评价等级为多交模糊集条件下的证据推理方法及应用

Evidential Reasoning Approach and Its Application under the Condition of Evaluation Grades Being Multi-intersection Fuzzy Set

针对目前模糊证据推理方法仅考虑两个相邻模糊评价等级之间存在交集的局限性,文章对多个(n≥3)连续的模糊评价等级两两存在交集情况下的组合概率分配函数以及模糊交集信度的再分配方法进行研究,结果发现:(1)不论模糊评价等级两两之间存在交集的数量如何变化,组合概率分配函数均可用统一的公式表达,但归一化系数则会随着交集数量的变化而变化;(2)模糊交集的组合信度再分配方法随着两个模糊等级交集状态的不同而不同,当两个模糊等级交集的最大隶属度小于1时,可采用既有的方法,而当两个模糊等级交集的最大隶属度等于1时,既有方法将不再适用,为此,文章提出一种新的组合信度再分配方法。实例分析表明,研究成果能够较好地适应《地铁及地下工程建设风险管理指南》对风险评判的要求,同时也为处理其他类似的多交模糊集条件下的多属性决策问题提供了参考。

Aiming at resolving the limitation of fuzzy evidential reasoning which considers only the intersection between two adjacent fuzzy evaluation grades,this paper makes a study on the aggregated probability masses and the reassigning method of belief degree of fuzzy intersection in the case of intersection existing between each two fuzzy evaluation grades.The results arc as follows:(1) no matter how many pairs of fuzzy evaluation grades intersect,the aggregated probability masses can be expressed by using a uniform formula, but the normalization coefficient will be different depending on the number of intersections;(2) the reassignments of belief degree of fuzzy intersection are different for the following two different intersection cases.When the maximum membership degree of an intersection of two fuzzy grades is less than l,the existing method in literature is still valid.However,when the maximum degree is equal to l,the abovementioned method is no longer applicable,and therefore,a new method in relation to the reassignment of belief degree is proposed in this paper.A case study is carried out and it shows that,the new formula can generate reasonable risk analysis results to make surc a project can meet the requirements of ,and also provide references for dealing with other similar multi-attribute decision-making problems under the condition of multi-intersection fuzzy set.