作者:\n\t王月，赵辉，乌伦华\n

Authors:\n\tWANG Yue,ZHAO Hui,WU Lunhua\n
摘要:\n\t针对新设计的一对q-Fuzzy和算子，及q-Fuzzy积算子，证明满足T三角模与S三角模条件，接着定义一种k-模糊测度，并在k-模糊测度空间下定义q-Fuzzy和概率积分；最后将q-Fuzzy和概率积分应用到医疗头盔性能优化上；对医疗头盔性能优化过程中采用优序图法和改进的反熵权法计算权重；其次应用模糊概率积分和结合最大概率原则对医疗头盔性能优化状态进行评估，并对评估结果进行排序；最后用模糊概率值得出的结果与模糊综合评价法得到的结果进行对比，结果是完全一致，验证了提出的q-Fuzzy和概率积分法更加精炼准确，克服了模糊综合评价结果的模糊性和辨识性。\n

Abstract:\n\tFor the newly designed pair ofq-Fuzzy sum operators andq-Fuzzy product operators， it is proved that they meet the conditions of T triangular modulus and S triangular modulus, and then a k-fuzzy measure is defined, and q-Fuzzy and probability integral are defined under the k-fuzzy Measure space; finally, q-Fuzzy and probability integral are applied to the performance optimization of medical helmets; the optimal sequence diagram method and improved anti-entropy weight method are used to calculate the weights in the process of optimizing the performance of medical helmets. Subsequently, fuzzy probability integrals combined with the principle of maximum probability are used to evaluate the performance optimization state of the medical helmet, and rank the evaluation results. Finally, the results obtained by fuzzy probability value are compared with the result obtained by the fuzzy comprehensive evaluation method, and the results are completely consistent. This validates the proposed q-Fuzzy and the probability integral method are more refined and accurate, overcoming the fuzziness and identification of the fuzzy comprehensive evaluation results.\n


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