In reality, because of the intricate nature of the socio-economic landscape and the uncertainty of human thought processes, DMs frequently utilize linguistic expressions to convey the assessment information of various attributes (Diao et al., 2022; Tang et al., 2022; Wang et al., 2024; Zhang, S.Q. et al., 2021; Zhao et al., 2021; Zuo et al., 2020). Therefore, Zadeh (1974) proposed fuzzy linguistic sets to describe qualitative evaluation information, but more often than not, DMs also use several linguistic terms to express the evaluation information of attributes (for example, when evaluating an artwork, an appreciator may use both “good” and “very good” to evaluate it). Inspired by the hesitant fuzzy set (Torra, 2010) and the linguistic term set (LTS) (Xu, 2004), Rodriguez et al. (2012) introduced the hesitant fuzzy linguistic term set (HFLTS). While the HFLTS is capable of conveying much of the evaluation information related to DM, it has two main drawbacks: firstly, the evaluation linguistic used by HFLTS is overly simplistic and the evaluation information is too generalized. Secondly, HFLTS fails to capture the significance of each hesitant fuzzy linguistic component. To compensate for its shortcomings, Gou et al. (2017) and Pang et al. (2016) proposed double hierarchy linguistic term set (DHLTS) and probabilistic linguistic term set (PLTS). Gou et al. (2021) later integrated the benefits of both approaches and introduced the PDHLTS. It consisted of multiple DHLTSs and corresponding probabilities. Its linguistic expression of “adverb+adjective” not only delicately described attribute evaluation information, but also conformed to people’s expression habits. In addition, the probability associated with it can more deeply express the DM’s preference information. Therefore, PDHLTS was more suitable for information expression in practical decision-making processes and was currently an important tool for dealing with MADM problems. Based on it, Gou et al. (2017) were the first to define PDHLTS along with its scoring function and distance metric. Furthermore, they adapted the traditional VIKOR approach for the PDHL context and introduced a PDHL-VIKOR method to address a real-world MADM issue related to intelligent healthcare. Subsequently, Lei et al. (2021) introduced a novel PDHLTS distance measure, which encompasses both Euclidean and Hamming distance measures, along with a new probability completion method. Furthermore, they integrated the prospect theory (Kahneman and Tversky, 1979) with CODAS method, extending a new distance measurement formula to the PDHL environment to construct a MADM model that can reflect DMs’ loss aversion psychology. The research on the expected function, score function, and distance measurement formula of PDHLTS by the two scholars mentioned above lays the foundation for identifying more classical methods to solve MADM problems in the PDHL environment in the future. For example, Wang (2022) proposed the PDHL-TOPSIS method and applied it to evaluate the teaching level of a teacher. Liu, P. et al. (2023a) combined WASPAS method with weight determination method and extended it to PDHLTSs environment to solve the risk assessment problem in PDHL environment.

In order to scientifically and effectively solve MADM problems, DMs need to choose appropriate decision information measurement tools and construct scientific and efficient MADM methods. The TODIM method proposed by Gomes and Lima (1991) in 2009 is a validated and effective approach for handling MADM. This method measures the degree of advantage of each alternative solution relative to other alternative solutions by using the overall value, and then evaluates and ranks the alternative solutions based on their overall advantage. In addition, compared with other classic MADM methods (FOR example: TOPSIS method (Hwang and Yoon, 1981), GRA method (Deng, 1989), SWARA method (Zavadskas et al., 2012), EDAS method (Keshavarz Ghorabaee et al., 2015), MABAC method (Pamucar and Cirovic, 2015), etc.), only the TODIM method is unique in that it takes into account the psychological factors affecting DMs, marking a significant advancement in addressing irrational behaviour in uncertain situations. Therefore, it has been applied in many fields (Hong et al., 2019; Liu and Teng, 2015; Wei and Wu, 2019; Zhang et al., 2017; Zindani et al., 2020) and has achieved significant results. Among them, Zhang et al. (2019) applied the improved intuitionistic fuzzy set (IFS) score function and exact function to the TODIM method, and constructed an IF-TODIM model for evaluating supplier production capacity while comparing the differences between IFSs. Sun et al. (2019) extended the classic TODIM method to interval IFSs and constructed a new MADM model, which made significant progress in solving emergency problems in hydraulic engineering. Wang et al. (2021) integrated the TODIM method with binary semantic Pythagorean fuzzy sets to develop innovative models and concepts for the scientific and comprehensive assessment of rural scientific and technological talent. Guo et al. (2020) first defined a new Probabilistic linguistic Hamming distance and improved the classical TODIM method, making the improved TODIM method more accurate and effective in industrial detection of carbon dioxide storage locations. Rosli et al. (2023) first aggregated expert evaluation information expressed in binary semantic sets using the LAMA (Linguistic Aggregation Majority Additive Operator) operator, and then ranked six candidate partners using the TODIM method, selecting the candidate partner with the highest score. Wu et al. (2020) first integrated DEMATEL method with entropy weight method to determine attribute weights, and then evaluated and ranked eight candidate hilly sites by combining PDHLTS and TODIM, and selected the best hilly site selection. Furthermore, to assess the rationality of product recycling channels from a scientific perspective, Hong et al. (2021) first established a complete evaluation index system, then used interval type-2 fuzzy numbers to represent decision information, and finally used TODIM method for sorting. Although the classic TODIM is built on the basis of PT (the value function and probability weight function in prospect theory function effectively reflect the loss aversion psychology of DMs and reveal the irrational factors of DM’s behaviour), the core idea of PT has not been reflected in it. To this end, Tian et al. (2019) introduced the PT theory to improve the TODIM method and constructed an enhanced TODIM method. This study introduces behavioural theory into decision theory, achieving further improvement of decision theory. This article will improve the traditional TODIM method from a new perspective by introducing a new behavioural theory-regret theory which are proposed by Loomes and Sugden (1982) and Bell (1982) to enhance the TODIM method. The improved TODIM method retains both the traditional TODIM method’s ability to represent DMs’ loss aversion attitudes and their regret aversion psychology.

Regret theory (RT) (Bleichrodt et al., 2010) is another important behavioural theory after PT, which combines emotional and motivational factors into the expectancy structure to express DM’s regret and disgust psychology. RT believes that DMs not only focus on its own chosen options, but also on other unselected options. When the outcomes of other unchosen options surpass those of the chosen option, DMs may experience regret; conversely, they may feel happiness if the selected option performs better. Currently, robust techniques have been utilized in the decision-making domain to tackle numerous real-world decision-making challenges (Hu, 2023; Li et al., 2021; Liao et al., 2022; Mondal et al., 2023; Wang et al., 2018). For instance, Liu et al. (2020) developed a comprehensive model for sustainable supplier selection that combines RT and QUALIFLEX methods within a two-dimensional uncertain linguistic context, significantly enhancing the reliability of DM’s evaluations. Jia and Wang (2020) introduced the PROMETHEE II method, grounded in RT, to address the selection of cloud services for universities in a PLTS. Hu (2023) noted that many existing MADM methods neglect the optimal efficiency of the MADM process and the preferences of DMs. To remedy this gap, the MADM method approach based on RT was suggested. Liang and Wang (2020) enhanced urban emergency response capabilities by developing interval hesitant fuzzy satisfaction models. Qian et al. (2019) incorporated RT into the MADM process and proposed a novel grey risk MADM method to tackle the challenge of selecting mall locations. Liu et al. (2023) introduced RT to establish an overall merit model for the urgent relief system of mines, addressing the complexity, ambiguity, and systematicity of the evaluation. Zhang et al. (2021) proposed a case retrieval method for handling multiple attributes and incomplete weight information based on RT and LINMAP methods. Zhao et al. (2023) incorporated RT into an uncertain linguistic context and introduced the interaction between doctors and patients in an online setting, along with the concept of stable matching model, conducting thorough research on the issue with incomplete information. Due to the complexity of construction projects, selecting capable managers is crucial for their success. Yan et al. (2023) integrated the RT with the fuzzy DEMATEL approach to create a MADM model for selecting construction project managers. Furthermore, to assess the specific combat capabilities of a particular fighter jet, Zhang et al. (2023a) adapted the RT and CRITIC methods for use in a Pythagorean hesitant fuzzy (PHF) context, introducing an enhanced method to address random issues within this environment. Additionally, to evaluate five renewable energy options, Ding et al. (2023) developed an improved hybrid MADM method that combines DEMATEL and RT. Considering the influence of fuzzy information and irrational behaviour in reality, DM often finds it difficult to make a decision. Therefore, Zhang et al. (2023b) introduced the VIKOR method utilizing RT to tackle the MADM issue in situations where the weight information is entirely unknown. In summary, utilizing PDHLTS to express decision information and establishing the TODIM method that considers DMs’ behavioural psychology based on RT in the PDHL environment has certain significance for the development of the decision-making field.

The organization of this article: the Section 2 offers a brief overview of essential theoretical concepts relevant to our research, including PDHLTS, RT theory, and traditional TODIM methods. In Section 3, we develop a weight calculation method utilizing the PDHLTS distance measure and PDHLWA operator for the PDHL context, referred to as the CCSD method. Additionally, we expand the perceived utility function in RT to assess the regret and joy associated with the overall advantage flow of alternatives determined by the TODIM method in the PDHL setting, leading to the creation of the MADM method that captures the regret and aversion feelings of DMs, called the RT-PDHL-TODIM method. Section 4 presents specific examples for information system investment project selection to demonstrate the effectiveness of the CCSD and RT-PDHL-TODIM methods proposed in this paper, along with a parameter analysis to further confirm their effectiveness, superiority, and innovation by comparing them to existing methods like PDHL-WASPAS and PDHL-TOPSIS. Finally, Section 5 concludes the article with a summary.

Fuzzy (linguistic) sets are an effective carrier for expressing evaluation information in the MADM process. The definition, conversion function, expectation, and standard deviation of PDHLTS set are introduced in this section. Definition 1

Let ℑ = { ℑ μ | μ = − A , … , − 1 , 0 , 1 , … , A } and ℜ = { ℜ ν | ν = − A , … , − 1 , 0 , 1 , … , A } be two independent LTSs, where ℑ, ℜ are the first and second hierarchy LTSs, respectively. The DHLTS is defined as follows: Θ = { ℑ μ ⟨ ℜ ν ⟩ | μ = − A , … , − 1 , 0 , 1 , … , A ; ν = − A , … , − 1 , 0 , 1 , … , A } .

Next, based on the RT theory, PDHLTS theory, and classic TODIM method, we will construct the PDHL-RT-TODIM method. The mathematical symbols required are described: let Λ = { Λ 1 , Λ 2 , … , Λ s }, Υ = { Υ 1 , Υ 2 , … , Υ t } represent sets of alternatives and evaluation attributes, and ω = ( ω 1 , ω 2 , … , ω t ) represent the weight vector of the evaluation attribute, satisfying ω j ⩾ 0 ,

∑ j = 1 t ω j = 1. The PDHL evaluation information of the attribute Υ j for the alternative Λ i is represented Z i j = { Z i j ( h ) ( p i j ( h ) ) | Z i j ( h ) ∈ Θ , p i j ( h ) > 0 , ∑ h = 1 # Z i j p i j ( h ) ⩽ 1 } and G = { Z i j } s × t is the decision matrix.