As a valuable tool for representing uncertain information, probabilistic hesitant fuzzy sets (PHFS) have gained considerable recognition and in‐depth discussion in recent years to increase the flexibility and manifest hesitant information in decision‐making problems. However, decision‐makers (DMs) cannot express all preferences only through a few probabilistic terms in actual decision‐making. Much critical information is hidden behind the original information provided by the DMs. Keeping that in mind, we are interested in mining deeper uncertain information from the original probabilistic hesitant fuzzy evaluation data. To achieve the target, we put forward a novel representation tool called the normal wiggly probabilistic hesitant fuzzy set (NWPHFS) to extract deeper uncertain preferences from original probabilistic information. NWPHFS retains the original evaluation information and carries and assesses the potential uncertain details for increasing the rationality of decision‐making outcomes. Herein, we propose some fundamental concepts of NWPHFS, for instance, some elementary operational laws, distance measures between two NWPHFSs, and score function. We also suggest two new aggregation operators, that is, the normal wiggly probabilistic hesitant fuzzy weighted averaging (NWPHFWA) and normal wiggly probabilistic hesitant fuzzy weighted geometric (NWPHFWG). A novel mechanism is proposed here to work out multiattribute decision‐making (MADM) in solving normal wiggly probabilistic decision‐making problems. Through a practical example of environmental quality assessment, the specific calculation steps of this method are epitomized. Finally, we have demonstrated the feasibility and advancement of the proposed approach via a comprehensive comparative study.

Generally, in real decision-making, all the pieces of information are used to find the optimal alternatives. However, in many cases, the decision-makers (DMs) only want “how good/bad a thing can become.” One possibility is to classify the alternatives based on minimum (tail) information instead of using all the data to select the optimal options. By considering the opportunity, we first introduce the value at risk (VaR), which is used in the financial field, and the probabilistic interval-valued hesitant fuzzy set (PIVHFS), which is the generalization of the probabilistic hesitant fuzzy set (PHFS). Second, deemed value at risk (DVaR) and reckoned value at risk (RVaR) are proposed to measure the tail information under the probabilistic interval-valued hesitant fuzzy (PIVHF) environment. We proved that RVaR is more suitable than DVaR to differentiate the PIVHFEs with example. After that, a novel complete group decision-making model with PIVHFS is put forward. This study aims to determine the most appropriate alternative using only tail information under the PIVHF environment. Finally, the proposed methods’ practicality and effectiveness are tested using a stock selection example by selecting the ideal stock for four recently enrolled stocks in China. By using the novel group decision-making model under the environment of PIVHFS, we see that the best stock is E₄ when the distributors focus on the criteria against 10% certainty degree and E₁ is the best against the degree of 20%, 30%, 40% and 50% using the DVaR method. On the other hand when RVaR method is used then the best alternative is E₄ and the worst is E₂ against the different certainty degrees. Furthermore, a comparative analysis with the existing process is presented under the PHF environment to illustrate the effectiveness of the presented approaches.