Proposed Aggregation Operators Research Articles

Improved q-Rung Orthopair Fuzzy WASPAS Method Based on Softmax Function and Frank operations for Investment Decision of Community Group-Buying Platform

The traditional WASPAS (Weighted Aggregated Sum Product ASsessment) method has attracted widely attention. Unfortunately, the decision-makers’ decision attitude or risk preference is ignored in the existing WASPAS methods. To overcome this shortcoming, this paper embedded expert’s decision attitude with risk preference into WASPAS method for solving multi-attribute group decision-making problems with q-rung orthopair fuzzy (q-ROF) information. We develop the q-ROF Frank softmax weighted averaging (q-ROFFSWA) and q-ROF Frank softmax weighted geometric (q-ROFFSWG) operators based on Frank operations and softmax function. The relevant properties and particular cases are explored, and the monotonicity of these operators’ score functions is analyzed. Then, the q-ROF multi-attribute group decision-making framework based on the improved WASPAS method is constructed. The weighted sum model and weighted product model in traditional WASPAS are replaced by the two proposed aggregation operators. The q-ROF distance measure is utilized to de fuzzy the performance values of alternatives. And a compromise function between optimistic and pessimistic decision attitudes with risk preferences is proposed. Lastly, the presented method is implemented in a real case of investment decision of community group-buying (CGB) platform, and sensitivity analysis and comparative study with existing methods are conducted to verify the practicality, robustness and effectiveness.

Combinative distance-based assessment method using linguistic T-spherical fuzzy aggregation operators and its application to multi-attribute group decision-making

Clean energy has become a hot topic worldwide because of the continuous rise in the climate's temperature. Reduced air pollution is only one of the many economic and environmental advantages of clean energy. An effective contractor with experience and knowledge in clean energy projects is always required to handle the complicated process of planning, implementing, and maintaining the new clean energy infrastructure. Contractor selection for renewable energy projects (REPs) is a multi-attribute group decision-making (MAGDM) problem. Linguistic T-spherical fuzzy set (LT-SFS) can be compatible with fuzzier information, and the contractor selection problem also has a lot of fuzzy information, which makes LT-SFS very suitable for contractor selection for REPs. Hence, the present work proposes a MAGDM methodology utilizing a combinative distance-based assessment (CODAS) method within the LT-SF context. For that, the Einstein and Frank t-norm and t-conorm has been used to define new and generalized operational laws for linguistic T-spherical fuzzy numbers. Then, the linguistic T-spherical fuzzy Einstein and linguistic T-spherical fuzzy Frank aggregation operators are proposed to integrate the information data provided by experts. Moreover, the proposed aggregation operators based-CODAS approach is designed to evaluate and rank the available alternatives. A real-life decision problem of selecting the best suitable contractor for a renewable energy project is solved to verify our suggested technique. Moreover, the sensitivity analysis is also carried out by changing the parameter's value to check the consistency of the rank order. Finally, the new model is compared with existing approaches to demonstrate its strength. The comparative analysis shows that the results of the suggested technique are more feasible and beneficial than those of existing approaches.

Complex q-rung orthopair fuzzy Yager aggregation operators and their application to evaluate the best medical manufacturer

In contemporary healthcare systems, the selection and judicious choice of the right medical device becomes paramount consideration for accurate diagnosis, patient care, mitigate risk and cost incurred on diagnosis of disease. Moreover, medical devices are requisite indispensable tools to help healthcare professionals for effective diagnosis, selection of the right treatment amongst different options, and continuous monitoring of the patient. Thus, to select the best manufacturing company is as equally important to achieve the desired goals. This paper presents a decision making algorithm based on fuzzy theory that helps the decision maker in selecting the most suitable worldwide medical device manufacturer. Fuzzy theory is extensively used in managing databases and analyzing data to summarize information and draw meaningful conclusions. This paper utilizes the aggregation operators within the context of the complex q-rung orthopair fuzzy environment by utilizing Yager t-norm and t-conorm operations. Some aggregation operators are applied, namely, complex q-rung orthopair fuzzy Yager weighted geometric operator, complex q-rung orthopair fuzzy Yager ordered weighted geometric operator, complex q-rung orthopair fuzzy Yager weighted averaging operator and complex q-rung orthopair fuzzy Yager ordered weighted averaging operator. Additionally, the notable properties of these operators are proved. These aggregation operators are generated specifically for multi-criteria decision-making. Decision making algorithm is used to choose the most relevant medical device manufacturer (alternative) to validate its efficacy. The results demonstrate the versatility of parameters, adaptability to multi-criteria decision making, and efficiency of the proposed aggregation operators and algorithm. Test with specific criteria is also conducted to verify the legality and validity of the decision making algorithm. At last, the acquired results underwent a comparative analysis against various established methodologies, confirming the method’s capacity to produce precise and accurate outcomes.

An evidential linguistic ELECTRE method for selection of emergency shelter sites

In many circumstances, decisions are based on subjective experience. However, some views can be vague, meaning that policymakers do not know exactly how they should express their opinions. Therefore, it is necessary for researchers to provide scientific decision frameworks, among which the multi-criteria decision making (MCDM) method in the linguistic environment is gradually favored by scholars. A large body of literature reports relevant approaches with regard to linguistic term sets, but existing approaches are insufficient to express the subjective thoughts of policymakers in a complex and uncertain environment. In this paper, we address this problem by introducing the concept of evidential linguistic term set (ELTS). ELTS generalizes many other uncertainty representations under linguistic context, such as fuzzy sets, probabilities, or possibility distributions. Measures on ELTS, such as uncertainty measure, dissimilarity measure and expectation function, provide general frameworks to handle uncertain information. Modeling and reasoning of information expressed by ELTSs are realized by the proposed aggregation operators. Subsequently, this paper presents a novel MCDM approach called evidential linguistic ELECTRE method, and applies it to the case of selection of emergency shelter sites. The findings demonstrate the effectiveness of the proposed method for MCDM problems under linguistic context and highlight the significance of the developed ELTS.

P, q-Spherical fuzzy sets and their aggregation operators with application to third-party logistic provider selection

The selection of an appropriate third-party logistics (3PL) provider has become an inescapable option for shippers in today’s business landscape, as the outsourcing of logistics activities continues to increase. Choosing the 3PL supplier that best meets their requirements is one of the most difficult difficulties that logistics consumers face. Effective decision-making (DM) is critical in dealing with such scenarios, allowing shippers to make well-informed decisions within a restricted timeframe. The importance of DM arises from the possible financial repercussions of poor decisions, which can result in significant financial losses. In this regard, we introduce p, q-spherical fuzzy set (p, q-SFS), a novel concept that extends the concept of T-spherical fuzzy sets (T-SFSs). p, q-SFS is a comprehensive representation tool for capturing imprecise information. The main contribution of this article is to define the basic operations and a series of averaging and geometric AOs under p, q-spherical fuzzy (p, q-SF) environment. In addition, we establish several fundamental properties of the proposed aggregation operators (AOs). Based on these AOs, we propose a stepwise algorithm for multi-criteria DM (MCDM) problems. Finally, a real-life case study involving the selection of a 3PL provider is shown to validate the applicability of the proposed approach.

A sustainability evaluation framework for the urban energy Internet using the Fermatean fuzzy Aczel-Alsina hybrid MCDM method

The evaluation of urban energy internet (UEI) is crucial for the establishment of low-carbon cities. This paper aims to present a hybrid decision-making framework to address UEI evaluation problems from a sustainability perspective. First, the Fermatean fuzzy Aczel-Alsina power aggregation operators are proposed to aggregate evaluation information, and the remarkable properties of these operators are explored. Then, the combined weight of the criteria is determined through the decision-making trial and evaluation laboratory method and the Shannon entropy-based power weighted method within the Fermatean fuzzy circumstance. Moreover, the classic multiobjective optimization by ratio analysis plus the full multiplicative form method is extended using the proposed aggregation operators. Finally, an index system was constructed from a sustainability perspective, and the level of development of the four UEI projects is assessed using the proposed method. The experimental results demonstrate that the proposed method can provide beneficial guidelines for the construction and development of the UEI. Furthermore, the reliability and effectiveness of the proposed decision-making framework are validated through sensitivity analysis and a comparative study with existing MCDM methods.

A novel group decision-making approach based on partitioned Hamy mean operators in q-rung orthopair fuzzy context

In multi-attribute group decision-making (MAGDM), the attributes can be placed into independent groups based on their properties through partitioning. First, the partitioned dual Hamy mean (PDHM) operator is introduced, along with its essential properties. This operator integrates these separate groups while preserving the relationships between the attributes within each group. Furthermore, the partitioned Hamy mean (PHM) and the PDHM operators are also constructed in the generalized orthopair fuzzy environment, namely the q-rung orthopair fuzzy PHM (q-ROFPHM), the q-rung orthopair fuzzy PDHM (q-ROFPDHM), and their weighted forms. Their essential properties are verified to ensure the validity of the proposed aggregation operators (AOs). Subsequently, a new MAGDM approach is developed, employing the proposed AOs. The MAGDM problem of selecting the best person is examined. Moreover, the research includes a sensitivity analysis in three directions and a comparative analysis of the proposed MAGDM approach with five different approaches. The findings indicate that applying attribute partitioning in the proposed approach mitigates the adverse impact of irrelevant attributes, leading to more feasible and reliable outcomes. Additionally, a practical case study focuses on selecting a suitable industry for investment among the five available options. This case study demonstrates the approach’s effectiveness by considering five distinct qualities and results that make the Internet industry the best place to invest. Furthermore, a comparative analysis with four similar papers is also performed, indicating that the developed method’s results are more reliable and consistent.

Q-Rung Orthopair Fuzzy Archimedean Aggregation Operators: Application in the Site Selection for Software Operating Units

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

Q-rung orthopair normal fuzzy Maclaurin symmetric mean aggregation operators based on Schweizer-Skla operations

In order to be able to make a good decision, we need to evaluate the uncertainty information of multiple attributes of different alternatives that obey the normal distribution, and the interrelationship among multiple attributes should be considered in the process of evaluating. This paper aims to propose a new multiple attribute decision-making (MADM) method, which uses a new aggregation operator to evaluate the uncertainty information that obey normal distribution comprehensively. We firstly extended Schweizer-Sklar (SS) t-norm (TN) and t-conorm (TCN) to q-rung orthopair normal fuzzy number (q-RONFN) and defined the Schweizer-Skla operational laws of q-rung orthopair normal fuzzy set (q-RONFs). Secondly, we developed q-rung orthopair normal fuzzy Maclaurin symmetric mean aggregation operators based on SS operations considering that the Maclaurin symmetric mean operator can reflect the interrelationship among multiple input variables. Furthermore, we discussed some desirable properties of the above operators, such as monotonicity, commutativity, and idempotency. Lastly, we proposed a novel MADM method based on developed aggregation operators. A numerical example on enterprise partner selection is given to testify the effectiveness of the developed method. The results of analysis indicated that our proposed aggregation operators have stronger information aggregation ability and are more general and flexible for MADM problems.

Evaluation of economic development policies using a spherical fuzzy extended TODIM model with Z̆-numbers.

Zadeh's Z̆-numbers are able to more effectively characterize uncertain information. Combined with "constraint" and "reliability". It is more powerful at expressing human knowledge. While the reliability of data can have a direct impact on the precision of decisions. The key challenge in solving a Z̆-number issue is reasoning about both fuzzy and probabilistic uncertainty. Existing research on the Z̆-number measure is only some, and most studies cannot adequately convey the benefits of Z̆-information and the properties of Z̆-number. Considering this study void, this work concurrently investigated the randomness and fuzziness of Z̆-number with Spherical fuzzy sets. We first introduced the spherical fuzzy Z-numbers (SFZNs), whose elements are pairwise comparisons of the decision-maker's options. It can be used effectively to make true ambiguous judgments, reflecting the fuzzy nature, flexibility, and applicability of decision making data. We developed the operational laws and aggregation operators such as the weighted averaging operator, the ordered weighted averaging operator, the hybrid averaging operator, the weighted geometric operator, the ordered weighted geometric operator, and the hybrid geometric operator for SFZ̆Ns. Furthermore, two algorithm are developed to tackle the uncertain information in the form of spherical fuzzy Z̆-numbers based to the proposed aggregation operators and TODIM methodology. Finally, we developed the relative comparison and discussion analysis to show the practicability and efficacy of the suggested operators and approach.

Q-rung orthopair fuzzy Aczel–Alsina aggregation operators with multi-criteria decision-making

q-rung orthopair fuzzy sets (q-ROFSs) are advantageous for accurately expressing the preferences of decision-makers (DMs) due to their membership and non-membership degrees. This paper presents new q-rung orthopair fuzzy aggregation operators (AOs) that are based on Aczel–Alsina (AA) operations. These operators offer several advantages when dealing with real-world problems. The paper introduces new q-ROFS operations, such as the Aczel–Alsina product, sum, exponent, and scalar multiplication. We developed many AOs namely, the “q-rung orthopair fuzzy Aczel–Alsina weighted averaging (q-ROFAAWA) operator”, “q-rung orthopair fuzzy Aczel–Alsina ordered weighted averaging (q-ROFAAOWA) operator”, “q-rung orthopair fuzzy Aczel–Alsina hybrid averaging (q-ROFAAHA) operator”, “q-rung orthopair fuzzy Aczel–Alsina weighted geometric (q-ROFAAWG) operator,” the “q-rung orthopair fuzzy Aczel–Alsina ordered weighted geometric (q-ROFAAOWG) operator”, and the “q-rung orthopair fuzzy Aczel–Alsina hybrid geometric (q-ROFAAHG) operator”. Various attributes of these operators have been defined, including monotonicity, boundary, idempotency and commutativity. The paper demonstrates these properties for the suggested AOs. An algorithm for multi-criteria decision-making has been developed using the proposed aggregation operators with multiple evaluations by DMs and partial weight information under q-ROFSs. To demonstrate the effectiveness of the proposed approach, the paper uses a scenario for selecting the best green supplier. Additionally, the paper provides sensitivity analysis and compares the proposed technique with existing approaches.

Algorithm for Energy Resource Selection Using Priority Degree-Based Aggregation Operators with Generalized Orthopair Fuzzy Information and Aczel–Alsina Aggregation Operators

Many aggregation operators are studied to deal with multi-criteria group decision-making problems. Whenever information has two aspects, intuitionistic fuzzy sets and Pythagorean fuzzy sets are employed to handle the information. However, q-rung orthopair fuzzy sets are more flexible and suitable because they cover information widely. The current paper primarily focuses on the multi-criteria group decision-making technique based on prioritization and two robust aggregation operators based on Aczel–Alsina t-norm and t-conorm. This paper suggests two new aggregation operators based on q-rung orthopair fuzzy information and Aczel–Alsina t-norm and t-conorm, respectively. Firstly, novel q-rung orthopair fuzzy prioritized Aczel–Alsina averaging and q-rung orthopair fuzzy prioritized Aczel–Alsina geometric operators are proposed, involving priority weights of the information. Several related results of the proposed aggregation operators are investigated to see their diversity. A multi-criteria group decision-making algorithm based on newly established aggregation operators is developed, and a comprehensive numerical example for the selection of the most suitable energy resource is carried out. The proposed aggregation operators are compared with other operators to see some advantages of the proposed work. The proposed aggregation operators have a wider range for handling information, with priority degrees, and are based on novel Aczel–Alsina t-norm and t-conorm.

Generalized q-rung picture linguistic aggregation operators and their application in decision making

The q-rung picture linguistic set (q-RPLS) is an effective tool for managing complex and unpredictable information by changing the parameter ‘q’ regarding hesitancy degree. In this article, we devise some generalized operational laws of q-RPLS in terms of the Archimedean t-norm and t-conorm. Based on the proposed generalized operations, we define two types of generalized aggregation operators, namely the q-rung picture linguistic averaging operator and the q-rung picture linguistic geometric operator, and study their relevant characteristics in-depth. With a view toward applications, we discuss certain specific cases of the proposed generalized aggregation operators with a range of parameter values. Furthermore, we explore q-rung picture linguistic distance measure and its required axioms. Then we put forward a technique for q-RPLSs based on the proposed aggregation operators and distance measure to solve multi-attribute decision-making (MADM) challenges with unknown weight information. At last, a practical example is presented to demonstrate the suggested approaches’ viability and to perform the sensitivity and comparison analysis.

A three-way decision-making technique based on Pythagorean double hierarchy linguistic term sets for selecting logistic service provider and sustainable transportation investments

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

Aggregation Operators for Decision Making Based on q-Rung Orthopair Fuzzy Hypersoft Sets: An Application in Real Estate Project

In this paper, a decision-making problem with a q-rung orthopair fuzzy hypersoft environment is developed, and two operators of ordered weighted average and induced ordered weighted average are developed. Several fundamental features are also derived. The induced ordered weighted average operator is essential in a q-ROFH environment as the induced ordered aggregation operators are special cases of the existing aggregation operators that already exist in q-ROFH environments. The main function of these operators is to help decision-makers gain a complete understanding of uncertain facts. The proposed aggregation operator is applied to a decision-making problem, with the aim of selecting the most promising real estate project for investment.

Probabilistic linguistic multi-attribute decision making approach based upon novel GMSM operators

<abstract><p>Probabilistic linguistic terms set (PLTS), a new tool for expressing uncertain decision information, is composed of all possible linguistic terms (LTs) and their related probabilities. It also increases the corresponding probability of LTs in hesitant fuzzy linguistic term set (HFLTS). On the other hand, aggregation operator is an important information fusion tool, the Maclaurin symmetric mean (MSM) operator can provide more flexibility and robustness in information fusion, and make it more suitable for solving MADM problems with independent attributes. This current study adopts the merits of PLTS and MSM operator, and then a novel probabilistic linguistic decision making approach are targeted. Firstly, the operations of two PLTSs are redefined based upon Archimedean t-norm (ATN) and Archimedean t-conorm (ATC); Secondly, the probabilistic linguistic generalized MSM operator (PLGMSM) is proposed based on ATN and ATC, some properties of PLGMSM are investigated, then some special PLGMSM operators have been studied in detail when the parameters take different values and the generator of ATN takes different functions. Thirdly, the weighted probabilistic linguistic generalized MSM operator (WPLGMSM) is studied along with some properties of PLGMSM, some special WPLGMSM operators have been also investigated in detail when the parameters take different values and the generator of ATN takes different functions. Finally, on the basis of our proposed aggregation operators, the aggregated-based decision making approach is designed and an example is supplied to manifest the effectiveness of the proposed approach. Furthermore, some comparison analyses with extant decision approaches are carried out to illustrate the validity and feasibility of the proposed approach.</p></abstract>

A novel decision model with Einstein aggregation approach for garbage disposal plant site selection under $ q $-rung orthopair hesitant fuzzy rough information

<abstract><p>Environmental science and pollution research has benefits around the globe. Human activity produces more garbage throughout the day as the world's population and lifestyles rise. Choosing a garbage disposal site (GDS) is crucial to effective disposal. In illuminated of the advancements in society, decision-makers concede a significant challenge for assessing an appropriate location for a garbage disposal site. This research used a multi-attribute decision-making (MADM) approach based on $ q $-rung orthopair hesitant fuzzy rough ($ q $-ROHFR) Einstein aggregation information for evaluating GDS selection schemes and providing decision-making (DM) support to select a suitable waste disposal site. In this study, first, q-ROHFR Einstein average aggregation operators are integrated. Some intriguing characteristics of the suggested operators, such as monotonicity, idempotence and boundedness were also explored. Then, a MADM technique was established using the novel concept of $ q $-ROHFR aggregation operators under Einstein t-norm and t-conorm. In order to help the decision makers (DMs) make a final choice, this technique aims to rank and choose an alternative from a collection of feasible alternatives, as well as to propose a solution based on the ranking of alternatives for a problem with conflicting criteria. The model's adaptability and validity are then demonstrated by an analysis and solution of a numerical issue involving garbage disposal plant site selection. We performed a the sensitivity analysis of the proposed aggregation operators to determine the outcomes of the decision-making procedure. To highlight the potential of our new method, we performed a comparison study using the novel extended TOPSIS and VIKOR schemes based on $ q $-ROHFR information. Furthermore, we compared the results with those existing in the literature. The findings demonstrate that this methodology has a larger range of information representation, more flexibility in the assessment environment, and improved consistency in evaluation results.</p></abstract>

Correlation coefficient measures and aggregation operators on interval-valued linear Diophantine fuzzy sets and their applications

Intuitionistic fuzzy sets, Pythagorean fuzzy sets, and q-rung orthopair fuzzy sets are rudimentary concepts in computational intelligence, which have a myriad of applications in fuzzy system modeling and decision-making under uncertainty. Nevertheless, all these notions have some strict restrictions imposed on the membership and non-membership grades (e.g., the sum of the grades or the sum of the squares of the grades or the sum of the qth power of the grades is less than or equal to 1). To relax these restrictions, linear Diophantine fuzzy set is a new extension of fuzzy sets, by additionally considering reference/control parameters. Thereby, the sum of membership grade and non-membership grade can be greater than 1, and even both of these grades can be 1. By selecting different pairs of reference parameters, linear Diophantine fuzzy sets can naturally categorize concerned problems and produce appropriate solutions accordingly. In this paper, the interval-valued linear Diophantine fuzzy set, which is a generalization of linear Diophantine fuzzy set, is studied. The interval-valued linear Diophantine fuzzy set is more efficient to deal with uncertain and vague information due to its flexible intervals of membership grades, non-membership grades, and reference parameters. Some basic operations on interval-valued linear Diophantine fuzzy sets are presented. We define interval-valued linear Diophantine fuzzy weighted average and interval-valued linear Diophantine fuzzy weighted geometric aggregation operators. Based on these new aggregation operators, we propose a method for multi-criteria decision-making based on supplier selection under the interval-valued linear Diophantine fuzzy environment. Besides, a real-life example, comparison study, and advantages of proposed aggregation operators are presented. We describe some correlation coefficient measures (type-1 and type-2) for the interval-valued linear Diophantine fuzzy sets and they are applied in medical diagnosis for Coronavirus Disease 2019 (COVID-19). Lastly, a comparative examination and the benefits of proposed correlation coefficient measures are also discussed.

Selection of Appropriate Global Partner for Companies Using q-Rung Orthopair Fuzzy Aczel–Alsina Average Aggregation Operators

The term “q-Rung orthopair fuzzy sets (q^{r}OFSs)” refers to the collection of the most differentiated ideas for expressing fuzzy data in decision-making rules. The q^{r}OFSs can gradually adapt the region of information by adjusting the parameter q ge 1 in response to the fluctuation degree, so assisting in the generation of more numerous possibilities. Aczel–Alsina triangular norm and conorm are superior operations that may create general and adaptable working principles for aggregating arguments. To make use of q^{r}OFSs and Aczel–Alsina triangular norms in “multiple attribute decision-making (MADM)” issues, a few q-rung orthopair fuzzy (q^{r}OF) Aczel–Alsina aggregation operators: q^{r}OF Aczel–Alsina weighted average (q^{r}OFAAWA) operator, q^{r}OF Aczel–Alsina order weighted average (q^{r}OFAAOWA) operator, q^{r}OF Aczel–Alsina hybrid average (q^{r}OFAAHA) operator for aggregating q^{r}OFSs are exhibited in this article to fix the MADM issues based on q^{r}OFSs. Some significant properties are additionally demonstrated. A technique for taking care of the MADM issues is proposed based on these created operators. The adequacy of the suggested technique is shown by means of a numerical example on enterprise partner selection, a lot of investigations and correlations with other existing strategies. The sensitivity of the proposed aggregation operators to decision-making findings is investigated. The demonstration outcomes suggest that the suggested technique has fulfilling universality and adaptability in aggregating q^{r}OF data and acquiring the correlations of criteria and the attitudes of “decision-makers (DMs)” and is doable and compelling for taking care of the MADM issues dependent on q^{r}OFSs.

Selection of Optimal E-Learning Tool with Type-2 Intuitionistic Fuzzy Einstein Interactive Weighted Aggregation Operator

Not only are daily life activities being disrupted by the COVID-19 pandemic, but so are educational systems. To some extent, encouraging the use of e-learning technology has helped to stabilize the situation. The suitable selection of the appropriate e-learning platform for the institution depends upon different criteria with uncertain information. As type 2 intuitionistic fuzzy (T2IF) sets are conceptually intriguing and they provide a lot of expressive potential for dealing with uncertainty in expert knowledge, this work investigates the best e-learning tool for higher education in a type 2 intuitionistic fuzzy environment. A type-2 intuitionistic fuzzy einstein interactive weighted averaging (T2IFEIWA) operator is proposed for this purpose. The desirable properties of the proposed aggregation operator are validated, and the operator is used to choose the best e-learning tool.