Power Average Operator Research Articles

Novel Approach to Multi-Criteria Decision-Making Based on the n,mPR-Fuzzy Weighted Power Average Operator

A significant addition to fuzzy set theory for expressing uncertain data is an n,m-th power root fuzzy set. Compared to the nth power root, Fermatean, Pythagorean, and intuitionistic fuzzy sets, n,m-th power root fuzzy sets can cover more uncertain situations due to their greater range of displayed membership grades. When discussing the symmetry between two or more objects, the innovative concept of an n,m-th power root fuzzy set over dual universes is more flexible than the current notion of an intuitionistic fuzzy set, a Pythagorean fuzzy set, and a nth power root fuzzy set. In this study, we demonstrate a number of additional operations on n,m-th power root fuzzy sets along with a number of their special aspects. Additionally, to deal with choice information, we create a novel weighted aggregated operator called the n,m-th power root fuzzy weighted power average (FWPAmn) across n,m-th power root fuzzy sets and demonstrate some of its fundamental features. To rank n,m-th power root fuzzy sets, we also define the score and accuracy functions. Moreover, we use this operator to identify the countries with the best standards of living and show how we can select the best option by contrasting aggregate results using score values. Finally, we contrast the results of the FWPAmn operator with the square-root fuzzy weighted power average (SR-FWPA), the nth power root fuzzy weighted power average (nPR-FWPA), the Fermatean fuzzy weighted power average (FFWPA), and the n,m-rung orthopair fuzzy weighted power average (n,m-ROFWPA) operators.

A novel decision-making method based on complex cubic q-rung orthopair fuzzy information

To improve the accuracy of decision results in complex fuzzy environments, complex cubic fuzzy sets are studied, which can not only measure the periodicity of decision-making data, but also use interval values and single values to act together on the data. However, the fuzzy sets do not provide a reasonable explanation for some special cases of input arguments. Thus, the power average operator is used to eliminate the influence of extreme input arguments on decision results, and the Maclaurin symmetric mean operator considers the correlation between inputs in this paper. Firstly, we define the operation rules, distance measures, evaluation index function, and evaluation criteria in a complex cubic q-rung orthopair fuzzy environment. Then, some aggregation operators are proposed to aggregate complex cubic q-rung orthopair fuzzy numbers, and their desirable properties and some special cases are discussed. Next, we use the subjective and objective fusion method to determine the weight of attributes. Further, a multi-attribute decision-making method is established by combining aggregation operator, evaluation function, and weight determination method. Finally, the proposed method is applied to a specific quality evaluation problem, and the effectiveness and practicability of the proposed method are illustrated by other methods and parameter analysis.

Probabilistic dual hesitant fuzzy MAGDM method based on generalized extended power average operator and its application to online teaching platform supplier selection

Probabilistic dual hesitation fuzzy set (PDHFS) is a new tool used to enhance fuzzy and imprecise information in a changing and complex decision-making environment. Compared with the existing fuzzy sets, PDHFS is more suitable for identifying uncertain evaluation data in complex and realistic decision-making situations. The extended power average (EPA) and generalized power average (GPA) operators provide more information for the information aggregation process, reflecting the mutual support among all aggregation values. To solve the evaluation problems related to decision analysis involving extremely complex information, especially in the case of extreme data in the consideration of decision problems. In this paper, the generalized extended power average (GEPA) operator is proposed in the PDHF environment. This research has the following four important contributions. First, we propose a probability splitting algorithm of normalizing PDHFE, and give some new basic operations, score function, distance measures and aggregation operators. Second, to better integrate the advantages of EPA and GPA operators, we developed the GEPA operator, weighted form (WGEPA) and ordered form (GEPOWA). Meanwhile, by adjusting the parameter in three types of operators, we can find that many existing operators are special forms of the three types of operators. Third, extended the three types of operators to the PDHF environment, the PDHFGEPA, PDHFWGEPA, PDHFGEPOWA operators and some special aggregation operators are obtained, and studied their valuable properties in detail. Finally, taking the application of PDHFWGEPA operator as an example, a new multi-attribute group decision-making (MAGDM) technique is developed and used to solve the problem of online teaching platform supplier selection (OTPSS). Through parameter sensitivity analysis, the flexibility and stability of MAGDM technique are illustrated, and compared with some existing decision-making methods, the effectiveness of MAGDM method is proved. In addition, this technique also provides some theoretical references for dealing with other complex MAGDM problems, and provides a new operator for the extension of GEPA operator in other fuzzy environments. The biggest advantage of several operators is that they can pay full attention to the special role of extreme data in decision-making.

Dual Probabilistic Linguistic Full Consistency Additive Ratio Assessment Model for Medical Equipment Supplier Selection

In comparison to probabilistic linguistic term sets (PLTSs), dual probabilistic linguistic term sets (DPLTSs) reveal the complexity and uncertainty of this realistic world more accurately. The power average operator can mitigate the consequences of some decision-makers’ strong biases while evaluating data. Additionally, the Dombi operators during the phase of aggregation are very adaptable with general parameter. Inspired by these topics, we propose some dual probabilistic linguistic Dombi power aggregation operators to aggregate the decision-making expert’s preferences and various elegant properties of these proposed dual probabilistic linguistic (DPL)-aggregating operators. Further, we establish an integrated method with the combination of proposed DPL-aggregation operators, full consistency method (FUCOM) and additive ratio assessment (ARAS) model called the “DPL-FUCOM-ARAS” methodology for solving multi-criteria decision analysis problems under dual probabilistic linguistic environment. In this methodology, the FUCOM is applied to determine criteria weight, while the ARAS model is presented to prioritize the options from dual probabilistic linguistic perspective. We present a case study on the selection of a medical equipment supplier to highlight the applicability and show the usefulness of the proposed DPL-FUCOM-ARAS methodology. Further, we discuss the sensitivity investigation and comparative discussion to check the stability and robustness of the proposed DPL-FUCOM-ARAS methodology.

A novel MADM-based efficient methodology with 2-tuple linguistic neutrosophic numbers and applications to physical education teaching quality evaluation

With the successful promotion of the new round of basic education curriculum reform, China’s physical education (PE) teaching ideology and PE teaching mode have undergone profound changes, and these changes urgently require schools to establish a PE teaching quality (PETQ) evaluation system that is compatible with them, and urgently resolve the contradiction between theory and practice. The evaluation of teaching quality is not only a value judgment of teachers’ teaching ability and teaching effect, but also a value judgment of students’ learning ability and learning achievement changes. Therefore, it is an important issue of higher education research to construct a university PE teaching quality evaluation system and actively promote the healthy development of university PE teaching evaluation. The PETQ evaluation is viewed as the multi-attribute decision-making (MADM). In order to take the full use of power average (PA) operator and Heronian mean (HM) operator, in this article, we combine the generalized Heronian mean (GHM) operator and PA with 2-tuple linguistic neutrosophic numbers (2TLNNs) to propose the generalized 2-tuple linguistic neutrosophic power weighted HM (G2TLNPWHM) operator. The G2TLNPWHM could relieve the influence of the awkward data through power weights and it could also consider the relationships between the attributes, and it can give more accurate ranking order then the existing methods. The new MADM method is built on G2TLNPWHM operators. Finally, an example for PETQ evaluation in is used to show the proposed methods.

Spherical fuzzy hamacher power aggregation operators based on entropy for multiple attribute group decision making

As an improved form of fuzzy sets (FSs), spherical fuzzy sets (SFSs) could provide decision makers (DMs) with more free space to express their preference information. In this article, we first develop some Hamacher power aggregation operators under SFSs by power operators and Hamacher operators, including spherical fuzzy Hamacher power average (SFHPA) operator, spherical fuzzy Hamacher power geometric (SFHPG) operator, spherical fuzzy Hamacher power weighted average (SFHPWA) operator, spherical fuzzy Hamacher power weighted geometric (SFHPWG) operator, spherical fuzzy Hamacher power ordered weighted average (SFHPOWA) operator, spherical fuzzy Hamacher power ordered weighted geometric (SFHPOWG) operator, spherical fuzzy Hamacher power hybrid average (SFHPHA) operator and spherical fuzzy Hamacher power hybrid geometric (SFHPHG) operator. At the same time, some properties of the proposed operators are investigated, and the relationships between these operators and existing operators are discussed. Furthermore, a novel spherical fuzzy entropy measure is introduced to calculate unknown attribute weights. Then, some novel multiple attribute group decision making (MAGDM) methods are established by the proposed operators as well as entropy measure under SFSs. Lastly, the practicability of the presented methods is verified with a numerical case. Moreover, the robustness, availability and superiority for the developed methods are demonstrated via sensitivity analysis and further comparation with the existing methods.

Development of feature extraction method based on interval-valued Pythagorean fuzzy decision theory

Feature extraction is an important step in image processing and the accuracy of the extraction affects the result of subsequent target detection. There are many feature extraction algorithms, but there are few theories and methods about the accuracy of the extraction. Moreover, most of the existing extraction methods are computationally complex, and they will expose deficiencies once they encounter a large number of standard cases. In order to fill this gap, this study proposes a new soft computing multi-criteria group decision-making (MCGDM) method based on interval-valued Pythagorean fuzzy set information to deal with situations where multiple criteria are involved in complex decisions. Thus, the power average operator is used to eliminate the effects of unreasonable input arguments on decision-making results, and the Maclaurin symmetric mean operator is used to comprehensively consider the mutual relationship between input arguments in this article. Combining with the concept of IVPFS, the interval-valued Pythagorean fuzzy power Maclaurin symmetric mean (IVPFPMSM) operator and weighted IVPFPMSM operator are proposed. Then, the TOPSIS method is used to determine the weight vector of decision-making set, and a MCGDM method is developed under the interval-valued Pythagorean fuzzy framework. Next, aiming at the defects of the existing evaluation criteria, we consider the different ranges of membership degree and non-membership degree to propose a new evaluation criterion of MCGDM method. Finally, the proposed method is applied to the optimal selection of characteristic interval of foreign fibers to verify its practicability and effectiveness. The proposed method has certain guiding significance for the extension of decision-making fuzzy operators and the exploration of feature extraction methods.

Multi‐attribute group decision‐making based on linguistic Pythagorean fuzzy copula extended power average operator

AbstractThis paper aims to propose a novel multi‐attribute group decision‐making (MAGDM) method based on linguistic Pythagorean fuzzy copula extended power average operator. Existing researches under linguistic Pythagorean fuzzy environment lack of the ability to handle with extreme values and the flexible operational rules. To fill these two gaps, this paper first provides the definition of Archimedean copula and co‐copula operational rules under linguistic Pythagorean fuzzy environment, which can reflect the connection among arguments and provide more choices for experts to express their preferences. Then, we gather the extended power average (EPA) operator to present some new aggregation operators, which can reduce the negative influence of extreme evaluation values. To show the application of the proposed method to MAGDM problems, we apply it to handle a case of takeout O2O platform assessment problem. The numerical case and comparative analysis with other existing methods illustrate that our proposed method is more scientific and flexible.

Multivalued neutrosophic power partitioned Hamy mean operators and their application in MAGDM.

The novel multivalued neutrosophic aggregation operators are proposed in this paper to handle the complicated decision-making situations with correlation between specific information and partitioned parameters at the same time, which are based on weighted power partitioned Hamy mean (WMNPPHAM) operators for multivalued neutrosophic sets (MNS) proposed by combining the Power Average and Hamy operators. Firstly, the power partitioned Hamy mean (PPHAM) is capable of capture the correlation between aggregation parameters and the relationship among attributes dividing several parts, where the attributes are dependent definitely within the interchangeable fragment, other attributes in divergent sections are irrelevant. Secondly, because MNS can effectively represent imprecise, insufficient, and uncertain information, we proposed the multivalued neutrosophic PMHAM (WMNPHAM) operator for MNS and its partitioned variant (WMNPPHAM) with the characteristics and examples. Finally, this multiple attribute group decision making (MAGDM) technique is proven to be feasible by comparing with the existing methods to confirm this method's usefulness and validity.

Prioritization of thermal energy techniques by employing picture fuzzy soft power average and geometric aggregation operators

Energy storage is a way of storing energy to reduce imbalances between demand and energy production. The ability to store electricity and use it later is one of the keys to reaching large quantities of renewable energy on the grid. There are several methods to store energy such as mechanical, electrical, chemical, electrochemical, and thermal energy. Regarding their operation, storage, and cost, the choice of these energy storage techniques appears to be interesting. This issue becomes very serious when there involves uncertainty. To consider this kind of uncertain information, a picture fuzzy soft set is found to be a more appropriate parameterization tool to deal with imprecise data. Based on the advanced structure of picture fuzzy soft set, here in this article, firstly, we have developed the notions of basic operational laws for picture fuzzy soft numbers. Then based on these developed operational laws, we have established the notions of picture fuzzy soft power average left({mathrm{PFS}}_{mathrm{ft}}mathrm{PA}right), weighted picture fuzzy soft power average left({mathrm{WPFS}}_{mathrm{ft}}mathrm{PA}right) and ordered weighted picture fuzzy soft power average left({mathrm{OWPFS}}_{mathrm{ft}}mathrm{PA}right) aggregation operators. Moreover, we have introduced the notions for picture fuzzy soft power geometric left({mathrm{PFS}}_{mathrm{ft}}mathrm{PG}right), weighted picture fuzzy soft power geometric left({mathrm{WPFS}}_{mathrm{ft}}mathrm{PG}right) and ordered weighted picture fuzzy soft power geometric left({mathrm{OWPFS}}_{mathrm{ft}}mathrm{PG}right) aggregation operators. Furthermore, we have established the application of picture fuzzy soft power aggregation operators for the selection of thermal energy storage techniques. For this, we have developed a decision-making approach along with an explanatory example to show the effective use of the developed theory. Furthermore, a comparative analysis of the introduced work shows the advancement of developed notions.

Non-linear averaging-based operators of pseudo-hesitant fuzzy elements and an application

Data modeling/aggregating, in many uncertain real-world' problems such as decision-making processes, has gotten more attention in recent years. Due to a variety of uncertainty sources, various types of fuzzy sets, and various types of averaging-based aggregation functions have been proposed. The power average operator (PAO), as a nonlinear operator, is more appropriate than other averaging-based functions for situations where different values are given on a single subject. In this paper, PAO will be extended to be used in the aggregation process of given pseudo-hesitant fuzzy elements (pseudo-HFEs), and some needed properties have been discussed, too. Then, four kinds of PAO with pseudo-HFEs, i.e., power average operator of pseudo-HFEs, power weighted average operator of pseudo-HFEs, power ordered weighted average operator of pseudo-HFEs and power hybrid average operator of pseudo-HFEs, will be defined. To solve a multi-attribute group decision-making (MAGDM) problem, the evaluation step done by both decision-makers and self-assessment will be quantified by pseudo-HFEs. Then the PAO will be applied to aggregate the row elements of the resulting decision matrix. The ranking orders of obtained pseudo-HFEs, show the options' orders. Finally, the proposed method will be used to solve a multi-attribute group decision-making problem, illustrated numerically, analyzed, and validated.

An Approach to MADM Based on Aczel-Alsina Power Bonferroni Aggregation Operators for q-Rung Orthopair Fuzzy Sets

The power Bonferroni mean (PBM) is a combined networking system that can benefit both the power average (PA) operator, which might attenuate the effects of irrational data provided by the prejudiced decision-makers (DMs), and the BM operator, which may incorporate the interconnections between any two attributes. In this paper, we defined the aggregation operators (AOs), such as the power average (PA) operator and the power Bonferroni mean (PBM) operator, based on the Aczel-Alsina (AA) operational rules under the environment of the q-Rung Orthopair fuzzy set (q-ROFS), and provided their specific characteristics for the solution of numerical problems. We extend the power Bonferroni mean (PBM) operator under the framework of q-ROFVs to establish the q-Rung Orthopair Fuzzy Aczel-Alsina power Bonferroni mean (q-ROFAAPBM) operator and the q-Rung Orthopair Fuzzy Aczel-Alsina weighted power Bonferroni mean (q-ROFAAWPBM) operator and discuss a few of the most useful properties of these AOs. After that, the q-ROFAAWPBM operator is used to solve the multi-attribute decision-making steps for q-ROFVs. The disease is diagnosed with the MADM method, which shows its usefulness and effectiveness. Finally, the comparison of our developed approach has been demonstrated to be superior and more effective than the existing literature, and we can conclude the result.

Picture fuzzy power Muirhead mean operators and their application to multi attribute decision making

<p style='text-indent:20px;'>The main objective of this paper is to develop some aggregating operators for Picture fuzzy sets (PFS) by integrating power average (PA) and Muirhead mean (MM) operators. This paper develops Picture fuzzy power Muirhead mean (PFPMM), Picture fuzzy weighted power Muirhead mean (PFWPMM), Picture fuzzy dual power Muirhead mean (PFDPMM) and Picture fuzzy weighted dual power Muirhead mean (PFWDPMM) operators along with some desirable properties and special cases. Some advantages of developed operators are that they define the interrelationship between all aggregated values and lead to a flexible aggregation process through a parameter vector. Further, a multi-attribute decision making (MADM) problem based on proposed operators has been presented. To exemplify the availability and practicability of the proposed study, a financial investment risk problem in an enterprise is solved numerically. A sensitivity analysis is conducted to examine the effect of different values of parameters on aggregated values, while a comparative analysis is carried out to compare the results with some other existing operators.</p>

A Novel Linguistic Interval-Valued Pythagorean Fuzzy Multi-Attribute Group Decision-Making for Sustainable Building Materials Selection

The linguistic interval-valued Pythagorean fuzzy (LIVPF) sets, which absorb the advantages of linguistic terms set and interval-valued Pythagorean fuzzy sets, can efficiently describe decision makers’ evaluation information in multi-attribute group decision-making (MAGDM) problems. When investigating aggregation operators of linguistic interval-valued Pythagorean fuzzy (LIVPF) information, we have to consider two important issues, viz. the operational rules of LIVPF numbers and aggregation functions. The classical Archimedean t-norm and t-conorm (ATT) are a famous t-norm and t-conorm, which can produce some special cases. Recently, ATT has been widely applied in different fuzzy decision-making information. Hence, in this paper, for the first issue, we propose some novel operational rules of LIVPF numbers based on ATT. The new operational laws are flexible and can generate some useful operations. For the second issue, we choose a powerful function, i.e., the extended power average (EPA) operator as the aggregation function. The prominent advantages of EPA are that it not only considers the relationship among input arguments, but also dynamically changes the weights of input arguments by employing a parameter. Hence, our proposed novel aggregation operators for LIVPFNs are flexible and is suitable to handle MAGDM problems in actual life. Afterward, we further present a novel MAGDM method under LIVPF conditions. The main finding of our study is a new MAGDM method, which is more powerful and flexible than existing ones. Finally, we apply the method in a sustainable building materials selection to show its effectiveness. Additionally, comparison analysis is provided to demonstrate the advantages and superiorities of the proposed method.

Expertise-Structure and Risk-Appetite-Integrated Two-Tiered Collective Opinion Generation Framework for Large-Scale Group Decision Making

The generation of collective preference assessments occupies a critical position in deriving accurate and reliable alternative rankings in the context of large-scale group decision making (LSGDM). In general, the collective opinion generation framework entails the following three phases, which are clustering analysis, weighting clusters, and preference aggregation. However, the clustering of experts has been frequently based on preference similarities among them without taking into account individual opinions in which knowledge elicitation plays a crucial role. The traditional collective opinion generation framework suffering from this drawback may result in unreliable decision outcomes. To this end, we propose an expertise-structure and risk-appetite-integrated two-tiered collective opinion generation framework to address this concern. The first tier of the two-tiered collective opinion generation framework divides the entire expert group into several subgroups based on individual expertise structures, which are extracted from hesitant fuzzy linguistic term set (HFLTS)-based preference assessments, and it then weighs the resulting clusters in accordance with the overall expertise levels. The second-tier clusters the first-tier subgroups conditioned on the indicator of individual assessment similarities and gathers the generated subgroup preference constructs in the use of the risk appetite-oriented power average operator. In addition, the notion of proportional HFLTSs was introduced to manifest collective evaluations in second-tier subgroups to eliminate information loss and distortion. The effectiveness and flexibility of the proposed collective opinion generation algorithm are eventually illustrated by a case study and a comparison analysis.

Power Muirhead mean operators of interval-valued intuitionistic fuzzy values in the framework of Dempster–Shafer theory for multiple criteria decision-making

Multiple criteria decision-making (MCDM) based on interval intuitionistic fuzzy value (IVIFV) is a process of aggregating decision criteria represented by multiple interval-valued intuitionistic fuzzy numbers to select the optimal alternative. Among them, an aggregation operator is an indispensable tool, and the properties of an aggregation operator directly affect the decision results. Existing aggregation operators based on IVIFV have satisfactory results in eliminating the correlation between criteria and removing the influence of outliers on the results. However, there are some unreasonable results due to some undesired properties of IVIFVs. In this paper, IVIFV operation under the Dempster-Shafer theory (DST) framework is applied to combine the power average and Muirhead mean operators and interval intuitionistic fuzzy power Muirhead mean operators under DST framework are presented. Then a method based on the presented operators for MCDM problems is proposed. Finally, a set of numerical experiments are conducted to demonstrate the proposed method. The experimental results suggest that the proposed method not only retains the robustness of the power average operator and the capability of the Muirhead mean operator, but also eliminates a shortcoming that existing interval intuitionistic fuzzy operators cannot handle the case where the weights are in IVIFVs.

Multiattribute Decision-Making Method Based on Hesitant Triangular Fuzzy Power Average Operator

In the decision-making process, it often happens that decision makers hesitate between several possible preference values, so the multiattribute decision-making (MADM) problem of hesitant triangle fuzzy elements (HTFEs) has been widely studied. In related research works, different operators are used to fuse information, and the weighting model is used to represent the degree of difference between information fusion on various indicators, but the mutual influence between information is often not considered. In this sense, the purpose of this paper is to study the MADM problem of the hesitant triangular fuzzy power average (HTFPA) operator. First, the hesitant triangular fuzzy power-weighted average operator (HTFPWA) and the hesitant triangular fuzzy power-weighted geometric (HTFPWG) operator are given, their properties are analyzed and special cases are discussed. Then, a MADM method based on the HTFPWA operator and the HTFPWG operator is developed, and an example of selecting futures products is used to illustrate the results of applying the proposed method to practical problems. Finally, the effectiveness and feasibility of the HTFPA operator are verified by comparative analysis with existing methods.

Trapezoidal Intuitionistic Fuzzy Power Heronian Aggregation Operator and Its Applications to Multiple-Attribute Group Decision-Making

Decision-making problems involve imprecise and incomplete information that can be modelled well using intuitionistic fuzzy numbers (IFNs). Various IFNs are available in the literature for modelling such problems. However, trapezoidal intuitionistic fuzzy numbers (TrIFNs) are widely used. It is mainly because of the flexibility in capturing the incompleteness that occurs in the data. Aggregation operators play a vital role in real-life decision-making problems (modelled under an intuitionistic fuzzy environment). Different aggregation operators are available in the literature for better decision-making. Various aggregation operators are introduced in the literature as a generalization to the conventional aggregation functions defined on the set of real numbers. Each aggregation operator has a specific purpose in solving the problems effectively. In recent years, the power average (PA) operator has been used to reduce the effect of biased data provided by decision-makers. Similarly, the Heronian mean (HM) operator has a property that considers the inter-relationship among various criteria available in the decision-making problem. In this paper, we have considered both the operators (HM, PA) to introduce a new aggregation operator (on the set of TrIFNs), which takes advantage of both properties of these operators. In this study, firstly, we propose the idea of a trapezoidal intuitionistic fuzzy power Heronian aggregation (TrIFPHA) operator and a trapezoidal intuitionistic fuzzy power weighted Heronian aggregation (TrIFPWHA) operator by combining the idea of the Heronian mean operator and power average operator in real numbers. Secondly, we study different mathematical properties of the proposed aggregation operators by establishing a few essential theorems. Thirdly, we discuss a group decision-making algorithm for solving problems modelled under a trapezoidal intuitionistic fuzzy environment. Finally, we show the applicability of the group decision-making algorithm by solving a numerical case problem, and we compare the proposed method’s results with existing methods.

A novel two-stage TOPSIS approach based on interval-valued probabilistic linguistic q-rung orthopair fuzzy sets with its application to MAGDM problems

Fuzzy theories are widely used in multi-attribute group decision-making (MAGDM) problems to describe uncertain and hesitant information. The recently proposed probabilistic linguistic q-rung orthopair fuzzy set (PLq-ROFS) is capable in dealing with quantitative and qualitative information simultaneously. However, in many actual situations, decision-makers (DMs) prefer to utilize interval values to express their minds and evaluations, this paper employs interval values to represent the probabilistic distribution of the membership degrees (MDs) and non-membership degrees (NMDs), and proposes the interval-valued PLq-ROFS (IVPLq-ROFS). Based on which, a novel two-stage TOPSIS approach is introduced. The IVPLq-ROFS weighted extended power average (IVPLq-ROFWEPA) operator is proposed to obtain the comprehensive matrix and weights of each attribute, while a further advanced TOPSIS model is constructed to get the final rank of alternatives. An example of a new-type smart city development evaluation problem is given to illustrate the efficacy of the proposed approach. Results show that our approach is more flexible, more adaptable, more accurate, more freedom, and has much lower calculation complexity in the calculation process of the MAGDM problem. The contributions of the proposed method are mainly manifested in giving the concept of IVPLq-ROFSs, and proposing a novel two-stage TOPSIS model for dealing with MAGDM problems under IVPLq-ROFSs.

Evaluation and selection model of community group purchase platform based on WEPLPA-CPT-EDAS method

Community group purchase has been a neoteric and high-growth shopping model in recent years. Group purchase leaders develop their sociability and cooperate with group purchase platforms to provide residents with a convenient and low-cost shopping experience. In this study, we construct a comprehensive evaluation system for community group purchase platforms based on the operation process and the literature review. By extending the original operator, a new extended probabilistic linguistic power average (EPLPA) operator and weighted EPLPA (WEPLPA) operator for probabilistic linguistic term sets (PLTSs) are proposed, which have excellent performance in interpretability and retain the extreme evaluation information. In addition, the WEPLPA-CPT-EDAS model is proposed on the basis of cumulative prospect theory (CPT) and evaluation based on distance from average solution (EDAS). A multi-attribute evaluation method for community group purchase platforms is ultimately formed. Finally, the whole process of the model is demonstrated with a practical case concerning the selection of a community group purchase platform, and the model is compared and analyzed to verify the validity.