Abstract
The article considers the use of fuzzy sets in determining the execution time of tasks. An approach is proposed that makes it possible to obtain an expert estimate of the time taken to complete a task by a specific employee in the form of a fuzzy set. A procedure is proposed for generalizing fuzzy sets defined on different bearing sets. To apply the proposed procedure, fuzzy sets are subject to continuity and monotonicity restrictions. The generalization procedure is based on the process of finding the value of a fuzzy set for a certain value of its membership function. For piecewise linear functions, the operation of calculating the points of the resulting function is defined. Piecewise nonlinear functions are considered and an algorithm for searching for individual values of the generalized membership function is described. In addition to generalizing fuzzy sets, an approach to calculating the interaction time of workers is proposed. Various approaches to defuzzification of fuzzy sets of task execution time are considered. The proposed approach will improve the work planning for sustainability of enterprise.
Highlights
Determining the time to complete a task is one of the main problems in planning work
Information on estimating task execution time and their relationship is used in the CPM (Critical Path Method) method (George E. 2016, Kiran D.R. 2019), which allows one to single out tasks of the so-called “Critical Path”, i.e. tasks, changing the runtime, which will lead to a change in the runtime of the entire project
In Gantt charts, in addition to automatic task setting by the CPM method, there is the possibility of manually changing the task start time
Summary
Determining the time to complete a task is one of the main problems in planning work. When developing science-intensive projects, the evaluation of the duration of individual tasks is impossible by the leader, since such work has not been carried out before. For such cases, an estimate of the time taken to complete the task directly by the employee or the leader of a small working group is used. An estimate of the time taken to complete the task directly by the employee or the leader of a small working group is used Such an assessment is almost impossible to give in cases when several workers perform the same task at the same time. The paper proposes an algorithm for performing the generalization operation for fuzzy functions defined on various bearing sets under certain restrictions
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