# A Study of an EOQ Model of Growing Items with Parabolic Dense Fuzzy Lock Demand Rate
### Motivation and Specific Study  
To find the novelty of this article, we have to find the research gap first. The research gaps in some recent major studies are given in Table 1.  
From the above literature review of fuzzy sets, we can see that none of the researchers defined the parabolic dense fuzzy lock set concept. To avoid complexity, most researchers considered linear membership function. However, in real life, this does not always happen. In PDFLS, we incorporate the learning experience and the nonlinearity concept. The PDFLS concept may be used for not only inventory problems but also any research problem where we use a fuzzy environment. Table 1 shows that many researchers studied growing items but none of them considered the demand rate or any other parameters as a fuzzy number. However, we all know that fuzziness plays a vital role in any inventory management problem. Recently, [PERSON] and [PERSON] [37] developed a two-echelon supply chain model of growing items. [PERSON] et al. [38] studied an inventory model for growing items. Here, the demand rate was price-sensitive under carbon emissions. After that, several researchers ([PERSON] and [PERSON] [39], [PERSON] and [PERSON] [40], and [PERSON] and [PERSON] [35]) discussed inventory models of growing items in a crisp environment. None of them considered fuzziness in their models. In this article, we describe the parabolic dense fuzzy number with its some basic arithmetic operations. Then, we define a parabolic dense fuzzy lock set. In this study, we also consider an EOQ model of growing items. Here, we mainly study the fishery culture using an EOQ model. We solve the EOQ model in a crisp sense first. Then, we consider the demand rate as a parabolic dense fuzzy lock number and solve the corresponding fuzzy model. A comparative study with some existing fuzzy environments is also presented, taking the numerical result from LINGO 18.0 software. Lastly, a sensitivity analysis and graphical illustration are included for better justification of the model.  
This paper is arranged as follows: in Section 2, some preliminary definitions are given. In Section 3, some basic arithmetic definitions of PDFN are presented. The crisp mathematical model is developed in Section 4. In Section 5, the corresponding fuzzy mathematical model is solved. A real case study with the numerical result and sensitivity analysis of the proposed problem is given in Section 6. Section 7 contains the graphical illustration of the proposed model. Lastly, an embracing conclusion is given in Section 8.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Authors**} & \multicolumn{2}{c}{**Product**} & \multirow{2}{*}{**Demand**} & \multicolumn{2}{c}{**Matter of**} & \multirow{2}{*}{**Solution Approach**} \\ \cline{2-2} \cline{5-6}  & **Conventional Items** & & & & **Growing Items** \\ \hline [PERSON] [14] & ✓ & & Crisp & Not included & Convex Optimization \\ \hline [PERSON] and [PERSON] [32] & ✓ & & Crisp & Not included & Statistical method \\ \hline [PERSON] [28] & & ✓ & Crisp & Non-specific & Convex Optimization \\ \hline [PERSON] et al. [29] & & ✓ & Crisp & Non-specific & Convex Optimization \\ \hline [PERSON] et al. [27] & & ✓ & Crisp & Poultry & Convex Optimization \\ \hline [PERSON] and & & ✓ & Crisp & Non-specific & Convex Optimization \\ \hline [PERSON] et al. [34] & ✓ & Crisp & Non-specific & Convex Optimization \\ \hline [PERSON] and [PERSON] [35] & ✓ & Crisp & Non-specific & Convex Optimization \\ \hline [PERSON] et al. [36] & ✓ & Crisp & Non-specific & Convex Optimization \\ \hline This Paper & ✓ & \begin{tabular}{c} Fuzzy (PDFS and PDFLS) \\ \end{tabular} & \
\begin{tabular}{c} Fishers \\ \end{tabular} &
\begin{tabular}{c} New solution algorithm \\ via new defuzzification \\ methods \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 1: Literature review of recent major studies of growing items.