Research On Multi-objective Reachability Problem Based On Fuzzy Kripke Structures

Zadeh put forward the fuzzy set theory in 1965 which can express and reflect the fuzzy concepts in daily life and scientific research.At present,fuzzy set theory has been successfully applied to various research in the computer field and has achieved good results.At the same time,there are many fuzzy system models based on fuzzy set theory.These models are better than those based on classical set theory in describing the inherent properties of fuzzy systems.There have been many papers addressing problems in fuzzy systems,but most of them are aimed at a single target,while in daily life people tend to consider multiple targets simultaneously.Therefore,the study of multi-objective problems in fuzzy systems has important theoretical significance and practical valueBased on the fuzzy Kripke structure,this paper defines and studies the multi-objective reachability of fuzzy systems.The main research contents are as follows:(1)The multi-objective state reachability problem over FKS based on t-norm is proposed.And,a method is given to transform the TSP problem with triangle characteristics into the multiobjective state reachability problem over FKS based on t-norm and it is proved that the problem is an NPC problem.Then,the multi-objective set reachability problem over FKS based on tnorm is proposed.This problem is also an NPC problem.And,we give a reduction between the TSP and this problem.(2)The problem of multi-objective state reachability over FKS based on Zadeh fuzzy logic is studied,the polynomial time algorithm of the problem is given,and the correctness and complexity of the algorithm are analyzed.We also study the complexity of multi-objective set reachability over FKS based on Zadeh fuzzy logic,which is also an NPC problem.In addition,we analyze the relationship between reachability problems including some problems raised by others and us.(3)We also investigate the multi-property reachability problem,which is different from the above problems and is also an NPC problem.Moreover,an algorithm is proposed that transforms a multi-property reachability problem to a multi-objective set reachability over FKS based on Zadeh fuzzy logic in polynomial time.