Abstract
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.
Highlights
Every day, everybody makes decisions, and most of them are with some hesitation
This study develops a new decision framework under the context of the probabilistic intervalvalued hesitant fuzzy environment, based on tail information and the framework has been applied to the tail group decision making
This paper introduced the concepts of the hesitant fuzzy set (HFS), the probabilistic hesitant fuzzy set (PHFS), the probabilistic interval-valued hesitant fuzzy set (PIVHFS), the PIVHFE, and the value at risk (VaR) as the basis of the proposed method to achieve the objective
Summary
Everybody makes decisions, and most of them are with some hesitation. For example, what to eat in breakfast, lunch, dinner, time to wake up, choice of clothing to wear, vehicle. Most of the decisions do not have a significant impact on life This is not a matter for any firm. Wang et al [4] investigated the trends and opportunities of the fuzzy set techniques in big data processing and decision making which are two frontier issues in the field. We may find that the general process in these decision-making techniques is the collection of all the fuzzy information used to classify and obtain the best alternative. In many decision-making processes, DMs may use limited/partial fuzzy information as a priority, all data is required. We discussed this issue under a fuzzy environment by introducing the VaR and developing the fuzzy VaRs. a new tail group decision-making model with PIVHFS is put forward to find the optimal alternative for extreme loss/gain. The above questions can be answered in this fuzzy decision-making process
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