AbstractIn this paper, we give some approximation properties by Stancu–Chlodowsky type λ-Bernstein operators in the polynomial weighted space and obtain the convergence properties of these operators by using Korovkin’s theorem. We also establish the direct result and the Voronovskaja type asymptotic formula.

Consumption of renewable energy is on the rise because new technologies have made it cheaper and easier to meet the needs of a long-term energy source. In the present study, the idea of optimal usage of sustainable energy is discussed, taking into consideration the environmental and economic conditions that exist in Pakistan’s textile manufacturing industry. By taking into account the regional potential for the application of renewable energy resources, solar energy generators are taken into consideration, and a fully intuitionistic fuzzy (FIF) textile energy model is constructed. Using the FIF model to determine the optimal distribution of solar energy units resulted in a tolerable number of unused energy units. These units may be returned to the central power supply station, which would save both money and energy.

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Fuzzy mathematics-informed methods are beneficial in cases when observations display uncertainty and volatility since it is of vital importance to make predictions about the future considering the stages of interpreting, planning, and strategy building. It is possible to realize this aim through accurate, reliable, and realistic data and information analysis, emerging from past to present time. The principal expenditures are treated as fuzzy numbers in this article, which includes a blurry categorial prototype with pattern-diverse stipulation and collapse with salvation worth. Multiple parameters such as a shortage, ordering, and degrading cost are not fixed in nature due to uncertainty in the marketplace. Obtaining an accurate estimate of such expenditures is challenging. Accordingly, in this research, we develop an adaptive and integrative economic order quantity model with a fuzzy method and present an appropriate structure to manage such uncertain parameters, boosting the inventory system’s exactness, and computing efficiency. The major goal of the study was to assess a set of changes to the company current inventory processes that allowed an achievement in its inventory costs optimization and system development in optimizing inventory costs for better control and monitoring. The approach of graded mean integration is used to determine the most efficient actual solution. The evidence-based model is illustrated with the help of appropriate numerical and sensitivity analysis through the related visual graphical depictions. The proposed method in our study aims at investigating the economic order quantity (EOQ), as the optimal order quantity, which is significant in inventory management to minimize the total costs related to ordering, receiving, and holding inventory in the dynamic domains with nonlinear features of the complex dynamic and nonlinear systems as well as structures.

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