Linguistic dynamic systems (LDS) are dynamic systems whose state variables are generalized from numbers to words. Generally speaking, LDS can model all evolving processes in word domains by using linguistic evolving l...Linguistic dynamic systems (LDS) are dynamic systems whose state variables are generalized from numbers to words. Generally speaking, LDS can model all evolving processes in word domains by using linguistic evolving laws which are naturally the linguistic extension of evolving laws in numbers. There are two kinds of LDS; namely, type-I and type-II LDS. If the word domain is modeled by fuzzy sets, then the evolving laws of a type-I LDS are constructed by applying the fuzzy extension principle to those of its conventional counterpart. On the other hand, the evolving laws of a type-II LDS are modeled by fuzzy if/then rules. Note that the state spaces of both type-I and type-II LDSs are word continuum. However, in practice, the representation of the state space of a type-II LDS consists of finite number while its computation actually involves a word continuum. In this paper, the existence of fixed points of type-II LDS is studied based on point-to-fuzzy-set mappings. The properties of the fixed point of type-II LDS are also studied. In addition, linguistic controllers are designed to control type-II LDS to goal states specified in words.展开更多
基金This work has been supported in part by Outstanding Overseas Scholar Award and Outstanding Young Scientist Research Fund.
文摘Linguistic dynamic systems (LDS) are dynamic systems whose state variables are generalized from numbers to words. Generally speaking, LDS can model all evolving processes in word domains by using linguistic evolving laws which are naturally the linguistic extension of evolving laws in numbers. There are two kinds of LDS; namely, type-I and type-II LDS. If the word domain is modeled by fuzzy sets, then the evolving laws of a type-I LDS are constructed by applying the fuzzy extension principle to those of its conventional counterpart. On the other hand, the evolving laws of a type-II LDS are modeled by fuzzy if/then rules. Note that the state spaces of both type-I and type-II LDSs are word continuum. However, in practice, the representation of the state space of a type-II LDS consists of finite number while its computation actually involves a word continuum. In this paper, the existence of fixed points of type-II LDS is studied based on point-to-fuzzy-set mappings. The properties of the fixed point of type-II LDS are also studied. In addition, linguistic controllers are designed to control type-II LDS to goal states specified in words.
