On the influence of fuzzy perception of the time passage speed on the solutions of optimization planning problems

Abstract

The paper considers an approach to the construction of fuzzy structured numerical sets based on the formation of a fuzzy original of a special type with subsequent replication on the number axis. The constructive principle of fuzzy original formalization is to define a fuzzy triangular number with the appropriate support. A variant of the formation of fuzzy numerical sets, formalizing the "fast" and "slow" passage of time, is proposed. The developed technique allows us to propose a solution to the problem associated with the formalization of the subjective perception of the time reference in processes involving a person, to obtain results and evaluate the impact of fuzzy description and taking into account the dynamics of the time reference on the solution of various optimization problems. A general approach to the formation and solution of fuzzy linear optimization problems is considered, the transition from fuzzy to parametric formulation in the Bellman-Zade form is described. Examples of the use of fuzzy flow of time for different statements of tasks that arise when determining the order of the set of tasks within a given time interval with or without additional restrictions on the execution process are considered. An approach is proposed for the correction of the initial time distribution plans, taking into account different rates of time counting. A mathematical model of the fuzzy traveling salesman problem is formulated as a problem of finding a route to visit a given number of cities without repetitions with a minimum travel time with time parameters specified as right fuzzy numbers, the support value in which depends on various external conditions and factors. The results of calculations of solutions of fuzzy optimization problems are obtained. The influence of the speed of the passage of time on the solution of the considered optimization problems is determined.