Interaction power Heronian mean aggregation operators for multiple attribute decision making with T-spherical fuzzy information

Applications of T-spherical fuzzy aczel-alsina power muirhead mean operators in identifying the most effective water purification process for commercial purpose

One of the key areas of research in ambiguous and inconsistent problems with decision-making is T-spherical multiple-attribute decision making (TSP-FMADM). The TSP-F number (TSP-FN), which is an extension of the fuzzy number, an intuitionistic fuzzy number, and other fuzzy structures, may deal with problems involving a significant amount of incorrect, incomplete, and inconsistent data. Being an extension of various fuzzy structures, the TSP-F sets (TSP-FSs) provide decision-makers greater freedom to voice their actual opinions and offer a broader range of acceptable membership grades. The Muirhead mean (MM) operator and power aggregation (PA) operators are illustrations of standard aggregation operators. They are better because they can reproduce the relationships amongst input qualities and eliminate the negative influence of obstinate data. Since its publication in 1982, Aczel and Alsina's t-norms have proven to be a highly effective and popular technique for generating aggregation operators of any kind. Furthermore, the parameter belongs to ( 0 , + ∞ ) converts the Aczel-Alsina t-norms into a specific instance of the algebraic t-norms. In this article, novel aggregation operators (AGOs) are suggested, considering the advantages of the TSP-FN, to handle the multi-criteria decision-making problems. These new AGOs consider how various input data are related to one another and can mitigate the impact of inaccurate data at the same time. To strengthen the adaptability of these new AGOs, this article proposes the T-spherical fuzzy Aczel-Alsina power Muirhead mean (TsP-FAAPMM) operator, T-spherical fuzzy Aczel-Alsina power dual Muirhead mean (TsP-FAAPDMM) operator which combines the Aczel-Asina operational rules with the power average/geometric operator and the Muirhead/dual Muirhead mean operators. A variety of fundamental characteristics and special cases with respect to the parameters are explored and it is retrieved that various existing AGOs are special cases of these newly initiated AGOs. Further, weighted forms of these AGOs are established. Then, we set up the multiple attribute decision making (MADM) technique using these AGOs that are suggested to solve MADM problems. We then give a numerical example about industrial water purification selection and compare it to other related MADM techniques that are already in use in the TsP-FN information to demonstrate the effectiveness and appropriateness of the anticipated technique.

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.

T-spherical uncertain linguistic MARCOS method based on generalized distance and Heronian mean for multi-attribute group decision-making with unknown weight information

The T-spherical uncertain linguistic (TSUL) sets (TSULSs) integrated by T-spherical fuzzy sets and uncertain linguistic variables are introduced in this article. This new concept is not only a generalized form but also can integrate decision-makers’ quantitative evaluation ideas and qualitative evaluation information. The TSULSs serve as a reliable and comprehensive tool for describing complex and uncertain decision information. This paper focuses on an extended MARCOS (Measurement of Alternatives and Ranking according to the Compromise Solution) method to handle the TSUL multi-attribute group decision-making problems where the weight information is completely unknown. First, we define, respectively, the operation rules and generalized distance measure of T-spherical uncertain linguistic numbers (TSULNs). Then, we develop two kinds of aggregation operators of TSULNs, one kind of operator with independent attributes is T-spherical uncertain linguistic weighted averaging and geometric (TSULWA and TSULWG) operators, and the other is T-spherical uncertain linguistic Heronian mean aggregation operators (TSULHM and TSULWHM) considering attributes interrelationship. Their related properties are discussed and a series of reduced forms are presented. Subsequently, a new TSUL-MARCOS-based multi-attribute group decision-making model combining the proposed aggregation operators and generalized distance is constructed. Finally, a real case of investment decision for a community group-buying platform is presented for illustration. We further test the rationality and superiorities of the proposed method through sensitivity analysis and comparative study.