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In the face of practical problems such as the increasing demand for shared bicycles and the number of faulty vehicles which are hard to handle and repair in time, shared bicycles operators tend to outsource recycling services to suppliers. To solve the problem of recycling supplier selection, this paper constructs a novel evaluation index system involving the three traditional dimensions and introduces an interval-valued Pythagorean fuzzy (IVPF) hybrid weighted decision-making model based on the self-confidence level. Subsequently, the self-confidence IVPF hybrid weighted average geometric operator and self-confidence IVPF ordered hybrid weighted average geometric operator are proposed by integrating the self-confidence level of experts, the superiority of the weighted and geometric average rules. The significant merit of the developed operators is that they can incorporate the self-confidence level of the expert as well as effectively combine the characteristics of the weighted and geometric average mechanism. A multi-attribute decision-making (MADM) framework is then constructed by using the proposed aggregation approach. Finally, on the basis of the established evaluation index system, a case concerning the green recycling supplier selection of shared bicycles is applied to display the superiority and practicability of the presented method.

The most important influence of this assessment is to analyze some new operational laws based on confidential levels (CLs) for complex Pythagorean fuzzy (CPF) settings. Moreover, to demonstrate the closeness between finite numbers of alternatives, the conception of confidence CPF weighted averaging (CCPFWA), confidence CPF ordered weighted averaging (CCPFOWA), confidence CPF weighted geometric (CCPFWG), and confidence CPF ordered weighted geometric (CCPFOWG) operators are invented. Several significant features of the invented works are also diagnosed. Moreover, to investigate the beneficial optimal from a large number of alternatives, a multi-attribute decision-making (MADM) analysis is analyzed based on CPF data. A lot of examples are demonstrated based on invented works to evaluate the supremacy and ability of the initiated works. For massive convenience, the sensitivity analysis and merits of the identified works are also explored with the help of comparative analysis and they're graphical shown.

Multiattribute decision making (MADM) approach is a well-known decision-making process utilized in a variety of fields such as solid waste management, renewable energy resources, air quality assurance, hotel location decision, sustainable supplier selection, partner recognition, green supplier enterprises, game theory, construction development authority, and weapon group target estimation. The aggregation operators (AOs) are essential components of the decision-making process and have a great capability to deal with ambiguous and unpredictable information in the different fields of fuzzy environments. In this article, we expressed the theory concepts of single-valued neutrosophic (SVN) sets (SVNS) and also characterized their basic operations. The power aggregation tools are allowed to input arguments to support each other among different arguments. Recently, Aczel–Alisna aggregation tools conquered great attention from several research scholars. We also exposed some reliable operations of Aczel–Alsina aggregation models under the consideration of SVN information. We established a series of new approaches, including the "single-valued neutrosophic Aczel–Alsina power weighted average" (SVNAAPWA) operator and "single-valued neutrosophic Aczel–Alsina power weighted geometric" (SVNAAPWG) operators. To show the effectiveness and compatibility of derived approaches, some prominent characteristics are also established. We constructed a MADM technique to solve an application of engineering and construction materials under consideration of our derived methodologies. An experimental case study is also presented to determine a suitable optimal option from a group of options. To find the flexibility of our proposed work, we provided a comparative study that compares the results of existing AOs with our proposed work. A comprehensive overview is also presented here. [ABSTRACT FROM AUTHOR]

Multiple-attribute group decision-making (MAGDM) technique is often used to make decisions when several optimal options are under consideration. It can be difficult to select a reasonable optimal option for the decision maker under consideration of insufficient information. The theory of Hamy mean (HM) operators are used to express correlation among different input arguments and provide a smooth approximation during the decision-making process. Recently, Aczel Alsina aggregating expressions gained a lot of attention from numerous mathematicians under different fuzzy circumstances. This article aims to illustrate the notion of a Pythagorean fuzzy (PyF) set (PyFS) with some restricted constraints, such as a sum of the square of truth membership value and falsity membership value. We developed a series of new approaches under consideration of the HM tools, including PyF Aczel Alsina Hamy mean (PyFAAHM), and PyF Aczel Alsina weighted Hamy mean (PyFAAWHM) operators. Further, we also extend the theory of Dual Hamy mean (DHM) operators and derived a series of new methodologies such as PyF Aczel Alsina Dual Hamy mean (PyFAADHM) and PyF Aczel Alsina weighted Dual Hamy mean (PyFAAWDHM) operators. To demonstrate the flexibility of our derived approaches, we illustrate an application of a multinational company considering the MAGDM technique. An experimental case study is also illustrated to evaluate a reasonable option from a group of options. We see the advantages and compatibility of our findings by comparing the results of existing approaches with the results of currently discussed methodologies. [ABSTRACT FROM AUTHOR]

Advancement in mobile phone (MP) technology has revolutionized the lifestyle. In recent years, we observed that MP technology had been involved in almost all aspects of life, such as communication purposes, e-commerce, mobile baking, and social media connectivity. So, it becomes a hot research topic to select the best MP that fulfills the desired feathers requirement. In this paper, the expert's familiarity with the examined objects is factored into the initial judgments under the T-spherical fuzzy sets (T-SFSs) environment. The T-SFS is the extension of the picture fuzzy (PF) set (PFS), which gives wider scope for finding the most precise options than existing fuzzy frameworks. The multiattribute decision-making (MADM) is a common and valuable method for aggregating information. For MADM, various aggregation operators (AOs) have been created over the years. The article introduces the newly proposed approach T-spherical fuzzy (T-SF) confidence level weighted averaging T − SFWA c and T-SF confidence level weighted geometric T − SFWG c . Also, some desired properties of AOs are discussed, and the T-SF entropy measure is introduced for selecting the weight criteria. A MADM framework is introduced, on the behalf of proposed operators. The proposed MADM framework is applied to solve the real-life example of consumers' preferences to show effectiveness and practicality. Lastly, the developed framework is set side by side with other prevailing approaches to demonstrate the superiority and significance of other existing AOs. [ABSTRACT FROM AUTHOR]

A T-spherical fuzzy set (TSFS) is an extended and logical algebraic representation to handle uncertainty, with the help of four functions describing four possible aspects of uncertain information. Aczel-Alsina triangular norm (TN) and conorm (TCN) are novel and proved to be more efficient than other existing TNs and TCNs. In our article, we establish the concept of a T-spherical fuzzy Aczel-Alsina graph (TSFAAG). We described the energy of TSFAAG along with the splitting and shadow energy of TSFAAG. Furthermore, we figured out the Randić energy of TSFAAG and obtained some useful results. Moreover, we give the notion of the Aczel-Alsina digraph (TSFAADG). To see the significance of the proposed TSFAADGs, we employed the energy and Randić energy of TSFAADGs for solving the problem of selecting the best investing company by using a decision-making algorithm. The sensitivity analysis of the variable parameters is also discussed and where the effect on ranking results is studied. To see the effectiveness of the proposed work, we did a comparative study and established some remarks. [ABSTRACT FROM AUTHOR]

The Multi-attribute decision-making (MADM) approaches are utilized to aggregate ambiguous and imprecise information based on different aggregation operators (AOs). The aim of this article is to explore the notion of single-valued neutrosophic (SVN) set (SVNS), wich is the modified structure of an intuitionistic fuzzy sets and picture fuzzy sets. Some appropriate operations of Aczel Alsina tools under the system of SVN information are also presented. By using the theory of prioritization aggregation model, we developed a class of new approaches including SVN Aczel Alsina prioritized average (SVNAAPA) and SVN Aczel Alsina prioritized geometric (SVNAAPG) operators. We also presented a series of new methodologies in the light of SVN information such as SVN Aczel Alsina prioritized weighted average (SVNAAPWA), and SVN Aczel Alsina prioritized weighted geometric (SVNAAPWG) operators. To verify discussed aggregation approaches, we also presented some notabe characteristics. We established a MADM technique to solve complexities and difficulties during decision-making in our real-life problems. By utilizing a practical numerical example to select an appropriate research scientist for the vacant post of a public university. To find the validity and flexibility of our invented approaches, sensitive analysis, and comparative study by comparing the results of existing approaches with currently proposed aggregation techniques. [ABSTRACT FROM AUTHOR]

T-spherical fuzzy (TSF) set is a suitable technique for depicting uncertain and vague information in real-life problems because it covered the truth, abstinence, falsity, and refusal grade with a suitable characteristic that is the sum of the q-power of the truth, abstinence, and falsity grades will be contained in the unit interval. The major objective of this article is to evaluate the novel theory of interaction operational laws for TSF information. Additionally, power Bonferroni mean (PBM) operators are the combination of two existing ideas such as Bonferroni and power aggregation operator and because of this reason, they are more general than the bundle of existing ideas. Inspired by the above valuable knowledge, we derive the PBM operators based on interaction operation laws for TSF values such as the TSF interaction PBM (TSFIPBM) operator and TSF weighted interaction PBM (TSFWIPBM) operator. Some special cases and the properties of the invented techniques are also examined. Furthermore, for addressing some real-life problems, we derive the multi-attribute decision-making (MADM) method in the consideration of the presented technique to enhance the stability and supremacy of the evaluated techniques. Finally, for comparing the proposed techniques with prevailing methods, we illustrate some numerical examples to show the supremacy and effectiveness of the derived theory. [ABSTRACT FROM AUTHOR]

To imitate the uncertainty and ambiguity in various decision-making problems, the T-spherical fuzzy set is more pragmatic and influential than the picture fuzzy set and q-rung orthopair fuzzy set. Because of the vagueness and fuzziness found in real-life problems, in which intuitionistic fuzzy sets may not give adequate results, the T-spherical fuzzy set is an efficient mathematical model to deal with them and can be handled effectively by using the notion of T-spherical fuzzy sets. In a different framework which is based on more opinions like yes, no, refusal, and abstaining, the T-spherical fuzzy set has been proven to be the most beneficial. In this article, we proposed the idea of T-spherical fuzzy Hamacher graphs (TSFHGs) based on Hamacher t-norm and t-conorm. We investigate the notion of the energy of TSFHGs, splitting TSFHGs, and shadow TSFHGs. Further, we introduce the Randić energy of TSFHG and studied its fundamental results. Moreover, we introduced the T-spherical fuzzy Hamacher digraphs (TSFHDGs) and discussed various results. We studied the applications of the proposed energies of TSFHGs in a decision-making problem by using an algorithm involving TSFHDGs and Hamacher aggregation operators. We also established a comparative study to see the significance of our proposed results. [ABSTRACT FROM AUTHOR]

A T-spherical fuzzy set is a more powerful mathematical tool to handle uncertain and vague information than several fuzzy sets, such as fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, q-rung orthopair fuzzy set, and picture fuzzy set. The Aczel–Alsina t-norm and s-norm are significant mathematical operations with a high premium on affectability with parameter activity, which are extremely conducive to handling imprecise and undetermined data. On the other hand, the Hamy mean operator is able to catch the interconnection among multiple input data and achieve great results in the fusion process of evaluation information. Based on the above advantages, the purpose of this study is to propose some novel aggregation operators (AOs) integrated by the Hamy mean and Aczel–Alsina operations to settle T-spherical fuzzy multi-criteria decision-making (MCDM) issues. First, a series of T-spherical fuzzy Aczel–Alsina Hamy mean AOs are advanced, including the T-spherical fuzzy Aczel–Alsina Hamy mean (TSFAAHM) operator, T-spherical fuzzy Aczel–Alsina dual Hamy mean (TSFAADHM) operator, and their weighted forms, i.e., the T-spherical fuzzy Aczel–Alsina-weighted Hamy mean (TSFAAWHM) and T-spherical fuzzy Aczel–Alsina-weighted dual Hamy mean (TSFAAWDHM) operators. Moreover, some related properties are discussed. Then, a MCDM model based on the proposed AOs is built. Lastly, a numerical example is provided to show the applicability and feasibility of the developed AOs, and the effectiveness of this study is verified by the implementation of a parameters influence test and comparison with available methods. [ABSTRACT FROM AUTHOR]

Many fuzzy concepts have been researched and described with uncertain information. Collecting data under uncertain information is a difficult task, especially when there is a difference between the opinions of experts. To deal with such situations, different types of operators have been introduced. This paper aims to develop the Maclaurin symmetric mean (MSM) operator for the information in the shape of the interval-valued spherical fuzzy set (IVSFS). In this article, a family of aggregation operators (AOs) is proposed which consists of interval valued spherical fuzzy Maclaurin symmetric mean operator (IVSFMSM), interval valued spherical fuzzy weighted Maclaurin symmetric mean (IVSFWMSM), interval valued spherical fuzzy dual Maclaurin symmetric mean (IVSFDMSM), and interval valued spherical fuzzy dual weighted Maclaurin symmetric mean (IVSFDWMSM) operators. In this paper, we studied an elucidative example to discuss the evaluation of multi-national companies for the application of the proposed operator. Then the obtained results from the proposed operators are compared. The results obtained are graphed and tabulated for a better understanding. [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]

Vendor management systems (VMSs) are web-based software packages that can be used to manage businesses. The performance of the VMSs can be assessed using multi-attribute decision-making (MADM) techniques under uncertain situations. This article aims to analyze and assess the performance of VMSs using MADM techniques, especially when the uncertainty is of complex nature. To achieve the goals, we aim to explore Hany mean (HM) operators in the environment of complex picture fuzzy (CPF) sets (CPFSs). We introduce CPF Hamy mean (CPFHM) and CPF weighted HM (CPFWHM) operators. Moreover, the reliability of the newly proposed HM operators is examined by taking into account the properties of idempotency, monotonicity, and boundedness. A case study of VMS is briefly discussed, and a comprehensive numerical example is carried out to assess VMSs using the MADM technique based on CPFHM operators. The sensitivity analysis and comprehensive comparative analysis of the proposed work are discussed to point out the significance of the newly established results. [ABSTRACT FROM AUTHOR]

The T-Spherical fuzzy set (TSFS) is the most generalized form among the introduced fuzzy frameworks. It obtains maximum information from real-life phenomena due to its maximum range. Consequently, TSFS is a very useful structure for dealing with information uncertainties, especially when human opinion is involved. The correlation coefficient (CC) is a valuable tool, possessing symmetry, to determine the similarity degree between objects under uncertainties. This research aims to develop a new CC for TSFS to overcome the drawbacks of existing methods. The proposed CCs are generalized, flexible, and can handle uncertain situations where information has more than one aspect. In addition, the proposed CCs provide decision-makers independence in establishing their opinion. Based on some remarks, the usefulness of the new CC is reviewed, and its generalizability is evaluated. Moreover, the developed new CC is applied to pattern recognition for investment decisions and medical diagnosis of real-life problems to observe their effectiveness and applicability. Finally, the validity of the presented CC is tested by comparing it with the results of the previously developed CC. [ABSTRACT FROM AUTHOR]

In the aggregation of uncertain information, it is very important to consider the interrelationship of the input information. Hamy mean (HM) is one of the fine tools to deal with such scenarios. This paper aims to extend the idea of the HM operator and dual HM (DHM) operator in the framework of complex intuitionistic fuzzy sets (CIFSs). The main benefit of using the frame of complex intuitionistic fuzzy CIF information is that it handles two possibilities of the truth degree (TD) and falsity degree (FD) of the uncertain information. We proposed four types of HM operators: CIF Hamy mean (CIFHM), CIF weighted Hamy mean (CIFWHM), CIF dual Hamy mean (CIFDHM), and CIF weighted dual Hamy mean (CIFWDHM) operators. The validity of the proposed HM operators is numerically established. The proposed HM operators are utilized to assess a multiattribute decision-making (MADM) problem where the case study of tourism destination places is discussed. For this purpose, a MADM algorithm involving the proposed HM operators is proposed and applied to the numerical example. The effectiveness and flexibility of the proposed method are also discussed, and the sensitivity of the involved parameters is studied. The conclusive remarks, after a comparative study, show that the results obtained in the frame of CIFSs improve the accuracy of the results by using the proposed HM operators. [ABSTRACT FROM AUTHOR]

In the process of decision-making, uncertain information is always challenging to deal with. T-spherical fuzzy set (TSFS) operates vagueness of data by analysing three independent functions, namely membership, non-membership, and abstinence function. The TSFS provides us robust scheme with parameter q ≥ 1 to handle the countless opportunities. Hence, this set proves its superiority over the existing picture fuzzy set (PFS) and spherical fuzzy set (SFS). Now a day, decision-makers usually assign impartial values throughout the assessment. This manuscript demonstrates some new operational laws by fusing the neutral characteristics of the degrees of membership and using the probability sum (PS) function. Meanwhile, we determine several aggregation operators (AOs) including weighted averaging neutral, ordered weighed neutral, and hybrid averaging neutral AOs to aggregate the data under T-spherical fuzzy (TSF) environment. As it came to the notice that weighted neutral averaging aggregation operators of the Pythagorean fuzzy set (PyFS), single-valued neutrosophic fuzzy set (SVNFS), and q -rung orthopair fuzzy set (q -ROFS) have some restrictions during the decision-making problems. So, to overcome this, we introduce a new multi-attribute group decision-making method (MAGDM) based on proposed AOs. Lastly, we provide various numerical instances to explain the method and exhibit its supremacy. Furthermore, a comparative analysis is conducted to compare the potential of proposed AOs with some other existing methods. [ABSTRACT FROM AUTHOR]

The framework of complex T-spherical fuzzy set (CTSFS) deals with unclear and imprecise information with the help of membership degree (MD), abstinence degree (AD), nonmembership degree (NMD), and refusal degree (RD). Due to this characteristic, the CTSFSs can be applied to any phenomenon having the involvement of human opinions. This article aims to familiarize some Hamacher aggregation operators (HAOs) grounded on CTSFSs. To do so, we define some Hamacher operational laws in the environment of CTSFS by using Hamacher t-norm (HTNM) and Hamacher t-conorm (HTCNM). A few numbers of AOs are developed with the help of defined operational laws based on HTNM and HTCNM including the complex T-spherical fuzzy (CTSF), Hamacher weighted averaging (HWA) (CTSFHWA), CTSF Hamacher ordered weighted averaging (CTSFHOWA) operator, CTSF Hamacher hybrid weighted averaging (CTSFHHWA) operator, CTSF Hamacher weighted geometric (CTSFHWG) operator, CTSF Hamacher ordered weighted geometric (CTSFHOWG) operator, and CTSF Hamacher hybrid weighted geometric (CTSFHHWG) operator. Some interesting properties of developed HAOs are investigated and then these HAOs are applied to the multi-attribute decision making (MADM) problem. For the significance of these HAOs, the results obtained from these HAOs are compared with existing aggregation operators (AOs). [ABSTRACT FROM AUTHOR]

The novel concept of the complex interval-valued T-spherical fuzzy set (CIVTSFS) is presented to handle the vagueness in the data. The proposed set takes the advantages of interval-valued spherical fuzzy sets and complex numbers to represent the information in terms of the interval-valued number of the truth, abstinence and falsity degrees. Various operation laws are stated to enrich the features of CIVTSFS. By utilising the proposed laws, several weighted operators are stated to aggregate the different preference of the experts towards the evaluation of the alternatives. Furthermore, a group decision-making algorithm is stated to solve the decision-making problems by utilising the uncertain data under CIVTSFS information. The presented algorithm is demonstrated through a numerical example and their advantages are indicated. [ABSTRACT FROM AUTHOR]

A contribution of this article is to introduce new q-rung Orthopair fuzzy (q-ROF) aggregation operators (AOs) as the consequence of Aczel–Alsina (AA) t-norm (TN) (AATN) and t-conorm (TCN) (AATCN) and their specific advantages in handling real-world problems. In the beginning, we introduce a few new q-ROF numbers (q-ROFNs) operations, including sum, product, scalar product, and power operations based on AATN and AATCN. At that point, we construct a few q-ROF AOs such as q-ROF Aczel–Alsina weighted averaging (q-ROFAAWA) and q-ROF Aczel–Alsina weighted geometric (q-ROFAAWG) operators. It is illustrated that suggested AOs have the features of monotonicity, boundedness, idempotency, and commutativity. Then, to address multi-attribute decision-making (MADM) challenges, we develop new strategies based on these operators. To demonstrate the compatibility and performance of our suggested approach, we offer an example of construction material selection. The outcome demonstrates the new technique's applicability and viability. Finally, we comprehensively compare current procedures with the proposed approach. [ABSTRACT FROM AUTHOR]

This manuscript aims to analyze the well-known and massive idea of competition graph (CG) in the presence of a new and dominant technique of complex q-rung orthopair fuzzy (CQROF) setting. The mathematical form of the CQROF setting is more flexible and massive consistent for demonstrating the beneficial option from the collection of objectives during the decision-making process. Additionally, the major concept of in-neighbourhood and out-neighbourhood using CQROF diagraph (CQROFDG) are also invented to enhance the quality of the diagnosed approach. The fundamental theory of CQROF k-competition, CQROF p-competition, CQROF neighbourhood and m-step CQROF neighbourhood graphs are also explored. In the availability of the above-described theories, the basic and significant results for the presented work are obtained to show the compatibility and worth of the invented approaches. To show the practicality of the developed approach, we try to verify the proposed work with the help of various examples. Further, to describe the validity and practicality of the invented work, we diagnosed an application using presented approaches based on the CQROF setting is to enhance the major weakness of the existing approaches. Finally, in the availability of the invented ideas, we discussed the sensitivity analysis of the described approaches. [ABSTRACT FROM AUTHOR]

The T-spherical fuzzy set (TSFS) is a modification of the fuzzy set (FS), intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PyFS), q-rung orthopair fuzzy set (q-ROFS), and picture fuzzy set (PFS), with three characteristic functions: the membership degree (MD) denoted by S , the nonmembership degree (NMD) denoted by D , and the abstinence degree (AD) denoted by I. It can be used to solve problems of uncertain information with no restrictions. The distance measure (DM) is a tool that sums up the difference between points, while the similarity measure (SM) is a method applied to calculate the similarity between objects within an interval of [ 0 , 1 ] . The current work aims to introduce novel DMs and SMs in the environment of TSFSs to show the limitations of the previously defined DMs and SMs. The suggested DMs and SMs provide more room for all three degrees to be selected without restriction. We investigated the effectiveness of the proposed DMs and SMs by applying a pattern-recognition technique, and we determined their applicability for multicriteria decision making (MCDM) using numerical examples. The newly proposed DMs and SMs are briefly compared to existing DMs and SMs, and appropriate conclusions are drawn. [ABSTRACT FROM AUTHOR]

Multi-attribute decision-making (MADM) is usually used to aggregate fuzzy data successfully. Choosing the best option regarding data is not generally symmetric on the grounds that it does not provide complete information. Since Aczel-Alsina aggregation operators (AOs) have great impact due to their parameter variableness, they have been well applied in MADM under fuzzy construction. Recently, the Aczel-Alsina AOs on intuitionistic fuzzy sets (IFSs), interval-valued IFSs and T-spherical fuzzy sets have been proposed in the literature. In this article, we develop new types of Pythagorean fuzzy AOs by using Aczel-Alsina t-norm and Aczel-Alsina t-conorm. Thus, we give these new operations Aczel-Alsina sum and Aczel-Alsina product on Pythagorean fuzzy sets based on Aczel-Alsina t-norm and Aczel-Alsina t-conorm. We also develop new types of Pythagorean fuzzy AOs including Pythagorean fuzzy Aczel-Alsina weighted averaging and Pythagorean fuzzy Aczel-Alsina weighted geometric operators. We elaborate some characteristics of these proposed Aczel-Alsina AOs on Pythagorean fuzzy sets, such as idempotency, monotonicity, and boundedness. By utilizing the proposed works, we solve an example of MADM in the information of the multinational company under the evaluation of impacts in MADM. We also illustrate the comparisons of the proposed works with previously existing AOs in different fuzzy environments. These comparison results demonstrate the effectiveness of the proposed Aczel-Alsina AOs on Pythagorean fuzzy sets. [ABSTRACT FROM AUTHOR]

T-spherical fuzzy set (TSFS) is a generalized version of the spherical fuzzy set (SFS) and picture fuzzy set (PFS) to manage awkward and unpredictable information in realistic decision issues. TSFS deals with yes, abstinence, no, and refusal type of fuzzy information. This manuscript aims to observe the drawbacks of some existing dice similarity measures (DSMs) and to propose some new DSMs in the environment of TSFSs. The validation of the new DSMs is proved. The defined DSMs are further extended to introduce some generalized DSMs (GDSMs) and their special cases are studied. Additionally, the TOPSIS method using the entropy measures (EMs) based on TSFSs is also explored and verified with the help of some examples. The proposed new GDSMs and TOPSIS method are applied to the problem of building material recognition, medical diagnosis, clustering, and the results obtained are investigated. A comparison of the new theory is established where the advancement of the proposed DSMs is elaborated under some conditions. The advantages of the new DSMs and the drawbacks of the previous DSMs of IFSs, PyFSs, and PFSs have been studied because of their applicability. The article is comprehensively summarized, and some possible future directions are stated. [ABSTRACT FROM AUTHOR]

The novel concept of the complex interval-valued T-spherical fuzzy set (CIVTSFS) is presented to handle the vagueness in the data. The proposed set takes the advantages of interval-valued spherical fuzzy sets and complex numbers to represent the information in terms of the interval-valued number of the truth, abstinence and falsity degrees. Various operation laws are stated to enrich the features of CIVTSFS. By utilising the proposed laws, several weighted operators are stated to aggregate the different preference of the experts towards the evaluation of the alternatives. Furthermore, a group decision-making algorithm is stated to solve the decision-making problems by utilising the uncertain data under CIVTSFS information. The presented algorithm is demonstrated through a numerical example and their advantages are indicated. [ABSTRACT FROM AUTHOR]

T-Spherical fuzzy set (TSFS) is an improved extension in fuzzy set (FS) theory that takes into account four angles of the human judgment under uncertainty about a phenomenon that is membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). The purpose of this manuscript is to introduce and investigate logarithmic aggregation operators (LAOs) in the layout of TSFSs after observing the shortcomings of the previously existing AOs. First, we introduce the notions of logarithmic operations for T-spherical fuzzy numbers (TSFNs) and investigate some of their characteristics. The study is extended to develop T-spherical fuzzy (TSF) logarithmic AOs using the TSF logarithmic operations. The main theory includes the logarithmic TSF weighted averaging (LTSFWA) operator, and logarithmic TSF weighted geometric (LTSFWG) operator along with the conception of ordered weighted and hybrid AOs. An investigation about the validity of the logarithmic TSF AOs is established by using the induction method and examples are solved to examine the practicality of newly developed operators. Additionally, an algorithm for solving the problem of best production choice is developed using TSF information and logarithmic TSF AOs. An illustrative example is solved based on the proposed algorithm where the impact of the associated parameters is examined. We also did a comparative analysis to examine the advantages of the logarithmic TSF AOs. [ABSTRACT FROM AUTHOR]

To evaluate objects under uncertainty, many fuzzy frameworks have been designed and investigated so far. Among them, the frame of picture fuzzy set (PFS) is of considerable significance which can describe the four possible aspects of expert's opinion using a degree of membership (DM), degree of nonmembership (DNM), degree of abstinence (DA), and degree of refusal (DR) in a certain range. Aggregation of information is always challenging especially when the input arguments are interrelated. To deal with such cases, the goal of this study is to develop the notion of the Maclaurin symmetric mean (MSM) operator as it aggregates information under uncertain environments and considers the relationship of the input arguments, which make it unique. In this paper, we studied the theory of MSM operators in the layout of PFSs and discussed their applications in the selection of the most suitable enterprise resource management (ERP) scheme for engineering purposes. We developed picture fuzzy MSM (PFMSM) operators and investigated their validity. We developed the multiattribute decision-making (MADM) algorithm based on the PFMSM operators to examine the performance of the ERP systems using picture fuzzy information. A numerical example to evaluate the performance of ERP systems is studied, and the effects of the associated parameters are discussed. The proposed aggregated results using PFMSM operators are found to be reliable as it takes into account the interrelationship of the input information, unlike traditional aggregation operators. A comparative study of the proposed PFMSM operators is also studied. [ABSTRACT FROM AUTHOR]

Linear Diophantine uncertain linguistic set (LDULS) is a modified variety of the fuzzy set (FS) to manage problematic and inconsistent information in actual life troubles. LDULS covers the grade of truth, grade of falsity, and their reference parameters with the uncertain linguistic term (ULT) with a rule 0 ≤ α AMG u AMG x + β ANG v AMG x ≤ 1 , where 0 ≤ α AMG + β ANG ≤ 1. In this study, the principle of LDULS and their useful laws are elaborated. Additionally, the power Einstein (PE) aggregation operator (AO) is a conventional sort of AO utilized in innovative decision-making troubles, which is effective to aggregate the family of numerical elements. To determine the interrelationship between any numbers of arguments, we elaborate the linear Diophantine uncertain linguistic PE averaging (LDULPEA), linear Diophantine uncertain linguistic PE weighted averaging (LDULPEWA), linear Diophantine uncertain linguistic PE geometric (LDULPEG), and linear Diophantine uncertain linguistic PE weighted geometric (LDULPEWG) operators; then, we discuss their useful results. Conclusively, a decision-making methodology is utilized for the multiattribute decision-making (MADM) dilemma with elaborated information. A sensible illustration is specified to demonstrate the accessibility and rewards of the intended technique by comparison with certain prevailing techniques. The intended AOs are additional comprehensive than the prevailing ones to exploit the ambiguous and inaccurate knowledge. Numerous remaining operators are chosen as individual incidents of the suggested one. Ultimately, the supremacy and advantages of the elaborated operators are also discussed with the help of the geometrical form to show the validity and consistency of explored operators. [ABSTRACT FROM AUTHOR]

Picture hesitant fuzzy set (PHFS) is a recently developed tool to cope with uncertain and awkward information in realistic decision issues and is applicable where opinions are of more than two types, i.e., yes, no, abstinence and refusal. Similarity measures (SMs) in a data mining context are distance with dimensions representing features of the objects. Keeping the advantages of the above analysis, in this manuscript, the authors proposed SMs for PHFSs, including cosine SMs for PHFSs, SMs for PHFSs based on cosine function, and SMs for PHFSs based on cotangent function. Further, entropy measure, TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) based on correlation coefficient are investigated for PHFSs. Further, some weighted SMs are also proposed and then applied to the strategic decision-making problem and the results are discussed. Moreover, we take two illustrative examples to compare the established work with existing drawbacks and also show that the existing drawback cannot solve the problem of established work. But on the other hand, the new approach can easily solve the problem of the existing drawback. Finally, the advantages of the new approach are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we propose some developments in fuzzy graph theory. An original notion of a T-spherical fuzzy graph is presented as a commonality of fuzzy graph, an intuitionistic fuzzy graph and a picture fuzzy graph. The originality, the imperativeness and the importance of this notion are discussed by showing some results, giving examples and graphical analysis. Some theoretical terms of graphs such as a T-spherical fuzzy subgraph, a complement of T-SFG, degree of T-SFG are clarified and their attributes and aspects are analyzed. Interestingly, three types of decision-making problems using the framework of T-SFGs are studied. These problems include the problem of the shortest path, the safe root for an airline journey and the problem of supply chain management in a T-spherical fuzzy network. The comparison of this new approach towards these problems with existing approaches is also established. A new algorithm is put forward in the event of T-SFGs and is used to seek out the shortest path problem. The overall analysis of the suggested notion under the prevailing theory is conducted. The advantages of the proposed approach are discussed based on the existing tools and a short comparison of the new with existing tools is established. [ABSTRACT FROM AUTHOR]

The framework of T-spherical fuzzy set is a generalization of fuzzy set, intuitionistic fuzzy set and picture fuzzy set having a great potential of dealing with uncertain events with no limitation. A T-spherical fuzzy framework can deal with phenomena of more than yes or no type; for example, consider the scenario of voting where one's voting interest is not limited to "in favor" or "against" rather there could be some sort of abstinence or refusal degree also. The objective of this paper is to develop some correlation coefficients for T-spherical fuzzy sets due to the non-applicability of correlations of intuitionistic fuzzy sets and picture fuzzy sets in some certain circumstances. The fitness of new correlation coefficients has been discussed, and their generalization is studied with the help of some results. Clustering and multi-attribute decision-making algorithms have been proposed in the environment of T-spherical fuzzy sets. To demonstrate the viability of proposed algorithms and correlation coefficients, two real-life problems including a clustering problem and a multi-attribute decision-making problem have been solved. A comparative study of the newly presented and pre-existing literature is established showing the superiority of proposed work over the existing theory. Some advantages of new correlation coefficients and drawbacks of the pre-existing work are demonstrated with the help of numerical examples. [ABSTRACT FROM AUTHOR]

A pythagorean fuzzy set is a generalized fuzzy structure that copes with imprecisions of real life accurately and with a larger domain. The aim of this manuscript is to develop the notion of graph for newly established concept of interval‐valued Pythagorean fuzzy set. We introduced the concept of interval‐valued Pythagorean fuzzy graph (IVPyFG) and discussed its related ideas with the help of examples. The significance of using interval‐valued fuzzy concepts over non‐interval‐valued fuzzy concepts are demonstrated numerically. Further, the advantages of using the new approach over the pre‐existing ideas are demonstrated with the help of numerical examples. The main goal of this article is to study three types of decision‐making problems using the framework of IVPyFGs. These three problems include the problem of selection of the best university in a network of universities, a supply chain management problem and the shortest path problem. The comparison of the new approach toward these problems with existing approaches is also established. [ABSTRACT FROM AUTHOR]

Recently, Jun et al. have introduced the concept of cubic set as a generalization of the concept of fuzzy set and that of the interval valued fuzzy set. This concept has been widely applied in many circumstances like pattern recognition, decision making etc. So far, no attention has been paid towards graph of cubic set therefore leads us in this manuscript to study the concepts of interval valued bipolar fuzzy graph (IVBFG) and cubic bipolar fuzzy graph (CBFG). Some graph theoretic terms for CBFGs are defined along with the several operations. Illustrative examples are provided to explain the defined terms and several results are discussed. As application, a cubic bipolar fuzzy influence graph in a social group is elaborated. [ABSTRACT FROM AUTHOR]

In this article, we combine the concept of a bipolar fuzzy set and a soft set. We introduce the notion of bipolar fuzzy soft set and study fundamental properties. We study basic operations on bipolar fuzzy soft set. We define extended union, intersection of two bipolar fuzzy soft set. We also give an application of bipolar fuzzy soft set into decision making problem. We give a general algorithm to solve decision making problems by using bipolar fuzzy soft set. [ABSTRACT FROM AUTHOR]

T-spherical fuzzy set (TSFS) is a fuzzy layout aiming to provide a larger room for the processing of uncertain information-based data where four aspects of unpredictable information are studied. The frame of picture fuzzy sets (PFSs) and intuitionistic fuzzy sets (IFSs) provide limited room for processing such kinds of information. On a scale of zero to one, similarity measures (SMs) are a tool for evaluating the degrees of resemblance between various items or phenomena. The goal of this paper is to investigate the shortcomings of picture fuzzy (PF) SMs in order to introduce a new SM in a T-spherical fuzzy (TSF) environment. The newly improved SM has a larger ground for accommodating the uncertain information with three degrees and is also responsible for the reduction of information loss. The proposed SM's validity is demonstrated mathematically and by examples. To examine the application of the suggested SM two real-life issues are discussed, including the concerns of medical diagnosis and pattern recognition. A comparison of the suggested SMs with current SMs is also made to assess the proposed work's reliability. Since symmetric triangular fuzzy numbers are quite useful in database acquisition, we will consider the proposed SM for symmetric T-spherical triangular fuzzy numbers in the near future. [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. In this analysis, we use the massive dominant and more consistent principle of power aggregation operators (PAOs) based on general t-norm and t-conorm, which manage awkward and inconsistent data in real-world dilemmas such as medical diagnosis, pattern recognition, cleaner production evaluation in gold mines, the analysis of the cancer risk factor, etc. The principle of averaging, geometric, Einstein, and Hamacher aggregation operators are specific cases of generalized PAOs. We combine the principle of complex intuitionistic fuzzy soft (CIFS) information with PAOs to initiate CIFS power averaging (CIFSPA), CIFS weighted power averaging (CIFSWPA), CIFS ordered weighted power averaging (CIFSOWPA), CIFS power geometric (CIFSPG), CIFS weighted power geometric (CIFSWPG), and CIFS ordered weighted power geometric (CIFSOWPG), and their flexible laws are elaborated. Certain specific cases (such as averaging, Einstein, and Hamacher operators) of the explored operators are also illustrated with the help of different t-norm and t-conorm operators. A MADM process is presented under the developed operators based on the CIFS environment. Finally, to investigate the supremacy of the demonstrated works, we employed a sensitivity analysis and geometrical expressions of the initiated operators with numerous prevailing works to verify the efficiency of the proposed works. This manuscript shows how to make decisions when there is asymmetric information about enterprises. [ABSTRACT FROM AUTHOR]

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of [ 0 ,   1 ] that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from [ 0 ,   1 ] intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work. [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]

T-spherical fuzzy set is a recently developed model that copes with imprecise and uncertain events of real-life with the help of four functions having no restrictions. This article's aim is to define some improved algebraic operations for T-SFSs known as Einstein sum, Einstein product and Einstein scalar multiplication based on Einstein t-norms and t-conorms. Then some geometric and averaging aggregation operators have been established based on defined Einstein operations. The validity of the defined aggregation operators has been investigated thoroughly. The multi-attribute decision-making method is described in the environment of T-SFSs and is supported by a comprehensive numerical example using the proposed Einstein aggregation tools. As consequences of the defined aggregation operators, the same concept of Einstein aggregation operators has been proposed for q-rung orthopair fuzzy sets, spherical fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and intuitionistic fuzzy sets. To signify the importance of proposed operators, a comparative analysis of proposed and existing studies is developed, and the results are analyzed numerically. The advantages of the proposed study are demonstrated numerically over the existing literature with the help of examples. [ABSTRACT FROM AUTHOR]

Similarity measures, distance measures and entropy measures are some common tools considered to be applied to some interesting real-life phenomena including pattern recognition, decision making, medical diagnosis and clustering. Further, interval-valued picture fuzzy sets (IVPFSs) are effective and useful to describe the fuzzy information. Therefore, this manuscript aims to develop some similarity measures for IVPFSs due to the significance of describing the membership grades of picture fuzzy set in terms of intervals. Several types cosine similarity measures, cotangent similarity measures, set-theoretic and grey similarity measures, four types of dice similarity measures and generalized dice similarity measures are developed. All the developed similarity measures are validated, and their properties are demonstrated. Two well-known problems, including mineral field recognition problems and multi-attribute decision making problems, are solved using the newly developed similarity measures. The superiorities of developed similarity measures over the similarity measures of picture fuzzy sets, interval-valued intuitionistic fuzzy sets and intuitionistic fuzzy sets are demonstrated through a comparison and numerical examples. [ABSTRACT FROM AUTHOR]

The framework of the T-spherical fuzzy set is a recent development in fuzzy set theory that can describe imprecise events using four types of membership grades with no restrictions. The purpose of this manuscript is to point out the limitations of the existing intuitionistic fuzzy Einstein averaging and geometric operators and to develop some improved Einstein aggregation operators. To do so, first some new operational laws were developed for T-spherical fuzzy sets and their properties were investigated. Based on these new operations, two types of Einstein aggregation operators are proposed namely the Einstein interactive averaging aggregation operators and the Einstein interactive geometric aggregation operators. The properties of the newly developed aggregation operators were then investigated and verified. The T-spherical fuzzy aggregation operators were then applied to a multi-attribute decision making (MADM) problem related to the degree of pollution of five major cities in China. Actual datasets sourced from the UCI Machine Learning Repository were used for this purpose. A detailed study was done to determine the most and least polluted city for different perceptions for different situations. Several compliance tests were then outlined to test and verify the accuracy of the results obtained via our proposed decision-making algorithm. It was proved that the results obtained via our proposed decision-making algorithm was fully compliant with all the tests that were outlined, thereby confirming the accuracy of the results obtained via our proposed method. [ABSTRACT FROM AUTHOR]

The objective of this manuscript is to present some new, improved aggregation operators for the T-spherical fuzzy sets, which is an extension of the several existing sets, such as intuitionistic fuzzy sets, picture fuzzy sets, neutrosophic sets, and Pythagorean fuzzy sets. In it, some new, improved operational laws and their corresponding properties are studied. Further, based on these laws, we propose some geometric aggregation operators and study their various relationships. Desirable properties, as well as some special cases of the proposed operators, are studied. Then, based on these proposed operators, we present a decision-making approach to solve the multi-attribute decision-making problems. The reliability of the presented decision-making method is explored with the help of a numerical example and the proposed results are compared with several prevailing studies' results. Finally, the superiority of the proposed approach is explained with a counter example to show the advantages of the proposed work. [ABSTRACT FROM AUTHOR]

The power Bonferroni mean (PBM) operator is a hybrid structure and can take the advantage of a power average (PA) operator, which can reduce the impact of inappropriate data given by the prejudiced decision makers (DMs) and Bonferroni mean (BM) operator, which can take into account the correlation between two attributes. In recent years, many researchers have extended the PBM operator to handle fuzzy information. The Dombi operations of T-conorm (TCN) and T-norm (TN), proposed by Dombi, have the supremacy of outstanding flexibility with general parameters. However, in the existing literature, PBM and the Dombi operations have not been combined for the above advantages for interval-neutrosophic sets (INSs). In this article, we first define some operational laws for interval neutrosophic numbers (INNs) based on Dombi TN and TCN and discuss several desirable properties of these operational rules. Secondly, we extend the PBM operator based on Dombi operations to develop an interval-neutrosophic Dombi PBM (INDPBM) operator, an interval-neutrosophic weighted Dombi PBM (INWDPBM) operator, an interval-neutrosophic Dombi power geometric Bonferroni mean (INDPGBM) operator and an interval-neutrosophic weighted Dombi power geometric Bonferroni mean (INWDPGBM) operator, and discuss several properties of these aggregation operators. Then we develop a multi-attribute decision-making (MADM) method, based on these proposed aggregation operators, to deal with interval neutrosophic (IN) information. Lastly, an illustrative example is provided to show the usefulness and realism of the proposed MADM method. The developed aggregation operators are very practical for solving MADM problems, as it considers the interaction among two input arguments and removes the influence of awkward data in the decision-making process at the same time. The other advantage of the proposed aggregation operators is that they are flexible due to general parameter. [ABSTRACT FROM AUTHOR]