Multi-attribute Group Decision-making Problems Research Articles

A VIKOR Method Based on the Relative Closeness on Interval Linguistic Neutrosophic Uncertain Linguistic Numbers

In actual multi-attribute group decision-making problems, due to the complexity and uncertainty of objective things and the ambiguity of human thinking, decision-makers find it hard to give accurate evaluation information by crisp numbers. Even the weights of attribute values and decision-makers are ambiguous. At this time, we are more inclined to adopt the intuitive form of linguistic variables such as "excellent", "good" or "bad" to describe attribute values and weights. So in this paper, based on a neutrosophic set (NS), we further propose interval linguistic neutrosophic uncertain linguistic number (ILNULN). ILNULN combines interval linguistic neutrosophic and uncertain linguistic numbers, and it has the advantages of both. At the same time, due to the weighted arithmetic Bonferroni mean operator considering the interrelationship between aggregation parameters, therefore we combine the ILNULN and weighted arithmetic Bonferroni mean operator to propose the interval linguistic neutrosophic uncertain linguistic weighted arithmetic Bonferroni mean (ILNULWABM) operator. Finally, under the environment of interval linguistic neutrosophic and uncertain linguistic numbers, this article uses the linguistic weights and ILNULWABM operator to make VIKOR decision based on the relative closeness, and gives a practical example.

A large-scale multi-attribute group decision-making method with R-numbers and its application to hydrogen fuel cell logistics path selection

AbstractThe large-scale multi-attribute group decision-making (LSMAGDM) problem has become a hot research topic in the field of decision science. An R-numbers large-scale multi-attribute group decision-making (R-LSMAGDM) model is proposed to be constructed in this paper based on the advantages of R-numbers in capturing risks. First, the most commonly used clustering method, k-means, is introduced to determine the sub-groups. Then, a new sub-group weighting determination model is constructed by considering sub-group size and sub-group entropy. Next, we also build an optimized consensus-reaching model by improving the calculation method of the mean value. Then, the R-numbers weighted Hamy mean (RNWHM) operator is proposed to aggregate the sub-group information. In addition, the logarithmic percentage change-driven objective weighting (LOPCOW) method and the compromise ranking of alternatives from distance to ideal solution (CRADIS) method are used for attribute weighting calculation and alternative ranking, respectively. Finally, the effectiveness of the model is verified by an application example of hydrogen fuel cell logistics path selection.

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.

Maximum consensus model with individual tolerance and mixed DEA prospect cross-efficiency for multi-attribute group decision-making

Experts are mostly not completely rational, and they generally exhibit different psychological attitudes and behaviors in multi-attribute group decision-making (MAGDM), which may lead to actual decisions deviating from the results obtained by traditional objective methods. Therefore, it is reasonable and necessary to capture individual tolerance and risk attitudes of experts when dealing with MAGDM problems. To achieve this intention, we design a MAGDM method that combines the maximum consensus model with individual tolerance and mixed DEA prospect cross-efficiency. In the consensus reaching process (CRP), we devise a maximum consensus model with individual tolerance, which can achieve a high consensus level with limited expert tolerance. In the selection process, we first define the prospect aggressive and benevolent cross-efficiency functions. Then, a mixed DEA prospect cross-efficiency ranking method is proposed, which reflects the attitudes of DMs (decision-makers) towards losses and gains. Moreover, this method avoids DMs’ hesitation and trouble in choosing between aggressive and benevolent DEA models. Subsequently, the algorithm and framework for the MAGDM method based on individual tolerance and risk attitude are proposed. Finally, the applicability of our method can be validated by an illustrative example. Sensitivity analysis and comparative analysis are supplied to indicate the rationality and superiority of our developed method.

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.

A new multi-attribute group decision-making method based on probabilistic multi-valued linguistic spherical fuzzy sets for the site selection of charging piles

Motivated by the concepts of low carbon and environmental protection, electric vehicles have received much attention and become more and more popular all around the world. The expanding demand for electric vehicles has driven the rapid development of the charging pile industry. One of the prominent issues in charging pile industry is to determine their sites, which is a complex decision-making problem. As a matter of factor, the process of charging piles sites selection can be regarded as multi-attribute group decision-making (MAGDM), which is the main topic of this paper. The recently proposed linguistic spherical fuzzy sets (LSFSs) composed of the linguistic membership degree, linguistic abstinence degree and linguistic non-membership degree are powerful tools to express the evaluation information of decision makers (DMs). Based on the concept of LSFSs, we introduce probabilistic multi-valued linguistic spherical fuzzy sets (PMVLSFSs), which can describe DMs’ fuzzy evaluation information in a more refined and accurate way. The operation rules of PMVLSFSs are also developed in this article. To effectively aggregate PMVLSFSs, the probabilistic multi-valued linguistic spherical fuzzy power generalized Maclaurin symmetric mean operator and the probabilistic multi-valued linguistic spherical fuzzy power weighted generalized Maclaurin symmetric mean are put forward. Based on the above aggregation operators, a new method for MAGDM problem with PMVLSFSs is established. Further, a practical case of suitable site selection of charging pile is used to verify the practicability of this method. Lastly, comparative analysis with other methods is performed to illustrate the advantages and stability of proposed method.

A MAGDM approach for evaluating the impact of artificial intelligence on education using 2-tuple linguistic q-rung orthopair fuzzy sets and Schweizer-Sklar weighted power average operator.

The impact of artificial intelligence (AI) in education can be viewed as a multi-attribute group decision-making (MAGDM) problem, in which several stakeholders evaluate the advantages and disadvantages of AI applications in educational settings according to distinct preferences and criteria. A MAGDM framework can assist in providing transparent and logical recommendations for implementing AI in education by methodically analyzing the trade-offs and conflicts among many components, including ethical, social, pedagogical, and technical concerns. A novel development in fuzzy set theory is the 2-tuple linguistic q-rung orthopair fuzzy set (2TLq-ROFS), which is not only a generalized form but also can integrate decision-makers quantitative evaluation ideas and qualitative evaluation information. The 2TLq-ROF Schweizer-Sklar weighted power average operator (2TLq-ROFSSWPA) and the 2TLq-ROF Schweizer-Sklar weighted power geometric (2TLq-ROFSSWPG) operator are two of the aggregation operators we create in this article. We also investigate some of the unique instances and features of the proposed operators. Next, a new Entropy model is built based on 2TLq-ROFS, which may exploit the preferences of the decision-makers to obtain the ideal objective weights for attributes. Next, we extend the VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) technique to the 2TLq-ROF version, which provides decision-makers with a greater space to represent their decisions, while also accounting for the uncertainty inherent in human cognition. Finally, a case study of how artificial intelligence has impacted education is given to show the applicability and value of the established methodology. A comparative study is carried out to examine the benefits and improvements of the developed approach.

TODIM-PROMETHEE method for tourism landscape planning design scheme evaluation based on the virtual reality technology under spherical fuzzy sets

How to explore the potential value of landscape, realize the organic combination of tourism landscape, enrich landscape elements and enhance tourism experience has become an important topic of tourism landscape planning and design, which is also a practical problem that needs to be solved urgently in the process of tourism landscape development and planning in different regions of China. The tourism landscape planning design scheme evaluation based on the virtual reality technology a typical multi-attribute group decision-making (MAGDM) problem. With the complexity of economic activities, uncertain information has an increasing impact on production activities. However, due to the ambiguity and uncertainty of human cognition, the factors affecting the risk of things cannot be accurately expressed. Therefore, selecting spherical fuzzy sets (SFSs) can make the expression of information more accurate and complete. On basis of the TODIM method and the PROMETHEE method, in this study, spherical fuzzy number TOMIM-PROMETHEE (SFN-TOMIM-PROMETHEE) method is implemented to solve the MAGDM problem under SFSs. Furthermore, CRITIC method under SFSs is implemented to determine relative weights. Then a numerical example for tourism landscape planning design scheme evaluation based on the virtual reality technology is selected to illustrate the effectiveness and practicality of the method. Finally, the comparative analysis shows that the SFN-TOMIM-PROMETHEE method under SFSs is an effective method to deal with MAGDM problems. The main contribution of this paper is managed: (1) the TODIM and PROMETHEE technique was extended to SFSs; (2) CRITIC technique is employed to manage the weight values under SFSs. (3) the SFN-TOMIM-PROMETHEE technique is founded to manage the MAGDM under IVPFSs; (4) a numerical example for tourism landscape planning design scheme evaluation based on the virtual reality technology and comparison analysis are constructed to verify the feasibility and effectiveness of the SFN-TOMIM-PROMETHEE technique.

Decision analysis with IDOCRIW-QUALIFLEX approach in the 2TLq-ROF environment: An application of accident prediction models in Pakistan

In Pakistan, the assessment of road safety measures within road safety management systems is commonly seen as the most deficient part. Accident prediction models are essential for road authorities, road designers, and road safety specialists. These models facilitate the examination of safety concerns, the identification of safety improvements, and the projection of the potential impact of these modifications in terms of collision reduction. In the context described above, the goal of this paper is to utilize the 2-tuple linguistic q-rung orthopair fuzzy set (2TLq-ROFS), a new and useful decision tool with a strong ability to address uncertain or imprecise information in practical decision-making processes. In addition, for dealing with the multi-attribute group decision-making problems in road safety management, this paper proposes a new 2TLq-ROF integrated determination of objective criteria weights (IDOCRIW)-the qualitative flexible multiple criteria (QUALIFLEX) decision analysis method with a weighted power average (WPA) operator based on the 2TLq-ROF numbers. The IDOCRIW method is used to calculate the weight of attributes and the QUALIFLEX method is used to rank the options. To show the viability and superiority of the proposed approach, we also perform a case study on the evaluation of accident prediction models in road safety management. Finally, the results of the experiments and comparisons with existing methods are used to explain the benefits and superiority of the suggested approach. The findings of this study show that the proposed approach is more practical and compatible with other existing approaches.

Decision algorithm for picture fuzzy sets and Aczel Alsina aggregation operators based on unknown degree of wights

Aggregation operators (AOs) are well-known and efficient mathematical tools that are utilized to overcome the impact of imprecise and vague information during the aggregation process. The theoretical concepts of Aczel Alsina aggregation expressions are an extension of triangular norms and become a hot research topic in the environment of the fuzzy framework. The power operators provide a smooth approximation and are used to mitigate the influence of redundant or insufficient information on the attributes or criteria. Some robust aggregation approaches are developed by combining two different theories, like power operators and Aczel Alsina aggregation tools. This article aims to explore the theory of picture fuzzy sets (PFSs), an extended version of fuzzy sets, and intuitionistic fuzzy sets. Some robust operations of Aczel Alsina aggregation tools are also present in light of the picture fuzzy environment. We established a class of new methodologies in the light of picture fuzzy information, including picture fuzzy Aczel Alsina power weighted average (PFAAPWA) and picture fuzzy Aczel Alsina power ordered weighted average (PFAAPOWA) operators. We also developed an appropriate approach like picture fuzzy Aczel Alsina power weighted geometric (PFAAPWG) and picture fuzzy Aczel Alsina power ordered weighted geometric (PFAAPOWG) operators. Notable properties and characteristics of proposed methodologies are also demonstrated. Our invented approaches not only aggregate complicated information but can clearly define interrelationships among several arguments. Moreover, we establish an algorithm for the multi-attribute group decision-making (MAGDM) problem to handle the impact of redundant and vague information on human opinions. Finally, we study an experimental case study to evaluate an appropriate optimal option from available options. To reveal consistency and effectiveness of developed approaches, influence study by changing various parametric values and comparative study by comparing results of existing approaches.

An extended multi-expert concept lattice-based heterogeneous multi-attribute group decision-making approach

In practical multi-attribute group decision-making (MAGDM) problems, it is common to utilize heterogeneous representation forms to express distinct preference information for different experts, primarily due to their diverse backgrounds. To address the problem of reducing information loss from the aggregation of experts' opinions in heterogeneous MAGDM as well as improving the interpretability of the decision-making process, this paper introduces a concept lattice-based heterogeneous MAGDM approach. The heterogeneous multi-expert formal context is first proposed to capture the heterogeneous evaluation information of alternatives provided by different experts. Then, extended multi-expert concept lattices are constructed to aggregate evaluation information of alternatives by different experts. In this case, all concepts are considered to minimize information loss during the aggregation process. Second, to obtain more reasonable decision results, the distance between the concept intents and the heterogeneous positive and negative ideal solutions is considered, and the alternatives are ranked based on this measure. In addition, the MAGDM process for each alternative is visualized using the extended multi-expert concept lattices. This representation aids in identifying key concepts, their interdependencies, and the overall impact on the decision result. Finally, numerical examples and comparative analysis validate the validity and rationality of the proposed approach in heterogeneous MAGDM.

A novel uncertain information modeling method based on cosine similarity and cross entropy under spherical uncertain linguistic fuzzy set

Multi-attribute group decision-making (MAGDM) is one of the research hotspots in human cognitive and decision-making theory. However, there are still challenges to the existing MAGDM methods in modeling uncertain linguistics of decision-makers’ (DMs’) cognitive information and objectively obtaining weights. Therefore, this paper aims to develop a new MAGDM method considering incomplete known weight information under spherical uncertain linguistic sets (SULSs) to model uncertain information in MAGDM problems. The method mainly includes the following aspects. Firstly, a new concept, which enables an intuitive evaluation of neutral membership and hesitancy degrees at the linguistic evaluation, has been is first developed for capturing the more uncertain information. Secondly, the cosine similarity measure (CSM) and cross-entropy measure (CEM) are widely used to measure ambiguous information because of their robustness of measurement results. The CSM and CEM are extended to SULSs to calculate the DMs’ and attributes weights quantitively, respectively. Thirdly, in terms of effective integration of fuzzy information to obtain more accurate decision results, the Hamy mean (HM) and dual Hamy mean (DHM) operators are valued due to their consideration of the interrelationships between inputs. Two extension operators, named spherical fuzzy uncertain linguistic weight HM and DHM, are proposed to integrate spherical fuzzy uncertain linguistic information in the third stage. In the experiment, a decision case is presented to illustrate the applicability of the proposed method, and results show the effectiveness, flexibility and advantages of the proposed method are demonstrated by numerical examples and comparative analysis.

Multiple-attribute group decision-making method of linguistic q-rung orthopair fuzzy generalized power average operator based on DEMATEL

Linguistic q-rung orthpair fuzzy sets (Lq-ROFSs) can facilitate describing the uncertainty and the vagueness information existing in the real world. Based on the advantages of Lq-ROFSs, this paper innovatively puts forward a new method to solve the multi-attribute group decision-making (MAGDM) problems when the attribute weight is completely unknown, and proves the feasibility and effectiveness of this method through illustrative examples. Firstly, we propose the linguistic q-rung orthopair fuzzy generalized power average (Lq-ROFGPA) operator, which considers not only the importance of the data itself, but also the interaction between the data, and prove its properties. In particular, the linguistic q-rung orthopair fuzzy weighted generalized power average (Lq-ROFWGPA) operator takes into account the weight between data, which can better aggregate evaluation information. Then, we introduce decision making trial and evaluation laboratory (DEMATEL) method of the linguistic q-rung orthpair fuzzy numbers (Lq-ROFNs) to analyze the causal relationship and key elements of complex systems. Based on DEMATEL method, we further develop a weight model to calculate the attribute weights, which can make up for the deficiency which is the influence of the interaction between attributes that the existing weight determination method for Lq-ROFNs does not consider. Finally, we present a new MAGDM method based on the Lq-ROFWGPA operator and DEMATEL method. Further, several practical examples are given to illustrate the effectiveness and superiority of this new method in comparison with other existing MAGDM methods.

Optimized distance measures on hesitant fuzzy numbers: An application

As the rapidly progressing applications of uncertainty theories, the need for modifications to some of their existing mathematical tools or creating new tools to deal correctly with them in various environments is also exposed. Hesitant fuzzy numbers (HFNs), as a particular case of fuzzy numbers, are not an exception to this rule. Considering the necessity of determining the distance between given HFNs in many of their practical applications, this article shows that the existing methods either do not provide correct results or are not able to meet the needs of users. This paper aims to present new methods for distance measures of hesitant fuzzy numbers. To do them, three prevalent distance measures, i.e., the generalized distance measure, the Hamming distance measure, and the Euclidean distance measure, will be optimized into three distinct trinal categories. With the approach of reducing error propagation via reducing some unnecessary mathematical computations, new distance measures on HFNs will be introduced, first. The middle is the modification of the first category, which is more suitable when the given HFNs are equal-distance by the previous formula. Also, as the third category, the weighted form of these distance measures has been proposed, to be used where the real and membership parts of HFNs are not of equal importance. As an application of these, a TOPSIS-based technique for solving multi-attribute group decision-making problems with HFNs has been proposed. A numerical example will be implemented to describe the presented method. Finally, along with the validation of the proposed method, its numerical comparison with some other existing methods will be discussed in detail.

A Multi-Attribute Group Decision-Making Method Based on Trust Relationship and DEA Regret Cross-Efficiency

In multiattribute group decision-making (MAGDM) problems, the data envelopment analysis (DEA) cross-efficiency method is an effective tool to evaluate each decision-making unit. However, this method usually assumes that the decision-maker (DM) is completely rational, which ignores the risk psychology of the DM in the decision-making process. To compensate for this deficiency, this article proposes an MAGDM method based on trust relationships and DEA regret cross-efficiency. First, we construct a modified model based on the CCR model. Then, we propose the DEA regret cross-efficiency method. This method involves the risk psychology of the DM in the decision-making process. Next, a weighting model is developed to aggregate the cross-efficiency comprehensive utility matrix. Subsequently, we construct trust propagation and trust aggregation models to obtain the weights of experts. Finally, the MAGDM method based on trust relationships and DEA regret cross-efficiency is designed to rank all alternatives. A numerical example is provided to illustrate the superiority and rationality of our proposed method.

Three-way decision-making methods with multi-intuitionistic β-neighborhood-based multiattribute group decision-making problems

Multiattribute group decision-making (MAGDM) is a decision analysis method used to address decision-making problems that have multiple attributes and multiple decision alternatives. It is generally believed that multigranulation rough sets (MGRSs) are a twofold scheme to solve MAGDM problems. Thus, in this paper, we aim to generalize MGRSs and decision-theoretic rough sets (DTRSs) to intuitionistic fuzzy β-covering (IFβC) information systems and propose a novel MAGDM method to handle decision-making problems, which not only deepens the cognition of the three-way decision (3WD) model but also expands its application in decision-making problems. The paper first introduces a novel conditional probability using the ideal positive degree of intuitionistic fuzzy numbers (IFNs) and then investigates its properties. Second, in the IFβC environment, we utilize the proposed conditional probabilities to construct two types of multigranulation decision-theoretic rough set (MGDTRS) models, an optimistic strategy and a pessimistic strategy, discuss their theoretical properties and explore the relationship between the two strategies. Third, a novel MAGDM method for multi-intuitionistic β-neighborhoods is established in accordance with the proposed MGDTRS model. We also establish an algorithm for the proposed MAGDM method. Fourth, we apply the proposed method to address several MAGDM problems. By conducting comparative analysis with existing methods, we demonstrate the effectiveness of the proposed method and discuss the advantages and limitations of the proposed method. Furthermore, we conduct extensive parameter experimentation analysis on the proposed method from different perspectives. The experimental results demonstrate the stability and effectiveness of our proposed method.

T-Spherical Fuzzy Information and Shweizer-Sklar Operations Based Maclaurin Symmetric Mean Operator and Their Applications

T-spherical fuzzy set (TSFS) is the generalization of the fuzzy set (FS) which extracts the information from the real-life scenario with certainty. Aside from the remarkable advantage of being able to account for the connections among the multi-input considerations, such as multi-attributes or multi-experts in the multi-attribute group decision-making (MAGDM), the Maclaurin symmetric mean operator (MSMO) is also the generalization of several different existing operators. Moreover, one important class of T-norms (TN) and T-conorms (TC) is the Schweizer-Sklar TN (SSTN) and TC (SSTC). In this article, the operational laws for TSFS based on SSTN and SSTC are introduced first. Then the introduced operations are used to develop a class of aggregation operators (AOs) to aggregate the information in the form of the T-spherical fuzzy values (TSFVs). The introduced operators in this article are the T-spherical fuzzy Schweizer-Sklar MSMO (TSFSSMSMO) and the T-spherical fuzzy Schweizer-Sklar weighted MSMO (TSFSSWMSMO). Further, the TSFSSMSMO and TSFWMSMO are applied to a specific multi-attribute group decision-making (MAGDM) problem to show the significance of the developed operators.

Decision-Making Based on Spherical Linear Diophantine Fuzzy Rough Aggregation Operators and EDAS Method

In everyday life, decision-making is a difficult task fraught with ambiguity and uncertainty. Many researchers and scholars have suggested numerous fuzzy set theories to resolve these ambiguities and uncertainties. The EDAS method (evaluation based on distance from average answer) is extremely beneficial in decision-making situations. In multi-attribute group decision-making (MAGDM) situations, this is especially true when there are more competing criteria. In this paper, we introduce the concept of spherical linear diophantine fuzzy rough sets (SLDFRSs). We develop basic operational laws and a number of propose aggregation operators. Furthermore, the necessary and desired features of SLDFRS are explored. This study proposes a new technique known as the spherical linear diophantine fuzzy rough set EDAS (SLDFRS-EDAS) method to deal with these uncertainties in the MAGDM problem. A MAGDM technique is intended to evaluate the emergency system based on the newly introduced operators. Furthermore, a comparison study of the activity and applicability of the suggested approach with earlier procedures is used to validate its viability and applicability.

Multi-attribute group decision-making based on Pythagorean fuzzy rough Aczel-Alsina aggregation operators and its applications to Medical diagnosis

The fusion of information is a very hectic process whenever we analyze the information. Several frameworks have been introduced to reduce the uncertainty while fusing the information. Among those techniques, the Pythagorean fuzzy rough set (PyFRS), which is based on approximations is a key idea for dealing with uncertainty when data is taken from real-world circumstances. Furthermore, the most adaptable and flexible operational laws based on the parameters for fuzzy frameworks are Aczel-Alsina t-norm (AATNM) and Aczel-Alsina t-conorm (AATCNM). The major goal of this work is to introduce some methods for the basic operations of the information in the shape of Pythagorean fuzzy rough (PyFR) values (PyFRVs). Consequently, the PyFR Aczel-Alsina weighted geometric (PyFRAAWG), PyFR Aczel-Alsina ordered weighted geometric (PyFRAAOWG), and PyFR Aczel-Alsina hybrid weighted geometric (PyFRAAHWG) operators are developed in this article based on AATNM and AATCNM. Further, some basic properties of the developed operators are observed and discussed. Further, the developed approaches are applied to the problem of multi-attribute group decision-making (MAGDM). The obtained results from the MAGDM problem are observed at various values of the parameters involved by AATNM and AATCNM. Moreover, the results are also compared with already existing techniques for the significance of the developed approach.

A novel fuzzy TOPSIS method based on T-spherical fuzzy Aczel–Alsina power Heronian mean operators with applications in pharmaceutical enterprises’ selection

One of the most significant and complete approaches to accommodate greater uncertainty than current fuzzy structures is the T-Spherical Fuzzy Set (TSPFS). The primary benefit of TSPFS is that current fuzzy structures are special cases of it. Firstly, some novel TSPF power Heronian mean (TSPFPHM) operators are initiated based on Aczel–Alsina operational laws. These aggregation operators (AOs) have the capacity to eliminate the impact of uncomfortable data and can simultaneously consider the relationships between any two input arguments. Secondly, some elementary properties and core cases with respect to parameters are investigated and found that some of the existing AOs are special cases of the newly initiated aggregation operators. Thirdly, based on these AOs and Aczel–Alsina operational laws a newly advanced technique for order of preference by similarity to ideal solution (TOPSIS)-based method for dealing with multi-attribute group decision-making (MAGDM) problems in a T-Spherical fuzzy framework is established, where the weights of both the decision makers (DMs) and the criteria are completely unknowable. Finally, an illustrative example is provided to evaluate and choose the pharmaceutical firms with the capacity for high-quality, sustainable development in the TSPF environment to demonstrate the usefulness and efficacy. After that, the comparison analysis with other techniques is utilized to demonstrate the coherence and superiority of the recommended approach.