Breast cancer is one of the common malignancies among females in Saudi Arabia and has also been ranked as the one most prevalent and the number two killer disease in the country. However, the clinical diagnosis process of any disease such as breast cancer, coronary artery diseases, diabetes, COVID-19, among others, is often associated with uncertainty due to the complexity and fuzziness of the process. In this work, a fuzzy neural network expert system with an improved gini index random forest-based feature importance measure algorithm for early diagnosis of breast cancer in Saudi Arabia was proposed to address the uncertainty and ambiguity associated with the diagnosis of breast cancer and also the heavier burden on the overlay of the network nodes of the fuzzy neural network system that often happens due to insignificant features that are used to predict or diagnose the disease. An Improved Gini Index Random Forest-Based Feature Importance Measure Algorithm was used to select the five fittest features of the diagnostic wisconsin breast cancer database out of the 32 features of the dataset. The logistic regression, support vector machine, k-nearest neighbor, random forest, and gaussian naïve bayes learning algorithms were used to develop two sets of classification models. Hence, the classification models with full features (32) and models with the 5 fittest features. The two sets of classification models were evaluated, and the results of the evaluation were compared. The result of the comparison shows that the models with the selected fittest features outperformed their counterparts with full features in terms of accuracy, sensitivity, and sensitivity. Therefore, a fuzzy neural network based expert system was developed with the five selected fittest features and the system achieved 99.33% accuracy, 99.41% sensitivity, and 99.24% specificity. Moreover, based on the comparison of the system developed in this work against the previous works that used fuzzy neural network or other applied artificial intelligence techniques on the same dataset for diagnosis of breast cancer using the same dataset, the system stands to be the best in terms of accuracy, sensitivity, and specificity, respectively. The z test was also conducted, and the test result shows that there is significant accuracy achieved by the system for early diagnosis of breast cancer.

We developed an economic order quantity (EOQ) model with a learning effect and carbon emissions under inflationary conditions and inspection for retailers where the items deteriorate naturally. Finally, the total profit of the retailer is maximized with respect to cycle length. A sensitivity analysis was also performed to understand the robustness of the model. In the sensitivity analysis, we discuss the impact of learning rate, inflation rate, and deterioration rate on lot size and length of the cycle, as well as the retailer’s entire profit function. Observations and managerial insights are discussed. The effect of inventory parameters on the total profit is shown in the sensitivity section.

Assuming the significance of sustainability, it is considered necessary to ensure the conservation of our natural resources, in addition to minimizing waste. To promote significant sustainable effects, factors including production, transportation, energy usage, product control management, etc., act as the chief supports of any modern supply chain model. The buyer performs the firsthand inspection and returns any defective items received from the customer to the vendor in a process that is known as first-level inspection. The vendor uses the policy of recovery product management to obtain greater profit. A concluding inspection is accomplished at the vendor’s end in order to distinguish the returned item as belonging to one of four specific categories, namely re-workable, reusable, recyclable, and disposable, a process that is known as second-level inspection. Then, it is observed that some defective items are suitable for a secondary market, while some are reusable, and some can be disassembled to shape new derived products, and leftovers can be scrapped at the disposal cost. This ensures that we can meet our target to promote a cleaner drive with a lower percentage of carbon emissions, reducing the adverse effects of landfills. The activity of both players in this model is presented briefly in the flowchart shown in the Thus, our aim of product restoration is to promote best practices while maintaining economic value, with the ultimate goal of removing the surrounding waste with minimum financial costs. In this regard, it is assumed that the demand rate is precise in nature. The learning effect and fuzzy environment are also considered in the present model. The proposed model studies the impacts of learning and carbon emissions on an integrated green supply chain model for defective items in fuzzy environment and shortage conditions. We optimized the integrated total fuzzy profit with respect to the order quantity and shortages. We described the vendor’s strategy and buyer’s strategy through flowcharts for the proposed integrated supply chain model, and here, in the flowchart, R-R-R stands for re-workable, reusable, and recyclable. The demand rate was treated as a triangular fuzzy number. In this paper, a numerical example, sensitivity analysis, limitations, future scope, and conclusion are presented for the validation of the proposed model.

An imprecise demand rate creates problems in profit optimization in business scenarios. The aim is to nullify the imprecise nature of the demand rate with the help of the cloudy fuzzy method. Traditionally, all items in an ordered lot are presumed to be of good quality. However, the delivered lot may contain some defective items, which may occur during production or maintenance. Inspection of an ordered lot is indispensable in most organizations and can be treated as a type of learning. The learning demonstration, a statistical development expressing declining cost, is necessary to achieve any cyclical process. Further, defective items are sold immediately after the screening process as a single lot at a discounted price, and the fraction of defective items follows an S-shaped learning curve. The trade-credit policy is adequate for suppliers and retailers to maximize their profit during business. In this paper, an inventory model is developed with learning and trade-credit policy under the cloudy fuzzy environment where the demand rate is treated as a cloudy fuzzy number. Finally, the retailer’s total profit is maximized with respect to order quantity. Sensitivity analysis is presented to estimate the robustness of the model.

Background. Increasing divorce rates is a major problem in Saudi society. Divorce has become the primary solution for many couples who are experiencing problems in their relationships, and the language of divorce has become prevalent in both the daily register of Saudi courts on a daily basis and in fictional works. This trend has become a threat to marital life and is particularly damaging for children and young people. There has been previous research on the increase in divorce rates; however, no one addresses this important issue statistically. The specific research question is what are the actual reasons for the increase in divorce rates mentioned in previous studies? Objective. This study contains a statistical analysis of the underlying reasons for rising divorce rates in Saudi society. Methods. An online survey was conducted that gathered quantitative data from 800 participants. The responses of factual relevance were examined via edge plan analysis, regression analysis, and analyses with SPSS software to determine the causes for the rise in divorces in Saudi society. A predesign of edge consisting of six factors and twelve trials is selected. The design is examined in all the data for each row of it and according to the factor or reason chosen, provided that all design items are fulfilled; after that, it is analyzed in two ways. Results. Some examples are presented, so the findings indicated that differences on the couples characters and the length of time the wife spent doing housework and amount of attention to the husband are factors that contributed to divorce. Conclusion. The Saudi Arabian government needs to develop an operational plan to study these causes of divorce and take action. Future studies could analyze the data using supersaturated prototypes, where a large number of variables are studied in just a few simulation trials.

Marketing refers to the strategies a company undertakes to promote its brands to its potential audience. Advertising provides useful venues for marketing to promote a company’s survives/goods to the audience. It has a positive impact on the sale of services or products. In this study, we consider a well‐known online medium called Twitter (the fourth most popular social media platform used by marketers) to check its impact on sales. For this purpose, the simple linear regression modeling approach is implemented to test the significance and usefulness of Twitter advertising on sale. Statistical tests such as t‐test and correlation test are adopted to test the hypothesis of the “impact of Twitter advertising on sales.” Based on the findings of this study, it is observed that Twitter advertising has a positive impact on sales. Furthermore, a new statistical model called the exponential T‐X exponentiated exponential is introduced. The proposed model is very interesting and possesses heavy‐tailed characteristics which are useful in finance and other related sectors. Finally, the applicability of the new model is illustrated by considering the sales data.