## 1 Introduction
[39] introduced the technique for ranking alternatives based on DTRSs, while [PERSON] et al. [40] extended this concept to multi-organizational DTRSs. In an attempt to integrate different theories, [PERSON] et al. [41] introduced fuzzy data with three-way decision-theoretic rough sets, while [PERSON] et al. [42] focused on DTRSs with single-valued neuromorphic data. Furthermore, several models and approaches for DTRSs have been proposed by experts [43; 44]. After conducting the analysis mentioned above, we have developed a new, more generalized, effective, and advanced approach. We created novel Aczel-Alsina aggregation operators for intuitionistic hesitant fuzzy data and further developed a three-way decision model based on the concept of decision-theoretic rough sets for IHFSs. Figure 1 presents a flow chart of the complete details of the proposed model. This paper contributes in the following ways:  
1. First, we presented novel aggregation operators and basic operational laws of IHFSs, exploring the fundamental notion of Aczel-Alsina \(T\_\mathcal{N}\) and \(T.\mathcal{CN}\). Using Aczel-Alsina \(T.\mathcal{N}\) and \(T.\mathcal{CN}\), we developed a series of novel operators, such as \(IHF\mathcal{A}_{\mathcal{A}}WA_{\omega}\) operators, and verified their novelty with some properties. To test the feasibility and reliability of our proposed operators, we designed a few special cases, including \(IHFA_{\mathcal{A}}\)-ordered weighted \((IHFA_{\mathcal{A}}OWA_{0})\) and \(IHF_{\mathcal{A}}A_{\mathcal{A}}\)-hybrid weighted \((IHFA_{\mathcal{A}}HWA_{0})\) average operators with their fundamental properties. 3. Additionally, we designed a novel three-way decision-theoretic rough set model in this article. This approach utilized new steps for 3 WD, including the design of Aczel Alsina aggregation operators and the development of score function and accuracy function to classify participants. 4. Using the proposed model, we provided a case study of business, where making the best decision for investment is a significant issue for investors. To address this issue, we developed a model consisting of different companies, and according to the Bayesian theory of risk, we discussed cost parameter tables from experts in detail under the variation of conditional probability. 5. We discussed an influenced study to visualize the effectiveness of the parametric values of the conditional probabilities on the results of our presented model. 6. Finally, we compared our developed approach with existing models of AOs to check its validity, authenticity, and effectiveness. Figure 1: Flow Chart of the proposed work. The rest of the paper is organized as follows: we quickly go over some of the core concepts of Aczel-Alsina \(T\).\(\mathcal{N}s\) and some generalizations of fuzzy sets and revisit the idea of DTRS in Section 2. In Section 3, we reorganize three-way decision rules based on DTRS using aggregation operators for IHFNs. In Section 4, we describe the series of novel Aczel-Alsina aggregation operation rules for the IHFNs, such as the IHF Aczel-Alsina weighted averaging \((IHF\mathcal{A}_{\mathcal{A}}WA_{0})\) operator, the IHF Aczel-Alsina order weighted averaging \((IHF\mathcal{A}_{\mathcal{A}}OWA_{0})\) operator, and the IHF Aczel-Alsina hybrid averaging \((IHF\mathcal{A}_{\mathcal{A}}HA_{0})\) operator, and their useful features. In Section 5, we develop an algorithm for handling 3 WD difficulties, where the characteristic values are represented as IHF data using the \(IHF\mathcal{A}_{\mathcal{A}}WA_{0}\) operator. In Section 6, an illustration of choosing a suitable company for investment evaluated by the suggested model is also given. We discuss how a parameter affects the classification order of options, and, to show the superiority and sensitivity of the developed approach, a comparative analysis is added in Section 7. Finally, Section 8 concludes the paper.