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Top1. Introduction
Effective management of inventory is one of the most important and challenging tasks for any business firm. For this, the classical economic ordered quantity (EOQ) model developed by Harris in 1913 is one of the basic tools adopted. Over the period of time, a lot of improvements in the EOQ model have been made by the researchers to get the maximum benefit of the model. Parallel to the development of different models of inventory management, the researchers have achieved some exceptional results in the field of fuzzy set theory introduced by Zadeh (1965). Researchers have devoted their work to conceptualize different fuzzy numbers and its defuzzification methods. The present article is an attempt to define a pentagonal dense fuzzy set (PDFS) and its novel defuzzification method. Further, the concept is implemented in the field of inventory management to recognize its worth.
After the invention of the fuzzy set theory, inventory practitioners have implemented the concept of fuzzy set theory in modelling the inventory system to capture the uncertainty associated with the inventory parameters. The first attempt to extend the EOQ model under a fuzzy environment was made by Park (1987). Subsequently, many researchers have contributed to develop inventory models under fuzzy environment. Some of the notable articles can be referred from the comprehensive review done by Shekarian et al. (2017) and Lakshmi et al. (2018). To represent the inventory parameters in a fuzzy sense, the researchers have used different fuzzy numbers such as triangular fuzzy number (TFN), trapezoidal fuzzy number (TpFN), pentagonal fuzzy number (PFN), hexagonal fuzzy number (HFN), and their various defuzzification methods namely; signed distance method, graded mean integration method, Yager’s ranking index method (1981), etc. It is observed that due to impreciseness in human judgment, sometimes uncertainty arises in more than four points. In such cases, numbers like TFN and TpFN are not adequate to represent the fuzziness associated with the data. Therefore, in the past few years, the concept of PFN has gained significant attention from decision-makers and inventory practitioners. Mondal and Mandal (2017) have discussed in detail various types of PFN having different membership functions such as linear, non-linear, symmetric, and asymmetric. In the present research work, the authors have considered PFN with linear membership function with symmetry to formulate the EOQ model under a pentagonal fuzzy environment. Selvam et al. (2017) have introduced some important arithmetic operations related to PFN and proposed a new ranking method for the same. Rama and Rosario (2018) have worked on a fuzzy inventory model by considering different fuzzy numbers and their various defuzzification methods. Chakraborty et al. (2019) have discussed in detail about various representations of PFN, its ranking methods, and defuzzification techniques. Recently, Jeyakumari et al. (2021) have presented an EOQ model without shortages by assuming inventory parameters like purchasing cost, storing cost, and yearly interest to be PFN. Further, in the recent years, many researchers are attaracted towards the development of new theories related to different kind of fuzzy numbers. Li and Liu (2015) have worked on parameterized nonlinear programming approach to solve matrix games with payoffs of I-fuzzy numbers. Fei et al. (2018) have developed new approach based on interval-valued fuzzy numbers. A new method of interval Banzhaf values of interval cooperative games has been studied by Liang and Li (2019). Li et al. (2020) extended generalized solidarity values to interval-valued cooperative games. Recently, Ye and Li (2021) presented a novel approach to compute triangular fuzzy banzhaf values of cooperative games based on TFN.