Heronian Mean Research Articles

Optimal power-type Heronian and Lehmer means inequalities for the complete elliptic integrals

In this paper, we prove that the inequalities H p ( K ( r ) , E ( r ) ) < π 2 , L q ( K ( r ) , E ( r ) ) < π 2 hold for all r ∈ ( 0 , 1 ) if and only if p ≤ − log ⁡ 3 / log ⁡ ( π / 2 ) and q<−1, where H p ( a , b ) and L q ( a , b ) are respectively the p-th power-type Heronian mean and q-th Lehmer mean of a and b, and K ( r ) and E ( r ) are respectively the complete elliptic integrals of the first and second kinds.

Evaluating Regional Potentials of Agricultural E-Commerce Development Using a Novel MEREC Heronian-CoCoSo Approach

In terms of both economy and sustainability, rural areas can greatly benefit from adopting E-commerce. The Chinese government is currently devoting significant efforts to developing agricultural E-commerce. However, one of the most significant problems is the lack of effective tools for evaluating regional potentials in this regard, possibly leading to inappropriate policymaking, investment allocation, and regional planning. To address this issue, this study proposes a novel and effective method for evaluating regional potentials for agricultural E-commerce development, integrating the method based on the removal effects of criteria (MEREC), Heronian mean operator, and combined compromise solution (CoCoSo) method. The method’s effectiveness is then tested and confirmed in the Chinese city of Yibin through an evaluation of its ten regions. The results suggest that such a method is robust, objective, and able to consider indicator interactions effectively. By applying this method, regional agricultural E-commerce development potentials can be thoroughly evaluated and ranked. This study contributes to the literature by providing new analytical techniques for agricultural studies, as well as by supporting political and investment decision-making for governments and E-commerce practitioners in the agriculture sector.

Bipolar Neutrosophic Dombi-Based Heronian Mean Operators and Their Application in Multi-criteria Decision-Making Problems

Dombi operations based on the Dombi t-norm (TN) and t-conorm (TCN) have the advantage in terms of operational parameter flexibility in dealing with varying degrees of uncertainty and aggregation requirements. Meanwhile, Heronian mean (HM) operator is an effective technique for capturing the interrelationship between any number of inputs. Bipolar neutrosophic set (BNS) offers the ability to represent both positive and negative information as well as indeterminate information. It is beneficial in cases where there is uncertainty or insufficient information. However, the existing Dombi operator under BNS do not take into account the interrelationship between input arguments. To overcome this limitation, this study incorporates Dombi operator into HM and propose the bipolar neutrosophic Dombi Heronian mean aggregation operator. This paper introduces two type of aggregation operators namely bipolar neutrosophic Dombi-based generalized weighted Heronian mean (BND-GWHM), and bipolar neutrosophic Dombi-based improved generalized weighted Heronian mean (BND-IGWHM). The proposed operators are integrated into MCDM procedure. The influence of different parameter values on decision-making results is discussed. Finally, a comparison analysis with existing methods is also provided.

T-Spherical fuzzy TOPSIS method based on distance measures and Hamacher Heronian mean averaging aggregation operators and its application to waste management

T-Spherical fuzzy sets provide a robust framework for handling uncertainty in real-world decision-making. This paper addresses the construction of T-Spherical fuzzy Heronian mean averaging aggregation operators using novel Hamacher operations. The study mathematically verifies the properties of these operators and develops new distance measures such as Hamming, Euclidean and Jaccard for quantifying dissimilarity between T-Spherical fuzzy numbers. Furthermore, the TOPSIS method is implemented using the proposed operators and distance measures to solve a practical decision-making problem in selecting the best transportation firm for medical waste disposal. A sensitivity analysis is made to assesses the efficacy of the proposed operators, while a comparison study with existing methods is exhibited to establish their efficiency.

Group Decision Making Based on Generalized Intuitionistic Fuzzy Yager Weighted Heronian Mean Aggregation Operator

Group Decision Making Based on Generalized Intuitionistic Fuzzy Yager Weighted Heronian Mean Aggregation Operator

Advancements in MADM with college English teaching quality evaluation: Integrating 2-tuple linguistic neutrosophic models with prioritized heronian mean techniques

With the continuous development of Internet era, teaching modes are also being innovated and developed, and online and offline blended teaching (OOBT) is one of them, which is mainly achieved by combining OOBT. By combining online and offline teaching modes with college English courses, teachers not only help students cultivate independent learning habits, but also help them think alone and improve their practical skills. This is also true for vocational and technical education, and it can be said that this approach is more relevant. The OOBT evaluation in college English teaching courses is deemed to multiple-attribute decision-making (MADM). In this study, we connected the geometric Heronian mean (GHM) technique and prioritized aggregation (PA) in line with 2-tuple linguistic neutrosophic numbers (2TLNNs) to produce the generalized 2TLNN power GHM (G2TLNPGHM) technique. Then, the G2TLNPGHM technique is implemented to process the MADM under 2TLNNs. Finally, the G2TLNPGHM technique is implemented as the numerical example of evaluating the OOBT in college English courses. Some comparative analysis of the impact of parameters are fully addressed.

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.

Which factors affect the repair for loss of social trust after public health emergency? An approach integrating 2-tuple linguistic WINGS and regret theory

Trust is generally regarded as the vital social capital for a country's economic growth, reducing transaction costs and promoting economic development. However, problematic vaccine events, a kind of public health emergency, often incur the serious loss of social trust. And it is necessary to systematically analyze the factors affecting the repair for loss of social trust and how to repair. Thus, we propose a new systematical analysis method integrated Weighted Influence Non-linear Gauge System (WINGS) and regret theory under 2-tuple linguistic environment in this paper. Firstly, considering the difference between experts’ psychological expectation and real evaluation, a modified utility function of regret theory with 2-tuple linguistic information is proposed. Then, due to the different interests, knowledge, social status, etc. of experts, an integrated approach based on conflict resolution mechanism and Heronian mean operation is presented to aggregate cause-effect relationship information from them. Thirdly, to analyze the main factors affecting the repair for loss of social trust, a novel method based on 2-tuple linguistic WINGS is put forward. Last but not least, the Changsheng Changchun vaccine event is utilized as an example to demonstrate practicality of the proposed method. And some sensitivity analyses and comparation analyses are also given to illustrate the effectiveness of the proposed method. Finally, the corresponding paths to the repair for loss of social trust are given.

Decision algorithm for educational institute selection with spherical fuzzy heronian mean operators and Aczel-Alsina triangular norm

This article presents a novel study of spherical fuzzy sets (SFSs), a more comprehensive framework of intuitionistic fuzzy sets and picture fuzzy sets. The SFS allows the decision-makers (DMs) to cope with complicated and insufficient information during the aggregation process. The Heronian mean (HrM) model theory is also utilized to express correlation among different input arguments or characteristics. Recently, the theory of Aczel Alsina triangular norms gained a lot of attention from various research scholars and has many capabilities to provide smooth approximations during decision analysis. In this article, we developed some appropriate operations of Aczel Alsina t-norms and t-conorms in light of spherical fuzzy (SF) information. We develop new mathematical ways to look at SF data to keep clarity and sufficient information. These are the SF Aczel Alsina Heronian mean (SFAAHrM) and SF Aczel Alsina weighted Heronian mean (SFAAWHrM) operators. Furthermore, we also present a list of new strategies based on Aczel Alsina operations, such as SF Aczel Alsina geometric Heronian mean (SFAAGHrM) and SF Aczel Alsina weighted geometric Heronian mean (SFAAWGHrM) operators. Some notable properties are also characterized to show the validity and effectiveness of our derived mathematical approaches. Considering our derived strategies, an algorithm for the multiple attribute decision-making (MADM) problem is established to resolve complicated real-life applications. A numerical example presents the compatibility of derived approaches and provides a solid mechanism to improve the performance of educational institutes. A comparison technique is also demonstrated to show the applicability and consistency of diagnosed approaches by contrasting the findings of pioneered approaches with existing methodologies.

Sustainability evaluation of sports tourism using a linguistic neutrosophic multi-criteria decision-making method.

Sports tourism represents a novel industrial manifestation of the profound integration between the tourism and sports sectors. The objective of this research is to examine an innovative multi-criteria decision-making (MCDM) method for the sustainability evaluation of sports tourism. The largest innovations are the expression and treatment of ambiguous data and interdependent evaluation criteria in the sports tourism sustainability evaluation process. On the one hand, intricate assessment data is represented using linguistic neutrosophic numbers (LNNs), which employ three linguistic variables to convey uncertainty and imprecision. On the other hand, to effectively capture the interrelationships among inputs, two novel aggregation operators are proposed. They are devised based on the Einstein operations and Heronian mean operators of LNNs. Subsequently, a linguistic neutrosophic evaluation method utilizing the aforementioned operators is presented. Comparative and sensitivity analyses conclude that great interdependence exists among five different dimensions of sustainability evaluation in sports tourism, and the proposed method can reflect the interrelations among inputs without redundant calculations.

A Hybrid Classifier Based on the Generalized Heronian Mean Operator and Fuzzy Robust PCA Algorithms

A Hybrid Classifier Based on the Generalized Heronian Mean Operator and Fuzzy Robust PCA Algorithms

A New Multi-Target Three-Way Threat Assessment Method with Heterogeneous Information and Attribute Relevance

Target threat assessment provides support for combat decision making. The multi-target threat assessment method based on a three-way decision can obtain threat classification while receiving threat ranking, thus avoiding the limitation of traditional two-way decisions. However, the heterogeneous situation information, attribute relevance, and adaptive information processing needs in complex battlefield environment bring challenges to existing methods. Therefore, this paper proposes a new multi-target three-way threat assessment method with heterogeneous information and attribute relevance. Firstly, dynamic assessment information is represented by heterogeneous information, and attribute weights are calculated by heterogeneous Criteria Importance Through Intercriteria Correlation (CRITIC). Then, the conditional probability is calculated by the heterogeneous weighted Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and the adaptive risk avoidance coefficients are constructed by calculating the uncertainty of the assessment value, and then the relative loss function matrices are constructed. Finally, the comprehensive loss function matrices are obtained by the weighted Heronian mean (HM) operator, and the comprehensive thresholds are calculated to obtain the three-way rules. The case study shows that compared with the existing methods, the proposed method can effectively handle the heterogeneous information and attribute relevance, and obtain the risk avoidance coefficients without presetting or field subjective settings, which is more suitable for the complex mission environment.

An integrated group decision-making framework for evaluating the urban fire emergency management capability based on PDHLWPHM and PDHLWPGHM operator

Urban fire accident is a common dangerous accident in urban sudden accidents, which threatens the safety of people’s lives and property. For this reason, in recent years, all cities have incorporated the prevention and emergency management of urban fire accidents into their urban development planning, and actively improved their fire accident emergency management capabilities. However, how to evaluate the urban fire accident emergency management capacity of each city to ensure that people’s lives and property are protected to the greatest extent is an urgent problem to be considered and solved. Therefore, this paper defines a class of probabilistic double hierarchy linguistic Heronian mean (PDHLHM) operator, probabilistic double hierarchy linguistic Power Heronian mean (PDHLPHM) operators, and their dual operators that can reflect the relationship between two attributes during aggregation. Taking urban fire accident risk monitoring and early warning capability, fire infrastructure and communication system, fire-fighting and rescue capability, recovery and reconstruction capability as evaluation attributes, the probabilistic double hierarchy linguistic weight Power Heronian mean (PDHLWPHM) operator model and the probabilistic double hierarchy linguistic weight Power geometric Heronian mean (PDHLWPGHM) operator model are constructed for group decision-making. In addition, the idempotence, boundedness and monotonicity of these operators are studied, and the sensitivity of the parameters involved in the operator model is analyzed. Finally, the new model proposed in this paper is compared with the existing model to verify its scientificity.

Archimedean Heronian mean operators based on complex intuitionistic fuzzy sets and their applications in decision-making problems

In this article, we derive the Archimedean aggregation operators for complex intuitionistic fuzzy sets, for this, first, we evaluate some Archimedean operational laws based on complex intuitionistic fuzzy values and then we discuss their special cases because the Archimedean norms are the general form of all existing norms, for instance, algebraic, Einstein, Hamacher, and Frank operational laws. Furthermore, we present the complex intuitionistic fuzzy Archimedean Heronian aggregation operator and complex intuitionistic fuzzy weighted Archimedean Heronian aggregation operator. Several special cases and the basic properties of the above-proposed operators are also diagnosed, because proposing the Heronian mean operators based on Archimedean norms are very challenging and complicated tasks, because of their features and structure. Additionally, a decision-making process is developed under the identified operators by using complex intuitionistic fuzzy information. Finally, we illustrate several examples to show the multi-attribute decision-making technique is more flexible than the prevailing works with the help of sensitive analysis between explored and certain prevailing works.

A novel multi-attribute decision-making approach based on T-spherical fuzzy Aczel Alsina Heronian mean operators

A novel multi-attribute decision-making approach based on T-spherical fuzzy Aczel Alsina Heronian mean operators

Prioritization of types of wireless sensor networks by applying decision-making technique based on bipolar complex fuzzy linguistic heronian mean operators

Wireless sensor networks are flexible monitoring systems that save track of, data, and communicate multipoint digital information interpretations to other devices. Wireless sensor networks meaningly enhance the accuracy, breadth, and extent of local data collection, commonly doing away with the requirement for expensive data wiring and recurring manual checks at risky, remote, or inaccessible locations. As a result, it is utilized to keep an eye on systems and environmental or physical parameters. In this manuscript, we expand the Heronian mean operators in the model of bipolar complex fuzzy linguistic set to concoct bipolar complex fuzzy linguistic arithmetic Heronian mean, bipolar complex fuzzy linguistic weighted arithmetic Heronian mean, bipolar complex fuzzy linguistic geometric Heronian mean and bipolar complex fuzzy linguistic weighted geometric Heronian mean operators. We also inspect the special cases of the invented bipolar complex fuzzy linguistic arithmetic Heronian mean and bipolar complex fuzzy linguistic geometric Heronian mean operators. Moreover, in this manuscript, we concoct a technique of decision-making in the model of a bipolar complex fuzzy linguistic set with the assistance of the invented operators. As the selection and prioritization of the various types of Wireless sensor networks is the decision-making dilemma, we prioritize various types of Wireless sensor networks by employing the concocted technique of decision-making and by taking artificial data in the model of the bipolar complex fuzzy linguistic set. To reveal the influence and excellence of the concocted work, a comparative study is given in this manuscript.

Complex Circular Intuitionistic Fuzzy Heronian Mean Aggregation for Dynamic Air Quality Monitoring and Public Health Risk Prediction

Complex Circular Intuitionistic Fuzzy Heronian Mean Aggregation for Dynamic Air Quality Monitoring and Public Health Risk Prediction

A novel CODAS approach based on Heronian Minkowski distance operator for T-spherical fuzzy multiple attribute group decision-making

T-spherical fuzzy sets (TSFSs) are more flexible and efficient tools to deal with ambiguous, uncertain and vague information in complex real-world decision-making problems than various extended intuitionistic fuzzy sets. This paper aims to develop a novel T-spherical fuzzy (TSF) Combinative Distance-Based ASsessment (CODAS) based on the Heronian Minkowski distance aggregation operator, this new method can capture interrelationship between input arguments. Some TSF weighted Heronian Minkowski distance (TSFWHMD) aggregation operators with generalization are developed based on Heronian mean and Minkowski-type distance, their properties are discussed as well as their families are analyzed. Furthermore, the TSF MAGDM methodology based on the improved CODAS is designed, where the Minkowski-type distance is used to define the TSF similarity for computing the expert weights and to construct the maximizing deviation method (MDM) for determining the attribute weights, respectively. The TSF ordered weighted Heronian Hamming distance (TSFOWHHD) and TSF ordered weighted Heronian Euclidean distance (TSFOWHED) operators derived from the TSFOWHMD operator are integrated into the CODAS method, which is an improved method for both measuring the deviation of the negative ideal solution from each alternative and capturing the correlation between attributes. Finally, the feasibility and practicality of developed methodology are illustrated with an example of CAE (Computer Aided Engineering) software selection for lithium-ion power battery (LiPB) design, sensitivity analysis and method comparisons are performed to elucidate the reliability and validity of the developed methodology.

Formula omitted]-spherical fuzzy Hamacher Heronian mean geometric operators for multiple criteria group decision making using SMART based TODIM method

T-spherical fuzzy set studied in this paper adequately defines the uncertain information of any decision making situations. This paper aims to provide a solution approach to a multiple criteria group decision making situation under T-spherical fuzzy context. Every group decision making process utilizes aggregation operators to combine the different expert’s opinions. This paper aims to construct several aggregation operators such as T-spherical fuzzy Hamacher Heronian mean-geometric, weighted geometric, ordered geometric, and hybrid geometric operators. The fundamental properties of the proposed operators are thoroughly investigated. The introduced operators are more potent in considering the criteria interrelationships. Criteria weights play an essential role while aggregating different criteria during multiple criteria decision making processes. This work adopts the simple multi-attribute rating technique (SMART) to compute the criteria weights. Utilizing the proposed operators and SMART technique, a multiple criteria group decision making approach called the TODIM (an acronym in Portuguese for Iterative Multi-Criteria Decision Making) is defined based on the Euclidean distance between the T-spherical fuzzy numbers. A decision making situation of selecting the most deserving one from a set of lecturers based on their research capacity is solved using the proposed TODIM approach to show its applicability. Sensitivity analysis is carried out to reveal the effect of parameters on the decision results. A comparative study is made to exhibit the feasibility of the proposed 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.