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.
It is quite beneficial for every company to have a strong decision-making technique at their disposal. Experts and managers involved in decision-making strategies would particularly benefit from such a technique in order to have a crucial impact on the strategy of their company. This paper considers the interval-valued linear Diophantine fuzzy (IV-LDF) sets and uses their algebraic laws. Furthermore, by using the Muirhead mean (MM) operator and IV-LDF data, the IV-LDF power MM (IV-LDFPMM) and the IV-LDF weighted power MM (IV-LDFWPMM) operators are developed, and some special properties and results demonstrated. The decision-making technique relies on objective data that can be observed. Based on the multi-attribute decision-making (MADM) technique, which is the beneficial part of the decision-making strategy, examples are given to illustrate the development. To demonstrate the advantages of the developed tools, a comparative analysis and geometrical interpretations are also provided.
A novel model termed a bipolar complex fuzzy N-soft set (BCFN-SS) is initiated for tackling information that involves positive and negative aspects, the second dimension, and parameterised grading simultaneously. The theory of BCFN-SS is the generalisation of two various theories, that is, bipolar complex fuzzy (BCF) and N-SS. The invented model of BCFN-SS helps decision-makers to cope with the genuine-life dilemmas containing BCF information along with parameterised grading at the same time. Further, various algebraic operations, including the usual type of union, intersection, complements, and a few others types, are invented. Certain primary operational laws for BCFN-SS are also invented. Moreover, a technique for order preference by similarity to the ideal solution (TOPSIS) approach is devised in the setting of BCFN-SS for managing strategic decision-making (DM) dilemmas containing BCFN-SS information. Keeping in mind the usefulness and benefits of the TOPSIS approach, two various types of TOPSIS approaches in the environment of BCFN-SS are devised and then a numerical example for exposing the usefulness of the devised TOPSIS approach is interpreted. To disclose the prominence and benefits of the devised work, the devised approaches with numerous prevailing work are compared.
The engineering and construction sector is vital to a country’s economic growth, financial activities, and development. These sectors generate opportunities for the unemployed, unskilled, and skilled workforce. Recently, a lot of researchers worked on the Aczel–Alsina t-norm (TN) and t-conorm (TCN), which are generalizing many other t-norms and producing reliable results. In this article, first, we developed some new aggregation operators (AOs) and fundamental operational laws of Aczel–Alsina operations, including Aczel–Alsina product, sum, and scalar multiplication based on the IVPF information. Furthermore, we introduced an innovative AOs in the form of IVPF Aczel–Alsina weighted averaging (IVPFAAWA) operators with some basic characteristics. Moreover, we also generalized Aczel–Alsina operations in the form of the IVPF Aczel–Alsina weighted geometric (IVPFAAWG) operator. For the solution of daily life problems by utilizing a multiattribute decision-making (MADM) approach, we also established an application under the system of engineering and construction sectors. We illustrated a numerical example to find the suitable construction material for the engineering and construction sectors. To find the validity and flexibility of our proposed AOs, we also studied a comprehensive comparative analysis, in which we compared the results of exiting AOs with the results of our current invented approaches. At the end, we sum up our whole article in a single paragraph.
In this article, we expose the notion of power operator to reduce the impact of negative information on the decision-making (DM) process. The power aggregation tools are also robust mathematical aggregation operators (AOs) which allow input arguments to support each other in the DM process. The Frank aggregation expressions are reliable and updated versions of triangular norms which are used to handle complex and complicated information in a decision-making process. The picture fuzzy (PF) set (PFS) is an extended version of the fuzzy sets (FSs) and intuitionistic FSs (IFSs). A PFS has four terms of an object simultaneously such as positive grade (PG), Abstained grade (AG), negative grade (NG) and refusal grade (RG). By using basic operations of Frank aggregation expressions, we propose a list of new appropriate methodologies under consideration of PF information, including ''picture fuzzy frank power average'' (PFFPA), and ''picture fuzzy frank power geometric'' (PFFPG) operators. We also present some new approaches to PFSs based on Frank aggregation tools such as ''picture fuzzy frank power weighted average'' (PFFPWA) and ''picture fuzzy frank power weighted geometric'' (PFFPWG) operators. Some appropriate properties and special cases of our currently proposed approaches are also studied. Moreover, to ratify the intensity and reliability of our derived strategies, we illustrated an algorithm of the multiattribute group decision-making (MAGDM) technique under a PF environment. Furthermore, we illustrated a practical case study to evaluate a suitable optimal option by considering our proposed approaches and analyzed the performance of our currently derived approaches by comparing the results of existing methodologies.INDEX TERMS Frank aggregation tools, picture fuzzy numbers, power aggregation operates, multi-attribute group decision-making process.
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