The generalized Heronian mean and its inequalities

Guan, Kaizhong; Zhu, Huantao

doi:10.2298/petf0617060g

Cited by 8 publications

(1 citation statement)

References 13 publications

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“…Butnariu and Klement [33] Te HM operator is an efcient tool to aggregate nonnegative positive real numbers. Guan and Zhu [39] generalized inequalities and properties of HM operators under FSs. Yu [40] proposed a MADM technique and discovered some new AOs using the HM operator's basic role.…”

Section: Introductionmentioning

confidence: 99%

Assessment of Solar Panel Using Multiattribute Decision-Making Approach Based on Intuitionistic Fuzzy Aczel Alsina Heronian Mean Operator

Hussain

Ullah

Pamučar

et al. 2023

International Journal of Intelligent Systems

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Multiattribute decision-making (MADM) approach is an effective method for handling ambiguous information in a practical situation. The process of the MADM technique has drawn a lot of interest from various academic and selection processes of extensive analysis. The aggregation operators (AOs) are the best mathematical tools and received a lot of attention from researchers. This article explored the theory of intuitionistic fuzzy IF sets (IFSs) and their certain fundamental operations. The theory of triangular norms also explores Aczel Alsina operations (AAOs) in advanced mathematical tools. The concepts of Heronian mean (HM) and geometric HM (GHM) operators are presented to define interrelationships among different opinions. We developed a list of certain AOs by utilizing AAOs under the system IF information, namely, IF Aczel Alsina HM (IFAAHM), IF Aczel Alsina weighted HM (IFAAWHM), IF Aczel Alsina GHM (IFAAGHM), and IF Aczel Alsina weighted GHM (IFAAWGHM) operators. Some particular characteristics of our invented methodologies are also presented. Solar energy is an effective, efficient resource to enhance electricity production and the country’s economic growth. Therefore, we studied an application of solar panel systems to solve real-life problems under a robust technique of the MADM approach by utilizing our invented approaches of IFAAWHM and IFAAWGHM operators. A numerical example was also given to select more suitable solar panels under our proposed methodologies. To find the competitiveness and feasibility of discussed methodologies, we make an inclusive comparative study in which we contrast the results of existing AOs with the consequences of current approaches.

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Section: Introductionmentioning

confidence: 99%