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This paper aims to design an inventory model for a retail enterprise with a profit maximization objective using the opportunity for a price discount facility given by a supplier. In the profit maximization objective, the demand should be increased. The demand can be boosted by lowering the selling price. However, lowering the selling price may not always give the best profit. Impreciseness plays a vital role during such decision-making. The decision-making and managerial activities may be imprecise due to some decision variables. For instance, the selling price may not be deterministic. A vague selling price will make the retail decision imprecise. To achieve this goal, the retailer must minimize impreciseness as much as possible. Learning through repetition may be a practical approach in this regard. This paper investigates the impact of fuzzy impreciseness and triangular dense fuzzy setting, which dilutes the impreciseness involved with managerial decisions. Based on the mentioned objectives, this article considers an inventory model with price-dependent demand and time and a purchasing cost-dependent holding cost in an uncertain phenomenon. This paper incorporates the all-units discount policy into the unit purchase cost according to the order quantity. In this paper, the sense of learning is accounted for using a dense fuzzy set by considering the unit selling price as a triangular dense fuzzy number to lessen the impreciseness in the model. Four fuzzy optimization methods are used to obtain the usual extreme profit when searching for the optimal purchasing cost and sale price. It is perceived from the numerical outcomes that a dense fuzzy environment contributes the best results compared to a crisp and general fuzzy environment. Managerial insights from this paper are that learning from repeated dealing activities contributes to enhancing profitability by diluting impreciseness about the selling price and demand rate and taking the best opportunity from the discount facility while purchasing.

Multi-criteria decision-making (MCDM) is now frequently utilized to solve difficulties in everyday life. It is challenging to rank possibilities from a set of options since this process depends on so many conflicting criteria. The current study focuses on recognizing symptoms of illness and then using an MCDM diagnosis to determine the potential disease. The following symptoms are considered in this study: fever, body aches, fatigue, chills, shortness of breath (SOB), nausea, vomiting, and diarrhea. This study shows how the generalised dual hesitant hexagonal fuzzy number (GDHHχFN) is used to diagnose disease. We also introduce a new de-fuzzification method for GDHHχFN. To diagnose a given condition, GDHHχFN coupled with MCDM tools, such as the fuzzy criteria importance through inter-criteria correlation (FCRITIC) method, is used for finding the weight of criteria. Furthermore, the fuzzy weighted aggregated sum product assessment (FWASPAS) method and a fuzzy combined compromise solution (FCoCoSo) are used to rank the alternatives. The alternative diseases are chosen to be malaria, influenza, typhoid, dengue, monkeypox, ebola, and pneumonia. A sensitivity analysis is carried out on three patients affected by different diseases to assess the validity and reliability of our methodologies.