Power Average Operator Research Articles

Analysis of Hamacher power aggregation operators for circular complex p, q-quasirung orthopair fuzzy 2-tuple linguistic sets and their application in green industry development

Green industry development focuses on balancing economic and financial growth with environmental stewardship and ensuring that companies and industries are contributing positively to both environmental sustainability and prosperity. This manuscript aims to develop the novel technique of circular complex p, q-quasirung orthopair fuzzy 2-tuple linguistic (CCp, q-QOF2-TL) set and their operational laws based on algebraic t-norms and Hamacher t-norms, where the algebraic t-norms and Einstein t-norms are the special cases of the Hamacher t-norms for parameter ϜℲs=l and ϜℲs=2. Further, we derive the Hamacher power aggregation operators based on any finite collection of CCp, q-QOF2-TL numbers (CCp, q-QOF2-TLNs), called CCp, q-QOF2-TL Hamacher power average (CCp, q-QOF2-TLHPA) operator, CCp, q-QOF2-TL Hamacher power weighted average (CCp, q-QOF2-TLHPWA) operator, CCp, q-QOF2-TL Hamacher power geometric (CCp, q-QOF2-TLHPG) operator, CCp, q-QOF2-TL Hamacher power weighted geometric (CCp, q-QOF2-TLHPWG) operator, and described their basic properties, called idempotency, monotonicity, and boundedness. Further, we demonstrate the technique of multi-attribute decision-making (MADM) problem based on the above operators to evaluate the major factor that will be playing in the development of the green industry. Finally, we compare the proposed ranking values with the obtained ranking values of existing techniques to show the supremacy and superiority of the initiated approaches.

MADM framework based on interval-valued neutrosophic aczel-alsina power average operator and application to translation teaching quality evaluation of college English

The huge demand for translation talents has prompted the universities to focus on improving the quality of translation teaching. As a necessary means to improve the quality of teaching, translation teaching quality evaluation plays a role in guiding, regulating and managing translation teaching, which is an important part of translation teaching. The translation teaching quality evaluation of college English is viewed as the multiple attribute decision making (MADM). The interval-valued neutrosophic sets (IVNSs) are used as an effective tool for characterizing uncertain information during the translation teaching quality evaluation of college English. In this paper, interval-valued neutrosophic number (IVNN) Aczel-Alsina power average (IVNNAAPA) operator is proposed based on the classical Aczel-Alsina operator and power average (PA) operator. Then, IVNNAAPA operator is employed to cope with MADM problem. Finally, the numerical decision example for translation teaching quality evaluation of college English is employed to illustrate the produced method and some comparative models are used to prove the effectiveness of the IVNNAAPA method.

Interval-valued T-spherical fuzzy extended power aggregation operators and their application in multi-criteria decision-making

Abstract As an effective tool to show the fuzziness of qualitative information, the interval-valued T-spherical fuzzy set can utilize three kinds of information, namely, membership, abstinence, and non-membership, to show the opinions of decision-maker. Given this advantage, many interval-valued T-spherical fuzzy multi-criteria decision-making (IVTSF-MCDM) methods have been designed. However, most of the existing IVTSF-MCDM methods have a common limitation that the inability to effectively show the impacts of extreme data. To address this limitation, this study develops a novel MCDM method based on interval-valued T-spherical fuzzy extended power aggregation operator. First, interval-valued T-spherical fuzzy cross-entropy (CE) and interval-valued T-spherical fuzzy symmetrical CE are defined to measure the difference between two interval-valued T-spherical fuzzy numbers, which are used to determine criteria weights in MCDM. Second, interval-valued T-spherical fuzzy extended power average operator and interval-valued T-spherical fuzzy extended power geometric operator are proposed, and their properties are investigated. Moreover, in view of that criteria may be assigned to different weights, this study defines interval-valued T-spherical fuzzy extended power weighted average operator and interval-valued T-spherical fuzzy extended power weighted geometric operator to derive the order of alternatives. Finally, the applicability of the proposed method is validated by the case about investment country selection, while the sensitivity and comparison analyses are also conducted to further prove its advantages and effectiveness.

A 2-order additive fuzzy measure identification method based on hesitant fuzzy linguistic interaction degree and its application in credit assessment

To reflect both fuzziness and hesitation in the evaluation of interactivity between attributes in the identification process of 2-order additive fuzzy measure, this work uses the hesitant fuzzy linguistic term set (HFLTS) to describe and depict the interactivity between attributes. Firstly, the interactivity between attributes is defined by the supermodular game theory. According to this definition, a linguistic term set is established to characterize the interactivity between attributes. Under the linguistic term set, the experts employ linguistic expressions generated by context-free grammar to qualitatively describe the interactivity between attributes. Secondly, through the conversion function, the linguistic expressions are transformed into the hesitant fuzzy linguistic term sets (HFLTSs). The individual evaluation results of all experts were further aggregated with the defined hesitant fuzzy linguistic weighted power average operator (HFLWPA). Thirdly, based on the standard Euclidean distance formula of the hesitant fuzzy linguistic elements (HFLEs), the hesitant fuzzy linguistic interaction degree (HFLID) between attributes is defined and calculated by constructing a piecewise function. As a result, a 2-order additive fuzzy measure identification method based on HFLID is proposed. Based on the proposed method, using the Choquet fuzzy integral as nonlinear integration operator, a multi-attribute decision making (MADM) process is then presented. Taking the credit assessment of the big data listed companies in China as an application example, the analysis results of application example prove the feasibility and effectiveness of the proposed method. This work successfully reflects both the fuzziness and hesitation in evaluating the interactivity between attributes in the identification process of 2-order additive fuzzy measure, enriches the theoretical framework of 2-order additive fuzzy measure, and expands the applicability and methodology of 2-order additive fuzzy measure in multi-attribute decision making.

Advanced Linguistic Complex T-Spherical Fuzzy Dombi-Weighted Power-Partitioned Heronian Mean Operator and Its Application for Emergency Information Quality Assessment

Against the background of a major change in the world unseen in a century, emergencies with high complexity and uncertainty have had serious impacts on economic security and sustainable social development, making emergency management an important issue that needs to be urgently resolved, and the quality assessment of emergency information is a key link in emergency management. To effectively deal with the uncertainty of emergency information quality assessment, a new fuzzy multi-attribute assessment method is proposed in this paper. First, we propose the linguistic complex T-spherical fuzzy set (LCT-SFS), which can deal with two-dimensional problems and cope with situations in which assessment experts cannot give quantitative assessments. Then, the advanced linguistic complex T-spherical fuzzy Dombi-weighted power-partitioned Heronian mean (ALCT-SFDWPPHM) operator, which incorporates the flexibility of Dombi operations, is proposed. The partitioned Heronian mean (PHM) operator can consider attribute partitioning and attribute correlation, the power average (PA) operator can eliminate the effect of evaluation singularities, and the advanced operator can circumvent the problem of consistent or indistinguishable aggregation results, which provides a strong comprehensive advantage in the evaluating information aggregation. Finally, a fuzzy multi-attribute assessment model is constructed by combining the proposed operator with the WASPAS method and applied to the problem of assessing the quality and sensitivity of emergency information; qualitative and quantitative comparison analyses are carried out. The results show the method proposed in this paper has strong feasibility and validity and can represent uncertainty assessment more flexibly while providing reasonable and reliable results. The method can provide new ideas and methods for the quality assessment of emergency information, and promoting sustainable, efficient, and high-quality development of emergency management.

Multiple-attribute group decision-making approach using power aggregation operators with CRITIC-WASPAS method under 2-dimensional linguistic intuitionistic fuzzy framework

The 2-dimensional linguistic intuitionistic fuzzy variables (2DLIFVs) provide an efficient tool to model the cognitive information of experts in practical circumstances while considering the reliability of the evaluation results. It is a hybrid model representing qualitative information, which derives from integrating the 2-dimensional linguistic variables (2DLVs) with linguistic intuitionistic fuzzy numbers (LIFNs). In this work, we first define a novel score function to establish a proper ranking order among the 2DLIFVs. Next, we define a new distance measure under a 2-dimensional linguistic intuitionistic fuzzy framework to determine the difference between 2DLIFVs. Some mathematical properties and special cases of the defined distance measure are also discussed. The power average (PA) operators provide aggregation tools, allowing aggregated arguments to support each other in the aggregation process. Motivated by the notion of power average (PA) and power geometric (PG), we define four new aggregation operators (AOs) to aggregate 2DLIFVs by considering information correlation in terms of support degree during the aggregation process. Several mathematical properties of the proposed AOs are also investigated. In addition, a new integrated 2DLIF-CRITIC-WASPAS methodology is developed in the 2-dimensional linguistic intuitionistic fuzzy environment to deal with complex decision issues. In this method, a “Criteria Importance Through Intercriteria Correlation (CRITIC)” approach is used to obtain the associate weights of the attributes, and the “Weighted Aggregated Sum Product Assessment (WASPAS)” method is executed to establish a valid ranking order among the alternatives.Moreover, a real problem of venture capital investment related to renewable energy projects is considered to demonstrate the applicability of the proposed methodology. The evaluation process considers four aspects: the management team, service or product, finance, and the market, which are related to 14 attributes. A sensitivity analysis is carried out to explain the reliability of the obtained results. Comparing the proposed method with some extant methods establishes the strength and robustness of the formulated method in real-world situations.

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.

Multi-attribute decision-making methods based on Aczel-Alsina power aggregation operators for English blended teaching quality evaluation under single-valued neutrosophic sets

As a new form of teaching, blended teaching can integrate the advantages of classroom teaching and online teaching and improve the overall quality and effectiveness of English teaching under the premise of changing the orientation of teachers and students. The English blended teaching quality evaluation is a multiple attribute decision making (MADM) issue. Aczel-Alsina t-norm and t-conorm operations have the true advantage of changeability by adjusting a decision parameter. power averaging (PA) operator allowed decision attributes to strengthen each other through weight information during fusion, thereby eliminating the influence of subjective weights on the decision results. Motivate through classical Aczel-Alsina operators, PA operator and the single-valued neutrosophic sets (SVNSs), in this paper, the single-valued neutrosophic number Aczel-Alsina power averaging (SVNNAAPA) operator and the single-valued neutrosophic number Aczel-Alsina power weighted averaging (SVNNAAPWA) operator are constructed under SVNSs. The SVNNAAPWA operator is built for MADM. Eventually, an example about English blended teaching quality evaluation and some selected comparative decision analysis is used to depict the SVNNAAPWA method.

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.

Schweizer-Sklar power aggregation operators based on complex intuitionistic fuzzy information and their application in decision-making

In 1960, Schweizer and Sklar introduced the novel Schweizer-Sklar t-norm and t-conorm which is used in the construction of aggregation operators. Schweizer-Sklar norms are more general than algebraic norms and Einstein norms. Additionally, computing the power operators based on the Schweizer-Sklar norms for complex Atanassov intuitionistic fuzzy (CA-IF) set is very awkward and complicated. In this manuscript, firstly, we propose the Schweizer-Sklar operational laws for CA-IF values, and secondly, we develop the CA-IF Schweizer-Sklar power averaging (CA-IFSSPA) operator, CA-IF Schweizer-Sklar power ordered averaging (CA-IFSSPOA) operator, CA-IF Schweizer-Sklar power geometric (CA-IFSSPG) operator, and CA-IF Schweizer-Sklar power ordered geometric (CA-IFSSPOG) operator. Some suitable and dominant properties for the above operators are also discussed. Furthermore, to simplify the above operators, we develop the procedure of decision-making technique, called multi-attribute decision-making (MADM) methods based on the proposed operators based on CA-IF values. Finally, we compare the proposed methods with some existing methods to describe the efficiency and capability of the discovered approaches by some examples.

3D seismic analysis of mine planning using Aczel–Alsina aggregation operators based on T-spherical fuzzy information

3D seismic attributes analysis can help geologists and mine developers associate subsurface geological features, structures, faults, and ore bodies more precisely and accurately. The major influence of this application is to evaluate the usage of the 3D seismic attributes analysis in gold mine planning. For this, we evaluate the novel theory of complex T-spherical hesitant fuzzy (CTSHF) sets and their operational laws. Furthermore, we derive the CTSHF Aczel–Alsina weighted power averaging (CTSHFAAWPA) operator, CTSHF Aczel–Alsina ordered weighted power averaging (CTSHFAAOWPA) operator, CTSHF Aczel–Alsina weighted power geometric (CTSHFAAWPG) operator, and CTSHF Aczel–Alsina ordered.com weighted power geometric (CTSHFAAOWPG) operator. Some properties are also investigated for the above operators. Additionally, we evaluate the problems of 3D seismic attributes analysis to mine planning under the consideration of the proposed operators, for this, we illustrate the problem of the multi-attribute decision-making (MADM) technique for the above operators. Finally, we demonstrate some examples for making the comparison between prevailing and proposed information to improve the worth of the derived operators.

A novel group decision-making method for interval-valued q-rung dual hesitant fuzzy information using extended power average operator and Frank operations

This paper advances the field of multi-attribute group decision making (MAGDM) by proposing a novel framework based on interval-valued q-rung dual hesitant fuzzy sets (IVq-RDHFSs). IVq-RDHFSs, which surpass most existing fuzzy sets, effectively represent complex fuzzy information by describing membership and non-membership degrees through interval value sets. However, prior MAGDM methods based on IVq-RDHFSs have been limited by the functions of operation rules and aggregation operators (AOs). This limitation is addressed through the construction of a new MAGDM framework, leveraging the robust Frank t-norm and t-conorm (FTT) operation and the extended power average (EPA) operator. The proposed framework features the interval-valued q-rung dual hesitant fuzzy Frank weighted extended power average (IVq-RDHFFWEPA) operator to obtain comprehensive evaluation values. The paper also introduces novel techniques for determining the weights of decision-makers and attributes. Practical applications of the proposed method are demonstrated through the assessment of desalination technology selection and rural green eco-tourism projects. Sensitivity and comparison analyses validate the superior functionality, accuracy, and flexibility of this method compared to many state-of-the-art methods. The contributions of this paper are two-fold: it develops efficient measurement techniques for IVq-RDHFSs, such as distance and weight calculation, and it introduces a comprehensive MAGDM method by integrating FTT and EPA under IVq-RDHFSs, which improves the efficiency of solving decision-making problems.

Aczel-Alsina power bonferroni aggregation operators for picture fuzzy information and decision analysis

Picture fuzzy set (PFS) is an expedient mathematical approach for interpreting imprecise and nebulous information, and the power Bonferroni mean (PBM) operator is a crucial generalization of the power average (PA) operator, and the Bonferroni mean (BM) operator. Based on the Aczel-Alsina (AA), operational principles of PFS, we expand the PBM operator to integrate PFVs and develop a few AOs, namely PF Aczel-Alsina PBM (PFAAPBM) operator, weighted PF Aczel-Alsina PBM (WPFAAPBM) operator, PF Aczel-Alsina PGBM (PFAAPGBM) operator, and weighted geometric PF Aczel-Alsina PBM (WGPFAAPBM) operators respectively. These newly suggested PF Aczel-Alsina PBM operators can detect the connections between the membership, abstinence, and non-membership functions, which also maintain the important characteristics of the PBM operator. After that, we analyze a few enticing characteristics along with the particular applications of the suggested operators. Based on our suggested technique, we built an illustrated numerical example for the selection of competent research scientists to cope with MADM issues under the framework of PFVs. Finally, we contrast a few of our suggested methodologies with other prevailing methods to determine the feasibility and legitimacy of our suggested strategies.

An interval AQI combination prediction model based on multiple data decomposition and information aggregation operator.

In this paper, an interval Air Quality Index (AQI) combination prediction model based on EEMD, VMD, and the weighted power average (WPA) operator is proposed. EEMD and VMD decompose complex AQI data effectively, while WPA operator reasonably aggregates the prediction results of different models. We validate the effectiveness of the proposed model using Shenzhen's daily interval AQI. Furthermore, three kinds of prediction models are compared with the proposed model to highlight its advantages from various perspectives. The results show that the introduction of data decomposition methods significantly improves the model's prediction accuracy, WPA operator further enhances the model's prediction capability, and the incorporation of EEMD and VMD enables the proposed model to have stronger feature extraction capabilities for complex time series. As a result, the model proposed in this paper demonstrates strong generalization ability and prediction accuracy, making it applicable not only for air quality prediction but also for other domains such as economics and environment.

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.

An intelligent decision methodology for triangular Pythagorean fuzzy MADM and applications to college English teaching quality evaluation

Abstract The development of contemporary college English teaching methods and practice should respect the subjective will of college students; fully tap their wisdom and potential; constantly innovate college English teaching methods, teaching practice activities, classroom teaching, and teaching evaluation models; create a good teaching atmosphere; and establish the concept of developmental evaluation. Through the innovation of teaching methods, college students’ actual language communication ability is cultivated, the teaching objectives and teaching methods of college English reading are innovated, and interactive, body language, role play, situational teaching, communicative teaching, and other teaching methods are used. The College English teaching quality evaluation is a classical multiple attribute decision making (MADM). In this article, the triangular Pythagorean fuzzy sets (TPFSs) are introduced, and the MADM problem is investigated under TPFSs. Based on the traditional dual generalized weighted Bonferroni mean operator and power average operator, the triangular Pythagorean fuzzy dual generalized power Bonferroni mean (TPFDGPBM) operator is proposed. Accordingly, the TPFDGPBM operator is employed to construct the triangular Pythagorean fuzzy MADM method. Finally, a numerical example for College English teaching quality evaluation is constructed to verify the TPFDGPBM technique.

Probabilistic linguistic q-rung orthopair fuzzy Archimedean aggregation operators for group decision-making

To express uncertain and imprecise information systematically, the concept of probabilistic linguistic q-rung ortho-pair fuzzy set (PLqROFS), which is an advanced version of linguistic intuitionistic fuzzy set and linguistic Pythagorean fuzzy set, considering the instantaneous occurrence of stochastic and non-stochastic-uncertainty. There isn't yet any literature on PLqROFSs that addresses the issue of the relative importance of experts and criteria. The evaluation's findings consequently become irrational. Additionally, the aggregation operators that are currently available on PLqROFSs are too rigid. The primary goal is to resolve these problems by creating a new methodology that makes use of a new flexible aggregation operator. In this paper, a novel integrated framework is suggested to address concerns with group decision-making in PLqROFSs settings by combining the strengths of the power average operator (PAO), the Archimedean operator, and the full consistency method (FUCOM). With the extended variance approach on PLqROFSs, the weight of decision experts is methodically determined in this line. Additionally, the FUCOM on PLqROFSs is used to determine the weight of the criterion. Some probabilistic linguistic q-rung ortho-pair fuzzy Archimedean weighted and power weighted aggregation operators are suggested to aggregate decision experts' preferences. To discuss the viability of the suggested technique, the challenge of choosing a CO2 storage location is given. As alternatives, we have taken into account oilfields, gas fields, basalt formations, and coal resources. Basalt is the best choice, according to the outcome. The stability of our method is demonstrated by the sensitivity analysis of the criteria weights. The comparative analysis demonstrates that, in comparison to the ones already in use, our model is more significant and realistic.

Generalized Orthopair Fuzzy Weighted Power Bonferroni Mean Operator and Its Application in Decision Making

The generalized orthopair fuzzy set is more favored by decision-makers and extensively utilized in areas like supply chain management, risk investment, and pattern recognition because it offers a broader decision information boundary than the intuitionistic fuzzy set and Pythagorean fuzzy set. This enables it to express fuzzy information more comprehensively and accurately in multi-attribute decision-making problems. To this end, this paper combines the ability of the power average (PA) operator to eliminate the impact of extreme values and the advantage of the Bonferroni mean (BMs,t) operator in reflecting the relationships between variables, then incorporates weight indicators for different attributes to define the generalized orthopair fuzzy weighted power Bonferroni mean operator. The effectiveness of this operator is demonstrated through aggregation laws for generalized orthopair fuzzy information. Subsequently, the desirable properties of this operator are discussed. Based on these findings, a novel generalized orthopair fuzzy multi-attribute decision-making method, with a correlation between attributes, is proposed. Lastly, an investment decision-making example illustrates the feasibility and superiority of this method.

An Extended TODIM Method and Applications for Multi-Attribute Group Decision-Making Based on Bonferroni Mean Operators under Probabilistic Linguistic Term Sets

Due to the complexity and uncertainty of decision-making, probabilistic linguistic term sets (PLTSs) are currently important tools for qualitative evaluation of decision-makers. The asymmetry of evaluation information can easily lead to the loss of subjective preference information for decision-makers, and the existing operation of decision-maker evaluation information fusion operators is difficult to solve this problem. To solve such problems, this paper proposes some new operational methods for PLTSs based on Dombi T-conorm and T-norm. Considering the interrelationships between the input independent variables of PLTSs, the probabilistic linguistic weighted Dombi Bonferroni mean Power average (PLWDBMPA) operators are extended and the properties of these aggregation operators are proposed. Secondly, the PLWDBMPA operator is used to fuse the evaluation information of decision-makers, avoiding the loss of decision information as much as possible. This paper uses social media platforms and web crawler technology to obtain online comments from users on decision-making to obtain the public’s attitude towards decision events. TF-IDF and Word2Vec are used to calculate the weight of alternatives on each attribute. Under traditional group decision-making methods and integrating the wisdom of the public, a novel multi-attribute group decision-making method based on TODIM method is proposed. Finally, the case study of Turkey earthquake shelter selection proves this method is scientific and effective. Meanwhile, the superiority of this method was further verified through comparisons with the PL-TOPSIS, PLWA, SPOTIS and PROMETHEE method.

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.