Abstract
Emergencies often occur irregularly, such as infectious diseases, earthquakes, wars, floods, the diffusion and leakage of chemically toxic and harmful substances, etc. These emergencies can bring huge disasters to people, even worse, the time left for people to make critical decisions is usually very limited. When an emergency occurs, the most important thing for people is to make reasonable decisions as soon as possible to deal with the current problems, otherwise, the situation may deteriorate further. The paper proposes an emergency decision-making algorithm under the constraints of the limited time and incomplete information, the research is mainly carried out from the following aspects, firstly, we use the data structure of the hesitant fuzzy probabilistic linguistic set to collect the basic data after careful comparison, which has three advantages, (1) considering the hesitation in the decision-making process, each evaluation information is allowed to contain multiple values instead of just one value; (2) each evaluation value is followed by a probability value, which further describes the details of the evaluation information; (3) the data structure allows some probability information to be unknown, which effectively expands the application scope of the algorithm. Secondly, the maximization gap model is proposed to calculate unknown parameters, the model can distinguish alternatives with small differences. Thirdly, all the evaluation information will be aggregated by the dynamic hesitant probability fuzzy weighted arithmetic operator. Subsequently, an instance is given to illustrate the effectiveness and the accuracy of the algorithm proposed in the paper. Finally, the advantages of the proposed algorithm are further demonstrated by comparing it with other outstanding algorithms. The main contribution of the paper is that we propose the maximization gap model to obtain the unknown parameters, which can effectively and accurately distinguish alternatives with small differences.
Highlights
Emergencies often occur irregularly, such as infectious diseases, earthquakes, wars, floods, the diffusion and leakage of chemically toxic and harmful substances, etc
In the above part of this section, we have mainly introduced the probabilistic linguistic term set with a finite number of possible elements, we find that it should be closer to reality when all values in a range are possible evaluation values
We find that there are some unknown parameters in the emergency evaluation decision matrix, such as, L2′ 1 = {0.87|0.5, 0.84|y, 0.80|0.5 − y}, it means that three evaluation values are given by the expert E2 for the alternative A1 and they are 0.87, 0.84 and 0.80 respectively, the probability of the first evaluation value 0.87 is 0.5, while, the probability of the second evaluation value 0.84 is uncertain, since the sum of all probability values of any probabilistic linguistic element (PLE) is 1, the probability value of the third evaluation value can be calculated, which is 0.5 − y
Summary
This section mainly introduces the mathematical definition and properties of the hesitant fuzzy probabilistic linguistic set, as well as aggregation algorithms and comparison methods, so as to provide basic theoretical support for the optimal decision-making . The probabilistic linguistic term set can preserve the evaluation values and record the occurrence probabilities, it is more suitable to describe the hesitation and uncertainty of complex systems compared with the hesitant fuzzy linguistic s et[22] It is one of the ideal mathematical support tools for emergency decision-making. If all the elements in the emergency decision matrix are equal to {1|1} , the alternative will be called the positive ideal s olution[30], which is shown as follows: Ap. the probability hesitation fuzzy element Lij = {0|1} indicates that the expert Ei completely disagree with the alternatives Aj without any doubt. The score values of the alternative Ax can be calculated according to the evaluation values of the alternative Ax , which is shown as follows: Ax
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