Modeling Decisions for Project Scheduling Optimization Problem Based on Type-2 Fuzzy Numbers

  • Margarita Knyazeva
  • Alexander BozhenyukEmail author
  • Janusz Kacprzyk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11288)


This paper examines type-2 fuzzy numbers implementation to resource-constrained scheduling problem (RCSP) for agriculture production system based on expert parameter estimations. Some critical parameters in production system are usually treated as uncertain variables due to environmental changes that influence agriculture process. Implementation of type-2 fuzzy sets (T2FSs) can handle uncertain data when estimating variables for solving decision-making problems. The paper focuses on estimation procedure of uncertain variables in scheduling that reflect level of preference or attitude of decision-maker towards imprecise concepts, relations between variables. Special profiles for activity performance allow to consider uncertainty in time variables, expert estimations, flexibilities in scheduling, resource levelling problem and combinatorial nature of solution methodology. An example of activities for agriculture production system is introduced. Heuristic decision algorithm based on enumeration tree and partial schedules is developed. It can handle both resource-constrained optimization problem under uncertain variables and activity profile switching. As initial activity profile we consider expert decision about best activity execution profile on each level of enumeration tree.


Type-2 fuzzy number Fuzzy graph Combinatorial optimization Scheduling 



This work has been supported by the Ministry of Education and Science of the Russian Federation under Project “Methods and means of decision making on base of dynamic geographic information models” (Project part, State task 2.918.2017).


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Southern Federal UniversityTaganrogRussia
  2. 2.Systems Research Institute Polish Academy of SciencesWarsawPoland

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