Multi-attribute group decision making based on p, q-quasirung orthopair fuzzy Yager prioritized weighted geometric aggregation operator of p, q-quasirung orthopair fuzzy numbers

A new method is developed to solve multi-attribute group decision making (MAGDM) problem in which the attribute values, attribute weights and expert weights are all in the form of 2-tuple linguistic information. First, the operation laws for 2-tuple linguistic information are defined and the related properties of the operation laws are studied. Then, some new hybrid geometric aggregation operators with 2-tuple linguistic information are developed, involving the 2-tuple hybrid weighted geometric average (THWAG) operator, the 2-tuple hybrid linguistic weighted geometric average (T-HLWG) operator and the extended 2-tuple hybrid linguistic weighted geometric average (ET-HLWG) operator. These hybrid geometric aggregation operators generalize the existing 2-tuple linguistic geometric aggregation operators and reflect the important degrees of both the given 2-tuples and the ordered positions of the 2-tuples. In the proposed decision method, using the ET-HLWG operators the individual overall preference v...

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

In some multi-attribute decision-making (MADM) models studying attributes’ interactive phenomena is very important for the minimizing decision risks. Usually, the Choquet integral type aggregations are considered in such problems. However, the Choquet integral aggregations do not consider all attributes’ interactions; therefore, in many cases, when these interactions are revealed in less degree, they do not perceive these interactions and their utility in MADM problems is less useful. For the decision of this problem, we create the Choquet integral-based new aggregation operators’ family which considers all pair interactions between attributes. The problem under the discrimination q-rung picture linguistic and q-rung orthopair fuzzy environments is considered. Construction of a 2-order additive fuzzy measure (TOAFM) involves pair interaction indices and importance values of attributes of a MADM model. Based on the attributes’ pair interactions for the identification of associated probabilities of a 2-order additive fuzzy measure, the Shapley entropy maximum principle is used. The associated probabilities q-rung picture linguistic weighted averaging (APs-q-RPLWA) and the associated probabilities q-rung picture linguistic weighted geometric (APs-q-RPLWG) aggregation operators are constructed with respect to TOAFM. For an uncertainty pole of experts’ evaluations on attributes regarding the possible alternatives, the associated probabilities of a fuzzy measure are used. The second pole of experts’ evaluations as arguments of the aggregation operators by discrimination q-rung picture linguistic values is presented. Discrimination q-rung picture linguistic evaluations specify the attribute’s dominant, neutral and non-dominant impacts on the selection of concrete alternative from all alternatives. Constructed operators consider the all relatedness between attributes in any consonant attribute structure. Main properties on the rightness of extensions are showed: APs-q-RPLWA and APs-q-RPLWG operators match with q-rung picture linguistic Choquet integral averaging and geometric operators for the lower and upper capacities of order two. The conjugation among the constructed operators is also considered. Connections between the new operators and the compositions of dual triangular norms (Tp,Spq) and (Tmin,Smax) are also constructed. Constructed operators are used in evaluation of a selection reliability index (SRI) of candidate service centers in the facility location selection problem, when small degree interactions are observed between attributes. In example MADM, the difference in optimal solutions is observed between the Choquet integral aggregation operators and their new extensions. The difference, however, is due to the need to use indices of all interactions between attributes.

Picture fuzzy set is an extension of intuitionistic fuzzy set, which allows interpreting uncertain data in decision-making problems. This study provides aggregation operators based on Choquet integral, namely Choquet integral picture fuzzy geometric aggregation (CIPFGA) operator and Choquet integral picture fuzzy hybrid geometric aggregation (CIPFHGA) operator with certain properties of these operators are established. We validate the functioning of the operators with illustrative examples. The CIPFHGA operator has an added benefit of combining the weights of positions along with capturing the comprehensive correlative relationships of the criteria. Further, the proposed operators enable us to solve a numerical problem in picture fuzzy Multi attribute decision-making problem and also allows to make a comparison study with the existing literature.

Based on the extended triangular norm, several new operational laws for linguistic variables and uncertain linguistic variables (ULVs) are defined. To avoid the limitations of existing linguistic aggregation operators, a series of extended uncertain linguistic (UL) geometric aggregation operators are proposed on the basis of the extended triangular norm. In addition, a multiattribute group decision making (MAGDM) method dealing with UL information is developed based on the extended UL geometric aggregation operators. Finally, an example is presented to show the efficiency of the developed approach in solving MAGDM problems.

Neutrosophic cubic sets (NCSs) can express complex multi-attribute decision-making (MADM) problems with its interval and single-valued neutrosophic numbers simultaneously. The weighted arithmetic average (WAA) and geometric average (WGA) operators are common aggregation operators for handling MADM problems. However, the neutrosophic cubic weighted arithmetic average (NCWAA) and neutrosophic cubic geometric weighted average (NCWGA) operators may result in some unreasonable aggregated values in some cases. In order to overcome the drawbacks of the NCWAA and NCWGA, this paper developed a new neutrosophic cubic hybrid weighted arithmetic and geometric aggregation (NCHWAGA) operator and investigates its suitability and effectiveness. Then, we established a MADM method based on the NCHWAGA operator. Finally, a MADM problem with neutrosophic cubic information was provided to illustrate the application and effectiveness of the proposed method.

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.

Trapezoidal-valued fermatean fuzzy numbers (TpVFFNs) are essential for handling daily decision-making issues in the engineering and management fields. Accumulation processes on the set of TpVFFN are used to address decision-making problems described in this environment as necessary. The primary goal of this paper is to provide the concept of Dombi t-norm (Dtn)- and Dombi t-conorm (Dtcn)-based accumulation operators on the class of TpVFFN, emphasizing how they behave symmetrically in aggregation processes to maintain consistency and fairness. To use s to illustrate mathematical circumstances, we first create a trapezoidal-valued fermatean fuzzy Dombi’s weighted geometric operator, hexagonal hybird geometric operator, fermatean fuzzy order weighted geometric operator. Second, we use a multi-attribute group decision-making (MAGDM) approach to compute the recommended accumulation operators. Finally, we demonstrate the potential practical application of the proposed decision-making problem related to the pink cab.

Enterprise resource planning (ERP) system selection involves multiple evaluation attributes with interaction. It can be attributed to a type of interactive multi-attribute group decision making (MAGDM). Linguistic hesitant fuzzy sets (LHFSs) are powerful tools to represent the uncertainty, hesitancy, and inconsistency of decision makers’ (DMs’) preference. This article proposes two new methods for interactive MAGDM with LHFSs based on comprehensive cloud (CC) power geometric (PG) aggregation operators. First, the CC of LHFS is defined and a distance measure between two CCs is offered. Considering the interaction among the aggregated LHFSs, we develop some CC PG aggregation operators of LHFSs. An uncertainty degree of LHFS is defined. Then, an approach is developed to derive the weights of DMs. An approach is proposed to derive the comprehensive attribute weights. Thus two new methods are presented for interactive MAGDM with LHFSs. An ERP selection example is provided to validate the proposed methods.

Describing uncertainties of more than one aspect is a hot research topic in fuzzy mathematics. Atanassov’s intuitionistic fuzzy set (IFS) and Cuong’s picture fuzzy set (PFS) are two featured fuzzy concepts. Recently, a novel framework of T-spherical fuzzy set (TSFS) and consequently spherical fuzzy set (SFS) are developed for handling those problems where uncertain situations have more than two aspects. This manuscript is based on some contribution to the area of SFS and TSFS. In this manuscript, some properties of aggregation tools of TSFS (SFS) are discussed and some ordered weighted geometric (OWG) and hybrid geometric (HG) operators are developed. It is discussed that these aggregation operators are generalizations of the aggregation operators of IFSs and PFSs. Multi-attribute decision making (MADM) process is comprehensively discussed in T-spherical fuzzy environment and elaborated with a numerical example. The results obtained are analyzed and their advantages over existing structures are studied.

Intuitionistic fuzzy geometric aggregation operators in the framework of Aczel-Alsina triangular norms and their application to multiple attribute decision making

Arithmetic aggregation operators and geometric aggregation operators of intuitionistic fuzzy values (IFVs) are common aggregation operators in the fields of information fusion and decision making. However, their aggregated values imply some unreasonable results in some cases. To overcome the shortcomings, this paper proposes an intuitionistic fuzzy hybrid weighted arithmetic and geometric aggregation (IFHWAGA) operator and an intuitionistic fuzzy hybrid ordered weighted arithmetic and geometric aggregation (IFHOWAGA) operator and discusses their suitability by numerical examples. Then, we propose a multiple attribute decision-making method of mechanical design schemes based on the IFHWAGA or IFHOWAGA operator under an intuitionistic fuzzy environment. Finally, a decision-making problem regarding the mechanical design schemes of press machine is provided as a case to show the application of the proposed method.

Some interval-valued 2-tuple linguistic aggregation operators and application in multiattribute group decision making

<abstract><p>The aims of this study is to define a cubic fuzzy set based logarithmic decision-making strategy for dealing with uncertainty. Firstly, we illustrate some logarithmic operations for cubic numbers (CNs). The cubic set implements a more pragmatic technique to communicate the uncertainties in the data to cope with decision-making difficulties as the observation of the set. In fuzzy decision making situations, cubic aggregation operators are extremely important. Many aggregation operations based on the algebraic t-norm and t-conorm have been developed to cope with aggregate uncertainty expressed in the form of cubic sets. Logarithmic operational guidelines are factors that help to aggregate unclear and inaccurate data. We define a series of logarithmic averaging and geometric aggregation operators. Finally, applying cubic fuzzy information, a creative algorithm technique for analyzing multi-attribute group decision making (MAGDM) problems was proposed. We compare the suggested aggregation operators to existing methods to prove their superiority and validity, and we find that our proposed method is more effective and reliable as a result of the comparison and sensitivity analysis.</p></abstract>

Assessing physical education (PE) classroom teaching enhancement through modern technologies remains a difficult task in the present era. The evaluation system contains four fundamental dimensions: student engagement, skill development effectiveness, cognitive impact, and feedback and assessment capability. Multi-attribute decision-making (MADM) is one of the most trending systems for ranking alternatives based on their attributes. The interval-valued circular intuitionistic fuzzy set is an advanced approach for assessing MADM problems, rather than the existing simple circular intuitionistic fuzzy set. The ordinary circular intuitionistic fuzzy set lacks a concept of intervals in membership degree (MD), non-membership degree (NMD), and circular degree (CD), resulting in a significant amount of information being lost. Dombi operations are a valuable approach to improving the precision of aggregated results. The interval-valued circular intuitionistic fuzzy set-based analytic hierarchy process (AHP) provides a structured and objective framework for evaluating various innovative teaching approaches, which can be complex. The evaluation process utilizes interval-valued circular intuitionistic fuzzy set-based AHP to assess three innovative PE teaching methods that help educators and policymakers maximize the effectiveness of their instruction. In the past, various approaches were defined within different fuzzy set-based frameworks; however, they lacked a proper method for evaluating the weightage of alternatives. There is a need to define new concepts using interval-valued circular intuitionistic fuzzy set-based information under AHP for the assessment of vague and uncertain MADM problems. By applying the concept of AHP, Dombi operations, and interval-valued circular intuitionistic fuzzy set, this study develops new theories, including interval-valued circular intuitionistic fuzzy Dombi weighted averaging (IV-CIFDWA) and interval-valued circular intuitionistic fuzzy Dombi weighted geometric (IV-CIFDWG) aggregation operators (AOs). The presence of AHP in the proposed approach makes it unique from other existing MADM approaches. We also investigate some desirable axioms of AOs. We offer an MADM algorithm based on a theory developed for precisely investigating fuzzy information. Solve the numerical problem of selecting the best PE platform using the MADM approach. We are ranking the set of considered alternatives like use of wearable fitness technology; game-based learning technology; video Feedback and performance analysis; task-based cooperative Learning. We noticed that use of wearable fitness technology is the best alternative is achieved by using the IV-CIFDWA and IV-CIFDWG operators. We compare our proposed methods with existing methods to verify their authenticity and accuracy. Lastly, we offer a conclusion.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-18080-0.