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An Application of Intuitionistic Fuzzy Differential Equation to the Inventory Model

In: Fuzzy Optimization, Decision-making and Operations Research

Author

Listed:
  • Mostafijur Rahaman

    (Indian Institute of Engineering Science and Technology, Department of Mathematics)

  • Shariful Alam

    (Indian Institute of Engineering Science and Technology, Department of Mathematics)

  • Abdul Alamin

    (Maulana Abul Kalam Azad University of Technology, Department of Applied Mathematics)

  • Sankar Prasad Mondal

    (Maulana Abul Kalam Azad University of Technology, Department of Applied Mathematics)

  • Payal Singh

    (Parul University, Department of Applied Sciences, Faculty of Engineering and Technology)

Abstract

The intuitionistic fuzzy set theory extends the notion of fuzzy set theory in a more generalized way, which includes the sense of belongingness (acceptance) as well as nonbelongingness (rejection). A decision-making phenomenon may go through a vague situation with the dilemma of acceptance and rejection. An economic order quantity (EOQ) model having a fixed goal to reduce the costs as much as possible can be a model of imprecise decision-making with an acceptance-rejection dilemma in the manager’s mind. Thus, an EOQ model may be considered in an intuitionistic fuzzy uncertain environment. In a situation where the parameters and decision variables are of the imprecise nature of the intuitionistic fuzzy type, it is better to describe the uncertain model with the help of intuitionistic fuzzy calculus. Thus, this chapter aims to discuss the classical EOQ model in uncertain intuitionistic fuzzy phenomena. The intuitionistic fuzzy differential equation approach is considered to describe the fuzzy model. Here, the demand and costs are taken as triangular intuitionistic fuzzy numbers (TIFNs). Also, a new defuzzification technique is established in this chapter, which is used to compare the results obtained for crisp and intuitionistic fuzzy models. The intuitionistic fuzzy environment with (i)-differentiability of q(t) appears to offer the best result for the cost minimization goal among the three discussed approaches, whereas the intuitionistic fuzzy environment with (ii)-differentiability of q(t)reveals the worst result, according to the numerical analysis.

Suggested Citation

  • Mostafijur Rahaman & Shariful Alam & Abdul Alamin & Sankar Prasad Mondal & Payal Singh, 2023. "An Application of Intuitionistic Fuzzy Differential Equation to the Inventory Model," Springer Books, in: Chiranjibe Jana & Madhumangal Pal & Ghulam Muhiuddin & Peide Liu (ed.), Fuzzy Optimization, Decision-making and Operations Research, chapter 0, pages 679-702, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-35668-1_30
    DOI: 10.1007/978-3-031-35668-1_30
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