On an Approach to Construction of Structured Fuzzy Sets and Their Application for Description of Fuzzy Time Response

摘要

An approach to the construction of fuzzy structured numerical sets based on the principle of formation of the fuzzy original set with its further replication on the numerical axis is considered. Formalization of the fuzzy original consists in the determination of a fuzzy triangular number with the corresponding carrier. The suggested technique enables formalization of the problem of fuzzy description of time dynamics. A variant of construction of fuzzy numerical sets formalizing "rapid" and "slow" course of time is considered. Examples of the use of the fuzzy description of time dynamics are given in the form of different statements of the mathematical optimization problems appearing on the determination of the content and order of execution of certain aggregates of tasks within the limits of the given time interval with considering or without considering supplementary constraints and for different objective functions.