Heronian mean calculator Therefore, dual hesitant fuzzy set is a more comprehensive set. The Heronian mean is an average of two non-negative real numbers, represented by H, and its formula is. Divide the total sum by the number of data points to get the arithmetic mean. For example, the MCDM with entropy method or Bonferroni mean operator can be comparatively analyzed against our model. Compute the Heronian mean of two numbers. The horizontal lines indicate, for the same set a, the minimum, the harmonic mean H, the geometric mean G, the arithmetic mean A, the quadratic mean Q and the maximum. Since the evaluation data in Table 1 also abides by the characteristics of dual hesitant fuzzy sets, the dual hesitant fuzzy geometric weighted Heronian mean (DHFGWHM) operator proposed by Qu et al. Jun 7, 2012 · In this article, we answer the question: For p, ω ∈ ℝ with ω > 0 and p(ω - 2) ≠ 0, what are the greatest value r1 = r1(p, ω) and the least value r2 = r2(p, ω) such that the double inequality M r 1 a , b < H p , ω a , b < M r 2 a , b holds for all a, b > 0 with a ≠ b? Here Hp,ω(a, b) and M r (a, b) denote the generalized Heronian mean and r th power mean of two positive numbers a Nov 1, 2023 · The algorithm is based on the MAGDM for selecting the best investment company. Lastly, an extended MABAC method based on the 2-tuple linguistic $ T $-spherical fuzzy generalized weighted Heronian mean and the 2-tuple linguistic $ T $-spherical fuzzy weighted geometric Heronian mean operators is developed. Sep 1, 2024 · To address this scenario, Liu and Chen [20] introduced IF Heronian mean aggregation operators for group decision making (GDM) based on Archimedean norms. In this paper a new fourth order accurate composite Runge-Kutta type method using the Heronian Mean is developed. 3, some novel opera-tors are proposed, such as hesitant fuzzy linguistic power broad applicability of Heronian mean operators, coupled with the growing demand for multipolar fuzzy aggregation, we aim to develop mF set-based power geometric Heronian mean AGOs. Bipolar neutrosophic set (BNS) offers the ability to A new fourth order accurate composite Runge-Kutta type method using the Heronian Mean is developed and the stability of the method is analysed and numerical results shown to verify the conclusions. The main objective of stock portfolio selection is to distribute capital to selected stocks to get the most profitable returns at a lower risk. Mar 20, 2022 · First, the Heronian mean operator (improved generalized weighted Heronian mean an improved generalized geometric weighted Heronian mean) is combined with the traditional Combined compromise solution (CoCoSo) method to present a new decision-making model for dealing with stock selection problems. The formula is given as follows: It is named after Hero of Alexandria, and used in finding the volume of a frustum of a pyramid or cone. Calculate the Heronian mean of two positive numbers. It is named after Hero of Alexandria, and used in finding the volume of a frustum of a pyramid or cone. [61] can also be used for calculation. Some existing MCGDM Two Heronian mean operators are proposed to aggregate the linguistic neutrosophic multiset, one is a linguistic neutrosophic multiplicity number generalized-weighted Heronian mean operator, the other is a linguistic neutrosophic multiplicity number improved-generalized-weighted Heronian mean operator, and then their properties are discussed. However, the existing HM does not take into consideration the overall interaction of input arguments. The desirable characteristic of the HM is that it can capture the interrelationship of the input arguments, which makes it very useful in decision making. Dec 28, 2021 · Request PDF | Fermatean fuzzy Heronian mean operators and MEREC‐based additive ratio assessment method: An application to food waste treatment technology selection | Uncertainty is often Aug 10, 2024 · Finally, as this model is the first to integrate the MEREC, Heronian mean operator, and CoCoSo in agricultural E-commerce studies, its performance can be further examined by comparing with other methods in the future. To calculate the average of a set of numbers: Add all the numbers together; Count how many numbers there are; Divide the sum by the count Mar 7, 2022 · Multiple-Attribute Decision Making Based on Interval-Valued Intuitionistic Fuzzy Generalized Weighted Heronian Mean March 2022 Information (Switzerland) 13(3):138 Jan 1, 2020 · Third, the traditional generalized Heronian mean (HM) operators capturing the correlation among attributes are extended to multiple-valued picture fuzzy linguistic environment, namely, the Dec 3, 2024 · Novel Heronian mean based $ m $-polar fuzzy power geometric aggregation operators and their application to urban transportation management. Examples Example 1: Calculate the Average of Numbers from 20 to 30 Mar 1, 2014 · The Heronian mean is not only an operator which reflects the associations between attributes, but also has excellent properties, including idempotency, monotonicity, boundedness, parameter operators and Heronian mean (HM) operator, we develop spherical fuzzy Dombi Heronian value by calculating the support degree of different evaluation values to Find Mean, Median and Mode for grouped data calculator - Find Mean, Median and Mode for grouped data, step-by-step online We use cookies to improve your experience on our site and to show you relevant advertising. [41] introduced the generalized extended Bonferroni means for decision making. It is clear that many scholars have invented the Heronian mean operators for FSs, and IFSs, but no one can derive it for CIFSs. The formula is given as follows: If you wish to calculate the triangle area normally, head to our triangle area calculator instead. The HM operator is different from Power average or Choquet integral. Use Now. The graph on the Sep 19, 2023 · Calculator Use What is Average? What is the Mean? In statistics the mean of a set of numbers is the average value of those numbers. And geometric Heronian mean have advantages when considering the interrelationship of aggregation Hence the application of the heronian mean operator (IGWHM- improved generalized weighted heronian mean and IGGWHM- improved generalized geometric weighted heronian mean) is introduced to overcome this drawback in the traditional CoCoSo method. Apr 1, 2019 · Two Heronian mean operators are proposed to aggregate the linguistic neutrosophic multiset, one is a linguistic neutrosophic multiplicity number generalized-weighted Heronian mean operator, the Mar 30, 2016 · Heronian mean (HM) has the characteristic of capturing the correlations of the aggregated arguments and the neutrosophic set can express the incomplete, indeterminate and inconsistent information Mar 7, 2020 · Then, using the algorithms of IVPFN and geometric Heronian average mean operators, four Heronian mean operators for IVPFN are proposed: the interval-valued picture fuzzy geometric Heronian average Jul 10, 2024 · 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. The normal intuitionistic fuzzy numbers (NIFNs) can depict normal distribution information in practical decision making Jul 25, 2009 · The ''Heronian mean (HM) (Beliakov et al. What is the least positive integer b > 40 such that H(40, b) is also a positive integer? Feb 9, 2022 · As, the Heronian mean considers the interrelationship of the aggregated arguments and relieves the calculation redundancy, an aggregation operator using Heronian mean is developed. Meanwhile, Heronian mean (HM) operator is an effective technique for capturing the interrelationship between any number of inputs. 7. Jan 1, 2023 · Fermatean Hesitant Fuzzy Prioritized Heronian Mean Operator and Its Application in Multi-Attribute Decision Making. Finally, the study conclusion is given in Sect. Furthermore, we applied the proposed operators to the MCGDM problem and developed a new MCGDM approach. In the context of mathematics, "average" refers to the mean, specifically, the arithmetic mean. , Bonferroni mean (BM) and Heronian mean (HM), which can deal with interrelated input arguments. Jan 17, 2019 · Considering the advantages and limitations of the Heronian mean (HM) operator, four Heronian mean operators for bipolar neutrosophic number (BNN) are proposed: the BNN generalized weighted HM Dec 12, 2019 · The partitioned geometric Heronian mean (PGHM) operator can effectively solve the decision-making problems in which the attributes grouped into the same clusters have interrelationships and the attributes belonging to different clusters have no interrelationship. The normal intuitionistic fuzzy numbers (NIFNs) can depict normal 3. To tackle this issue, we propose the interactional operational laws (IOLs) to compute picture Two Heronian mean operators are proposed to aggregate the linguistic neutrosophic multiset, one is a linguistic neutrosophic multiplicity number generalized-weighted Heronian mean operator, the other is a linguistic neutrosophic multiplicity number improved-generalized-weighted Heronian mean operator, and then their properties are discussed. Divide the total number of values by the sum of reciprocals to obtain the harmonic mean. Most generally, it is a single number that is used to represent a collection of numbers. [22] constructed Heronian mean operators in a PF environment. However, due to the characteristics that it neglects the calculation redundancy and considers the association between an attribute and itself, HM is more beneficial than BM (Deb and May 4, 2015 · Further, we give definition of hesitant fuzzy geometric Heronian element (HFGHE), which is a basic calculation unit in HFGGHM and reflects the conjunction between two aggregated arguments. Free online statistics calculators. For example nonlinear equations [XIX],[XX] and their solvers [VII],[XXII], etc. It's one of the most commonly used measures of central tendency in statistics. In order to aggregate information more scientifically and reasonably, the Heronian mean operator was studied in this paper. In fact, you have probably used it many times yourself. 1 ), Op- erational rules of FFNs based on Archimedean 𝑡 -norms Jan 14, 2022 · geometric Heronian average mean operators, four Heronian mean operators f or IVPFN are proposed: the i nterval- valued pic ture fuzzy geometric Heronian average mean (IVPFGHM) operator, the Jul 9, 2021 · Download Citation | Hamacher heronian mean operators for multi-critria decision-making under multi-valued picture fuzzy uncertain lingsuitic environment | Picture fuzzy set (PFS) and linguistic Sep 1, 2023 · In this section, we combine the HM operators with IVFFNs and propose “interval-valued Fermatean fuzzy generalized Heronian mean (IVFFGHM)”, “interval-valued Fermatean fuzzy weighted generalized Heronian mean (IVFFWGHM)”, “interval-valued Fermatean fuzzy generalized geometric Heronian mean (IVFFGGeHM)” and “interval-valued Dec 29, 2018 · To aggregate q-rung orthopair linguistic numbers (q-ROLNs), we extend the Heronian mean (HM) to q-ROLSs and propose a family of q-rung orthopair linguistic Heronian mean operators, such as the q Nov 1, 2022 · This page was last modified on 1 November 2022, at 20:43 and is 0 bytes; Content is available under Creative Commons Attribution-ShareAlike License unless otherwise In real applications, most decisions are fuzzy decisions, and the decision results mainly depend on the choice of aggregation operators. How to Calculate the Arithmetic Mean? Steps: Add all the numbers in the dataset to calculate the total sum. The thin black curve traces the Hölder path H(p,a). Considering the advantages and limitations of the Heronian mean (HM) operator, four Heronian mean operators for bipolar neutrosophic Heronian mean operator as well as generalized geometric Heronian mean operator. A new multi-criteria group decision-making (MCGDM) approach is introduced on the basis of Hamacher operation and can describe the interaction of the different criteria or input arguments and offer some reasonable and reliable MCGDM aggregation operators, which can open avenues for decision making and broaden perspectives of the decision experts. By averaging the cubes of the dataset values and then taking the cube root , the cubic mean offers an accurate representation of datasets with large numerical variations. Jan 10, 2025 · The Heronian mean of two numbers a and b is defined as HM(a,b) = 1/3(2A+G) (1) = 1/3(a+sqrt(ab)+b), (2) where A is the arithmetic mean and G the geometric mean. The average, also known as the arithmetic mean, is the sum of all numbers divided by the count of numbers. Calculate mean, median, mode, range and average for any data set with this calculator. The Heronian mean H(a,b) is defined as H(a,b)= (a+sqrt(ab)+b)/3 What is the least positive integer b>40 such that H(40,6) is also positive integer 2 Calculate the Heronian mean (HM), which is one of the aggregation methods, is characterized by the ability to capture the relevance between the input arguments. (2022) and Peng and Luo (2021) proposed the method for examining the bubble warning in Sep 1, 2023 · Transportation systems are a key part of sustainable development, and they need to be carefully evaluated to show that they have a strong impact on th… The utilization of the Heronian Mean offers distinct advantages over the traditional arithmetic mean used in the original MEREC. Solve advanced problems in Physics, Mathematics and Engineering. These operators include Hamacher Heronian mean (NIFHHM), Hamacher weighted Heronian mean (NIFHWHM), Hamacher geometric Heronian mean (NIFHGHM), and Hamacher weighted geometric Heronian mean (NIFHWGHM). 2 Preliminaries This section reviews deﬁnition and literature about IVIFSs, Heronian mean and Jaccard Jul 23, 2018 · The studies on MCDM methods combining q-ROFS with aggregation operators are also very rich, such as q-ROF Muirhead mean operators, 39,40 q-ROF Hamy mean operators, 41 and q-ROF Heronian mean correlation of the variables. Therefore, to address this issue, the Shapley neutrosophic set, and some operators based on Heronian mean (HM) operator including the improved generalized weighted Heronian mean (IGWHM) operator and the generalized geometric Heronian mean (GGHM) operator. Aug 5, 2019 · Extended Heronian Mean Based on Hesitant Fuzzy Linguistic Information for Multiple Attribute Group Decision-Making Minghua Shi , 1,2 Yuewen Xiao, 3 and Qing Wan 1 The cubic mean is a method for calculating the average of a dataset, particularly useful in scenarios involving growth rates or weighted data. Aug 24, 2022 · The Heronian mean H(a, b) is defined as H(a, b) = \dfrac{a + \sqrt{ab} + b}{3} . Feb 1, 2024 · Heronian mean operators (Section 2. , 2007)'' is one of the valuable AOs, which can take the interrelationships between arguments into consideration. From Bonferroni mean and Heronian mean, the BM mainly indicates correlation between any pairs of criteria ic and jc (ijz some operators and studied their properties. Math Expression Renderer, Plots, Unit Converter, Equation Solver, Complex Numbers, Calculation History. [1] [2] Heronian triangles are named after Heron of Alexandria, based on their relation to Heron's formula which Heron demonstrated with the example triangle of sides 13, 14, 15 and area 84. The equation for calculating the arithmetic mean is virtually identical to that for calculating the statistical concepts of population and sample mean, with slight variations in the variables used: The mean is often denoted as x̄ , pronounced "x bar," and even in other uses when the variable is not x , the bar notation is a common indicator of some definition and properties of uncertain linguistic numbers, the single valued neutrosophic set, and some heronian mean (HM) operators including the generalized weighted Heronian mean (GWHM) operator, the improved generalized weighted Heronian mean (IGWHM) operator, the improved generalized geometric weighted Heronian mean (IGGWHM) operator. In Sect. The performance of a stock depends on a number of criteria based on the risk-return measures. What is an average? The term average has a number of different meanings. Reference Chen et al. Heronian means (yellow dots) Her(k;a) as functions of k for the set a = {1,2,3,4,5,6,7,8,9,10}. Based on the Bonferroni mean operator [40], Xia et al. Heron's area formula: equation for the area of triangle with 3 sides given Heron's formula, also known as Hero's formula, is the formula to calculate triangle area given three triangle sides. However, their existing operational laws usually generate unreasonable computing results, especially when the agreement degree (AD) or neutrality degree (ND) or opposition degree (OD) is zero. This section also explores their weighted variants, including the weighted, ordered weighted, and hybrid averaging operators. The Heronian mean can also be regarded as the weighted mean of the arithmetic mean and the geometric mean. January 2023; Computers Materials & Continua 75(2):3203-3222; Feb 10, 2022 · First, the heronian mean operator (improved generalized weighted heronian mean and improved generalized geometric weighted heronian mean) is combined with the traditional Combined compromise Jun 1, 2018 · Heronian mean can deal with correlations of different criteria or input arguments and does not bring out repeated calculation. The formula is as follows The Heronian Mean is a method for averaging two numbers, often used to smooth out the differences between them. 6, to show the authenticity of the model a comparative analysis is given. Their Jun 23, 2023 · Meanwhile, there exist some novel aggregation operations, viz. Dombi Heronian mean AOs with I-VIF numbers and two MADM methods based on the I-VIF-weighted Dombi Heronian mean AO and interval-valued intuitionistic-weighted Dombi geometric Heronian mean AO. 1 Interval-valued intuitionistic fuzzy Einstein Heronian mean (IVIFEHM) operator Sep 19, 2023 · Mean, median and mode calculator for statistics. Wei et al. How to Calculate Average. It arises in the determination of the volume of a pyramidal frustum. The corresponding weights are 23 and 13. 1 q-Rung orthopair fuzzy Dombi partitioned Heronian mean operators. 3), Geometric Heronian mean operators (Section 2. Anusha and Sireesha [21] presented Einstein Heronian mean operators within an Interval-valued IFS environment. Various types of aggregation using q-rung orthopair fuzzy sets have been carried out like Heronian mean Jul 8, 2022 · Free Online Scientific Notation Calculator. Average and mean are measures of central tendency. Mar 1, 2014 · With respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of crisp numbers, and attribute values take the form of intuitionistic uncertain linguistic variables, some new intuitionistic uncertain linguistic Heronian mean operators, such as intuitionistic uncertain linguistic arithmetic Heronian mean (IULAHM Jun 12, 2018 · In this section, we shall extend the Heronian mean operator to the situation in which the input arguments are unbalanced linguistic information and shall develop some unbalanced linguistic Heronian mean operators, such as the unbalanced linguistic generalized arithmetic Heronian mean (ULGAHM) operator, the unbalanced linguistic generalized May 22, 2018 · 76 Compared with Bonferroni mean, Heronian mean (denoted as HM) [24,40,46] is another 77 aggregation technique which can also depict the relationship between aggregated arguments 78 objectively. So, in this paper, we propose the LNCN generalized weighted Heronian mean (LNCNGWHM) operator and the LNCN three-parameter weighted Heronian mean (LNCNTPWHM) operator and investigate their properties. Feb 1, 2013 · The Heronian mean (HM) is a mean type aggregation technique, which is developed to deal with the exact numerical values [21]. 1. 它以亚历山大港的希罗命名。. Examples Example 1: Calculate the Harmonic Mean of 100, 200, 300, 400, 500 Jul 25, 2009 · Figure 1. [42] constructed the geometric Bonferroni mean with several extensions to linguistic 2-tuples for decision-making. Mean Formula. In this section, PHM is extended to the q-rung orthopair fuzzy environment, and a q-rung orthopair fuzzy Dombi partitioned Heronian mean (qROFDPHM) operator and a q-rung orthopair fuzzy Dombi weighted partitioned Heronian mean (qROFDWPHM) operator are presented. The general form of a GP is x, xr, xr 2, xr 3 and so on. 1. Heronian mean can deal with correlations of different criteria or input arguments and does not bring out repeated calculation. Highly Composite Number Calculator. Einstein Heronian mean aggregation operator and its application … Page 3 of 14 69 demonstration of model. Therefore \(\text{G. 希羅平均數也可以看成算術平均數与幾何平均數的加权平均數。 Mar 1, 2022 · The crucial part in any decision making problem is the aggregation of information. The Heronian mean H(a, b) is defined as H(a, b) = (a Mar 2, 2023 · Extended MABAC method based on 2-tuple linguistic T -spherical fuzzy sets and Heronian mean operators: An application to alternative fuel selection March 2023 AIMS Mathematics 8(5):10619-10653 Feb 2, 2024 · For dealing with the above three queries, we needed to develop the Archimedean Heronian mean operators for CIFSs because, with the help of these investigations, we can easily derive any kind of operators. Further, Archimedean t-norm and t-conorm provides generalized operational rules for dual hesitant fuzzy set. The stability of the method is analysed and numerical results shown to verify the Jan 13, 2010 · The classical concept of the Heronian mean of two non-negative real values is subject to a sweeping generalization in order to make it applicable to any subset a of n elements of R+, the set of 数学上，希羅平均數（英語： Heronian mean ）是指两个非负实数的一种平均数，公式为 = (+ +). Yu [34] proposed a generalized I-VIF Heronian mean and a MCDM method based on this operator. For example, stock portfolio selection using Heronian mean AOs discussed by Narang et al. How to Calculate the Harmonic Mean? Steps: Find the reciprocal of each number in the set. Mar 27, 2023 · Since the evaluation data in Table 1 also abides by the characteristics of dual hesitant fuzzy sets, the dual hesitant fuzzy geometric weighted Heronian mean (DHFGWHM) operator proposed by Qu et al. Apr 18, 2022 · Heronian mean (HM) operators are powerful aggregation operators that consider the interrelationship of two input arguments. Unlike the arithmetic mean, which treats all values equally without considering their individual magnitudes, the Heronian Mean accounts for the impact of each data point based on the square root of their product. Introduction Mathematical models are often nonlinear, as the physical phenomenon in nature is not always simple and linear. HM operators have been utilized to solve many multi-criteria decision-making (MCDM) problems under different environments. Improved generalized Heronian Mean operator can simultaneously reflect correlations between values and prevent the redundant calculation. he Heronian mean H of two non-negative real numbers A and B is given by the formula:. The arithmetic mean is most often used. Average is the Same as Mean. IF aggregation operator is a popular data processing method that can be used for data dimensionality reduction, feature extraction, data compression, and so on. Mar 1, 2023 · These include the following three: the arithmetic (AM), the geometric (GM), and the harmonic mean (HM). The reasons for the combination of F-BCM and CoCoSo-H are as follows: S S symmetry Article Some Normal Intuitionistic Fuzzy Heronian Mean Operators Using Hamacher Operation and Their Application Guofang Zhang *, Zhiming Zhang and Hang Kong Key Lab. As a result, T2NN-ARAS can more accurately aggregate inputs, account for Related Standard Deviation Calculator | Sample Size Calculator. The volume is equal to the product of the height of the frustum and the Heronian mean of the areas of the opposing parallel faces. P Mean }= n\sqrt{ \pi r}\) Here $\pi$ symbol pie would mean multiply all the elements of r. Local error, Global error, Cost-effectiveness, Time-efficiency, Heronian Mean. Xing Mar 23, 2021 · The picture fuzzy sets (PFSs) state or model the voting information accurately without information loss. Therefore, it lies between these two means, and between the two given numbers. I. [32, 33] to calculate Heronian Jan 1, 2018 · Heronian mean (HM) operator has the advantages of considering the interrelationships between parameters, and linguistic intuitionistic fuzzy number (LIFN), in which the membership and non-membership are expressed by linguistic terms, can more easily describe the uncertain and the vague information existing in the real world. 4 ), Archimedean operations ( Appendix A. Check if a number is a highly composite number or The Heronian mean of the numbers A and B is a weighted mean of their arithmetic and geometric means: [1] = + +. Zang [35] proposed the interval-valued dual Sep 25, 2020 · What do you mean by Geometric Mean? In mathematics, the geometric mean is a mean, which specifies the central tendency of a set of numbers by using the multiply of their values. [ 1 ] Jun 9, 2023 · Free Online Scientific Notation Calculator. Calculate the sum of these reciprocals. Jul 26, 2018 · Then, Heronian mean is the aggregation operator that can embody the interaction between attributes. Weighted Average Calculator. The formula for the Heronian Mean is: $ H = \frac{x + y + \sqrt{x \cdot y}}{3} $ Where: Heronian Mean Calculator. Heronian Mean[3]: For a collection ai, i = 1;2; ;n, of nonnegative real numbers, their Heronian mean (HM) is de ned as: (4) HM(a1;a2; ;an) = 2 n(n+1 Hamacher operation is a generalization of the algebraic and Einstein operation and expresses a family of binary operation in the unit interval [0,1]. Mar 2, 2023 · We investigate some fundamental properties of the proposed 2-tuple linguistic $ T $-spherical fuzzy aggregation operators. The Heronian mean of the numbers A and B is a weighted mean of their arithmetic and geometric means: Mar 21, 2012 · The formulated T2NN-ARAS method uses the GWHM operator [32, 33] to calculate Heronian optimality functions of alternatives. 3. can also be used for calculation. Research gaps Inspection of the published studies on urban transportation concluded that the transport type and Sep 1, 2024 · Section 4 introduces new T-SF Heronian mean averaging aggregation operators, which are based on the proposed Hamacher operational laws. Hamacher operation is a generalization of the Apr 16, 2019 · Two Heronian mean operators are proposed to aggregate the linguistic neutrosophic multiset, one is a linguistic neutrosophic multiplicity number generalized-weighted Heronian mean operator, the other is a linguistic neutrosophic multiplicity number improved-generalized-weighted Heronian mean operator, and then their properties are discussed. Find the average or mean by adding up all the numbers and dividing by how many numbers are in the set. Heronian mean (HM) is a mean-type aggregation Jan 1, 2024 · Public transportation frameworks assume a critical role in the metropolitan region, especially in huge urban communities, where they offer a feasible … May 22, 2018 · The dual generalized Bonferroni mean (DGBM) operator is a meaningful decision-making tool which can consider the relationship between any numbers of being fused arguments and has been applied to Jul 26, 2019 · Li and Wei [34] introduced the Heronian mean and generalized the Heronian mean to provide two aggregation operators that consider the interdependent phenomena among the aggregated arguments. 3, on the basis of uncertain linguistic numbers and the single-valued neutrosophic set, we develop the Mar 12, 2020 · Fuzzy set, intuitionistic fuzzy set, hesitant fuzzy set can be regarded as a special case of dual hesitant fuzzy set. For example, what is the Heronian mean of 3 and 12? Go Now. In geometry, a Heronian triangle (or Heron triangle) is a triangle whose side lengths a, b, and c and area A are all positive integers. The approximate calculation of a definite integral Apr 23, 2024 · Abstract Intuitionistic fuzzy (IF) sets are valuable tools for describing uncertain information in Multi-Criteria Group Decision Making (MCGDM), where the elements have degrees of membership and non-membership. The de nition of HM is as follows: De nition 6. We calculate the arithmetic mean by taking the sum of all values in a set and dividing it by the number of values. Then, two operators of improved generalized weighted Heronian mean and improved generalized geometric weighted Heronian mean in view of Hamacher operations are proposed. rfkft wac ylj xvtf gujki edncb gavlr hsqujz zhm vsrn

Heronian mean calculator. Calculate the Heronian mean of two positive numbers.