rung orthopair fuzzy environment. Ultimately, a realistic instance is stated to substantiate the created model and to exhibit its applicability and viability. [ABSTRACT FROM AUTHOR]

The operations of t-norm and t-conorm introduced by Dombi was known as Dombi operations can have a lead of good flexibility with the general parameter. The Dombi operations have so far not yet been applied for bipolar fuzzy sets. Motivated from Dombi operations, we have proposed bipolar fuzzy Dombi weighted averaging operator, bipolar fuzzy Dombi order weighted averaging operator, bipolar fuzzy Dombi hybrid weighted averaging operator, bipolar fuzzy Dombi weighted geometric operator , bipolar fuzzy Dombi order weighted geometric operator and bipolar fuzzy Dombi hybrid weighted geometric operator as these operators have good advantage of flexibility in operational behavior. Many properties of these operators are investigated. Then, we developed a model for multiple attribute decision-making problem for bipolar fuzzy Dombi aggregation operators under the bipolar fuzzy environment. Finally, a practical example for selection of investment alternatives is given to demonstrate for the utility and application of the proposed work. [ABSTRACT FROM AUTHOR]

The operations of t‐norm and t‐conorm, developed by Dombi, were generally known as Dombi operations, which may have a better expression of application if they are presented in a new form of flexibility within the general parameter. In this paper, we use Dombi operations to create a few Pythagorean fuzzy Dombi aggregation operators: Pythagorean fuzzy Dombi weighted average operator, Pythagorean fuzzy Dombi order weighted average operator, Pythagorean fuzzy Dombi hybrid weighted average operator, Pythagorean fuzzy Dombi weighted geometric operator, Pythagorean fuzzy Dombi order weighted geometric operator, and Pythagorean fuzzy Dombi hybrid weighted geometric operator. The distinguished feature of these proposed operators is examined. At that point, we have used these operators to build up a model to remedy the multiple attribute decision‐making issues under Pythagorean fuzzy environment. Ultimately, a realistic instance is stated to substantiate the created model and to exhibit its applicability and viability. [ABSTRACT FROM AUTHOR]

In the process of talent selection and evaluation, it is important to know the personality traits, ability, knowledge level, and development potential of the candidates. However, the above evaluation indicators are difficult to describe with precise values, and personnel evaluation often needs to be done through group decision making (GDM). In this paper, we establish a GDM method under the interval‐valued intuitionistic fuzzy (IVIF) environment based on Dombi aggregation operations, which are the extension of existing operations. First, IVIF operations are introduced. Second, a series of IVIF Dombi aggregation operators are proposed, such as IVIF Dombi weighted averaging operator, IVIF Dombi‐ordered weighted averaging (IIFDOWA) operator, IVIF Dombi geometric weighted geometric (IIFDWG) operator, and IVIF Dombi‐ordered weighted geometric (IIFDOWG). The desirable properties of these proposed aggregation operators are well studied. Finally, the GDM method based on these Dombi aggregation operators under the IVIF environment is presented; the case study about personnel evaluation based on the proposed method is presented to show its validity and rationality. The comparison with other methods is presented to show the difference and advantage of the GDM method proposed in this paper. [ABSTRACT FROM AUTHOR]

Abstract The operations of t -norm and t -conorm, developed by Dombi, were generally known as Dombi operations which may have a better expression of application if they are presented in a new form of flexibility within the general parameter. To the best of our knowledge, Dombi operations are yet to be applied in exhibiting picture fuzzy sets in an appropriate form and shape. Inspired by the established theory of Dombi operations and by applying picture fuzzy numbers (PFNs), in the present study, we propose picture fuzzy Dombi weighted average (PFDWA) operator, picture fuzzy Dombi order weighted average (PFDOWA) operator, picture fuzzy Dombi hybrid weighted average (PFDHWA) operator, picture fuzzy Dombi weighted geometric (PFDWG) operator, picture fuzzy Dombi order weighted geometric (PFDOWG) operator and picture fuzzy Dombi hybrid weighted geometric (PFDHWG) operator in a new light. These aforesaid operators are enormously used in the operational parameter to help a successful solution of the given problem. Here in our endeavored study, we develop a model for picture fuzzy Dombi aggregation operators to solve multiple attribute decision making (MADM) methods in an updated way. And at the end of our study a practical application of the deducted decision over investment alternatives is reported in accordance with the enjoyment or utility of the proposed work. Highlights • Present Dombi t -norm and Dombi t -conorm operations of the picture fuzzy set. • Define picture fuzzy Dombi arithmetic/ geometric aggregation operators. • Study some desired properties of these aggregation operators. • Develop a model for these operators to solve multiple attribute decision making method. • One numerical example is provided to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

The neutrosophic cubic set can describe complex decision-making problems with its single-valued neutrosophic numbers and interval neutrosophic numbers simultaneously. The Dombi operations have the advantage of good flexibility with the operational parameter. In order to solve decision-making problems with flexible operational parameter under neutrosophic cubic environments, the paper extends the Dombi operations to neutrosophic cubic sets and proposes a neutrosophic cubic Dombi weighted arithmetic average (NCDWAA) operator and a neutrosophic cubic Dombi weighted geometric average (NCDWGA) operator. Then, we propose a multiple attribute decision-making (MADM) method based on the NCDWAA and NCDWGA operators. Finally, we provide two illustrative examples of MADM to demonstrate the application and effectiveness of the established method. [ABSTRACT FROM AUTHOR]

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

A linguistic cubic variable (LCV) is comprised of interval linguistic variable and single-valued linguistic variable. An LCV contains decision-makers’ uncertain and certain linguistic judgments simultaneously. The advantage of the Dombi operators contains flexibility due to its changeable operational parameter. Although the Dombi operations have been extended to many studies to solve decision-making problems; the Dombi operations are not used for linguistic cubic variables (LCVs) so far. Hence, the Dombi operations of LCVs are firstly presented in this paper. A linguistic cubic variable Dombi weighted arithmetic average (LCVDWAA) operator and a linguistic cubic variable Dombi weighted geometric average (LCVDWGA) operator are proposed to aggregate LCVs. Then a multiple attribute decision making (MADM) method is developed in LCV setting on the basis of LCVDWAA and LCVDWGA operators. Finally, two illustrative examples about the optimal choice problems demonstrate the validity and the application of this method.

The Sine Hyperbolic q-rung orthopair fuzzy sets (sinh -q-ROFSs) are the important concept of accepting more uncertainty than the q-rung orthopair fuzzy sets (q-ROFSs). The well-known sine hyperbolic function preserves the origin's periodicity and symmetric existence, and so fulfills the expert's expectations for the multi-time process' parameters. The aim of this study is to offer some robust sine hyperbolic Dombi operation laws (sinh DOLs) for q-ROFSs in order to preserve these qualities and the significance of sinh -q-ROFSs. Score and accuracy functions for the sinh -q-ROFSs' are also defined. We define a number of new averaging/geometric aggregation operators (AOs) based on Dombi t-norm and conorm operations. The fundamental properties of the defined operators were discussed. Then, using defined AOs, we provide a group decision-making (DM) approach for solving DM problems. We demonstrate a numerical example to verify the defined method. • We develop a new approach to fuzzy set which is called Sine Hyperbolic q-rung orthopair fuzzy sets. • The sine hyperbolic Dombi aggregation operators. • The fundamental properties of the defined aggregation operators. • Develop a decision making models based on proposed aggregation operators. • The comparison analysis show the effective and reliability of the proposed model. [ABSTRACT FROM AUTHOR]

Multi-attribute decision-making (MADM) is commonly used to investigate fuzzy information effectively. However, selecting the best alternative information is not always symmetric because the alternatives do not have complete information, so asymmetric information is often involved. Expressing the information under uncertainty using closed subintervals of [0, 1] is beneficial and effective instead of using crisp numbers from [0, 1]. The goal of this paper is to enhance the notion of Dombi aggregation operators (DAOs) by introducing the DAOs in the interval-valued T-spherical fuzzy (IVTSF) environment where the uncertain and ambiguous information is described with the help of membership grade (MG), abstinence grade (AG), non-membership grade (NMG), and refusal grade (RG) using closed sub-intervals of [0, 1]. One of the key benefits of the proposed work is that in the environment of information loss is reduced to a negligible limit. We proposed concepts of IVTSF Dombi weighted averaging (IVTSFDWA) and IVTSF Dombi weighted geometric (IVTSFDWG) operators. The diversity of the IVTSF DAOs is proved and the influences of the parameters, associated with DAOs, on the ranking results are observed in a MADM problem where it is discussed how a decision can be made when there is asymmetric information about alternatives. [ABSTRACT FROM AUTHOR]

This study aims to introduce a series of novel distance measures of an intuitionistic fuzzy set and an extended Multi-attributive Border Approximation Area Comparison method to address multi-criteria group decision-making problems. To aggregate the intuitionistic fuzzy information, we propose two aggregation operators, namely, the intuitionistic fuzzy Dombi generalised λ -Shapley Choquet arithmetical average operator and intuitionistic fuzzy Dombi generalised λ -Shapley Choquet geometric average operator. These aggregation operators consider the importance of combinations and correlations among combinations of input arguments. Furthermore, an illustrative example of a human resource management problem is presented to verify the effectiveness of the proposed method, and sensitivity and comparison analyses are conducted to demonstrate the technique's stability and advancements. Finally, conclusions are drawn. [ABSTRACT FROM AUTHOR]

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

Keeping in 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]

A linguistic cubic variable (LCV) is comprised of interval linguistic variable and single-valued linguistic variable. An LCV contains decision-makers' uncertain and certain linguistic judgments simultaneously. The advantage of the Dombi operators contains flexibility due to its changeable operational parameter. Although the Dombi operations have been extended to many studies to solve decision-making problems; the Dombi operations are not used for linguistic cubic variables (LCVs) so far. Hence, the Dombi operations of LCVs are firstly presented in this paper. A linguistic cubic variable Dombi weighted arithmetic average (LCVDWAA) operator and a linguistic cubic variable Dombi weighted geometric average (LCVDWGA) operator are proposed to aggregate LCVs. Then a multiple attribute decision making (MADM) method is developed in LCV setting on the basis of LCVDWAA and LCVDWGA operators. Finally, two illustrative examples about the optimal choice problems demonstrate the validity and the application of this method. [ABSTRACT FROM AUTHOR]