直觉模糊测度的计算树逻辑

发布时间：2018-06-17 11:20

本文选题：直觉模糊Kripke结构 + 直觉模糊测度　；参考：《计算机科学与探索》2017年09期

【摘要】：建立了直觉模糊Kripke结构(intuitionistic fuzzy Kripke structure,IFKS)模型,提出了基于直觉模糊Kripke结构的直觉模糊测度空间理论,阐述了IFKS的一系列性质。证明了任一路径转移的直觉模糊可达度(intuitionistic fuzzy probability,IFP)为初始状态的直觉模糊测度与各转移的IFP所取下确界,任一状态出发的所有路径上路径转移的IFP为所有路径可达度的上确界。给出了路径转移矩阵P及其传递闭包P~+的概念,给出了通过计算路径转移矩阵传递闭包,计算路径可达度的算法,并分析了算法的复杂度。提出了直觉模糊计算树逻辑(intuitionistic fuzzy computation tree logic,IFPCTL)理论,讨论了一组IFPCTL、可能测度计算树逻辑(possibilistic computation tree logic,PoCTL)和经典计算树逻辑(computation tree logic,CTL)公式的等价性。最后给出了一组等价的IFPCTL和PoCTL公式以及一组不等价的IFPCTL和CTL公式。
[Abstract]:The intuitionistic fuzzy Kripke structure (IFKS) model is established, and the intuitionistic fuzzy Kripke structure IFKS model is established. The intuitionistic fuzzy measure space theory based on intuitionistic fuzzy Kripke structure is proposed, and a series of properties of IFKS are expounded. It is proved that the intuitionistic fuzzy probability (IFP) of any path transition is an intuitionistic fuzzy probability (IFP), and that the intuitionistic fuzzy probability (IFP) of any path transition is the upper bound of the reachability of all paths. In this paper, the concept of path transfer matrix P and its transitive closure P ~ are given, and the algorithm of calculating path reachability by calculating path transfer matrix transfer closure is given, and the complexity of the algorithm is analyzed. In this paper, the intuitionistic fuzzy computation tree logic theory of intuitionistic fuzzy computation tree logic is put forward, and the equivalence of a set of IFPCTL, possibilistic computation tree logic PoCTL) and classical computational tree logic computation tree logics is discussed. Finally, a set of equivalent IFPCTL and PoCTL formulas and a set of non-equivalent IFPCTL and CTL formulas are given.
【作者单位】：商洛学院数学与计算机应用学院;陕西师范大学计算机科学学院;
【基金】：国家自然科学基金(No.61228305) 陕西省教育厅专项科研计划项目(No.2015JK0605) 商洛学院科研项目(No.15SKY001)~~
【分类号】：O159

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