In this paper we introduce definitions of generalized neutrosophic sets. After given the fundamental defin itions of generalized neutrosophic set operations, we obtain several properties, and discussed the relationship between generalized neutrosophic sets and others. Finally, we extend the concepts of neutrosophic topological space [9], intuition istic fuzzy topological space [5,6], and fu zzy topological space [4] to the case of generalized neutrosophic sets. Possible applicat ion to GIS topology rules are touched upon.

Purpose of the present research is to detail the importance of using a fuzzy soft-β-open set and study its characteristics and applications. Also, we introduce more basic fuzzy-soft topological concepts, namely, fuzzy soft-β-interior, fuzzy soft-β-closure, operators based on fuzzy soft-β-open set, and also present more of their properties. The connections between them as well as other concepts are listed. This notion is used to introduce a proposed approximation of fuzzy-soft space as per the fuzzy soft-β set as a generalization for the fuzzy-soft approximation space. This research also attempted on revealing that this model presents higher accuracy calculation and is better as compared to all other models. The results are given using the MATLAB program. It occurs in many areas of science and technology.

Introduction: Nephrolithiasis is a common problem worldwide, especially in hot areas like Saudi Arabia. This retrospective study investigated the current prevalence and risk factors of renal stones in Jeddah and Riyadh, Saudi Arabia. Methods: A non-interventional cross-sectional study was conducted from November 2018 to June 2019 at King Abdulaziz University Hospital, Jeddah, Saudi Arabia. This study included 1031 participants (age ≥18 years) from Jeddah (n = 652, 63.30%) and Riyadh (n = 379, 36.80%). Of them, 169 (16.40%) had renal stones while 862 (83.60%) had no renal stones. All participants filled out a questionnaire distributed via social media, which contained questions regarding eating and drinking habits. Results: Significant differences were found between the groups regarding frequencies of intake of black tea and orange/lemon juice. The number of patients who consumed cow meat was significantly higher among those without renal stones than among those with renal stones. Significant high risk for renal stones was found in those who consumed energy drink >1 can/day, black tea >1 cup/day, and orange/lemon juice >1 glass/day. Conclusion: This study revealed that some eating habits play a major role in the development of urinary stones in the Saudi population. Therefore, a dietary intervention on a large scale and health, education in this regard may be helpful in preventing the 25 related to renal stones.

Real-world applications are now dealing with a huge amount of data, especially in the area of high-dimensional features. Trait reduction is one of the major steps in decision making problems. It refers to the determination of a minimum subset of attributes which preserves the final decision based on the entire set of attributes. Unfortunately, most of the current features are irrelevant or redundant, which makes these systems unreliable and imprecise. This paper proposes a new paradigm based on fuzzy soft relationship and level fuzzy soft relationship, called Union -Intersection decision making method. Using these new principles, the decision-making strategy is structured to choose a fuzzy set of optimal elements from the alternatives on the basis of a fuzzy soft set. Finally, we used our proposed method in medical application to make the decision to diagnose COVID-19. Moreover, we used MATLAB programming to obtain the results; this has coincided with the announcement by the World Health Organization and an accurate proposal was examined, which competes with that of the method of Zhao.

Real-world applications now deal with enormous amounts of data, especially in the area of high dimensional features. In the present study, we provide an approach for the rough set which is simply* alpha open set (briefly, S MÃ Àa open set). This approach was used to introduce a new concept of separation axioms, from which fundamental properties and theorems of preservation were studied. The relationship between basic properties and preservation theorems was also discussed. New near continuous function definitions have also been developed and their characteristics have been discussed. Through an application presented in the work, the relationship between the simply* alpha open set and near continuous function was justified. The simply* alpha open set was studied by the rough set and accordingly new accuracies were obtained. Moreover, an accurate proposal was examined, which competes with that of the methods of Yao and Pawlak. To obtain the results, MATLAB software has been used.