Search

Many problems of practical interest can be modeled and solved by using interval-valued fuzzy graph (IVFG) algorithms. An IVFG is a very useful and effective tool for studying various calculations, fields of intelligence, and computer science, such as networking, imaging, and other fields, such as biological sciences. In different applications, they present an appropriate construction means. There were limitations in the definition of fuzzy graphs (FGs), which prompted us to propose a new definition for IVFGs. Some interesting properties related to the new IVFGs are investigated, and enough conditions under which the level graph on IVFGs is equivalent are obtained. Therefore, in this study, we present the properties of a level graph (LG) of an IVFG, and four operations, the Cartesian product (CP), composition (CO), union, and join, are investigated on it. Today, in a treatment system, one of the issues that can be very valuable and important to the quality of service to patients is finding qualified and efficient people in each department, which is not an easy task. But the interval-valued fuzzy graph, as an important fuzzy graph, can help us by considering the ability of each person in the form of intervals of numbers and the effectiveness of each one on the other (according to the relationships between them) in order to find the most worthy people. So, an application of IVFG to find the most effective person in a hospital information system has been introduced. [ABSTRACT FROM AUTHOR]

An important development in geometric algebra in recent years is the new system known as point geometry, which treats points as direct objects of operations and considerably simplifies the process of geometric reasoning. In this paper, we provide a complete formal description of the point geometry theory architecture and give a rigorous and reliable formal verification of the point geometry theory based on the theorem prover Coq. Simultaneously, a series of tactics are also designed to assist in the proof of geometric propositions. Based on the theoretical architecture and proof tactics, a universal and scalable interactive point geometry machine proof system, PointGeo, is built. In this system, any arbitrary point-geometry-solvable geometric statement may be proven, along with readable information about the solution's procedure. Additionally, users may augment the rule base by adding trustworthy rules as needed for certain issues. The implementation of the system expands the library of Coq resources on geometric algebra, which will become a significant research foundation for the fields of geometric algebra, computer science, mathematics education, and other related fields. [ABSTRACT FROM AUTHOR]

Fuzzy graph models enjoy the ubiquity of being in natural and human-made structures, namely dynamic process in physical, biological and social systems. As a result of inconsistent and indeterminate information inherent in real-life problems which are often uncertain, it is highly difficult for an expert to model those problems based on a fuzzy graph (FG). Vague graph structure (VGS) can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problem, where fuzzy graphs may fail to reveal satisfactory results. Likewise, VGSs are very useful tools for the study of different domains of computer science such as networking, capturing the image, clustering, and also other issues like bioscience, medical science, and traffic plan. The limitations of past definitions in fuzzy graphs have led us to present new definitions in VGSs. Operations are conveniently used in many combinatorial applications. In various situations, they present a suitable construction means; therefore, in this research, three new operations on VGSs, namely, maximal product, rejection, residue product were presented, and some results concerning their degrees and total degrees were introduced. Irregularity definitions have been of high significance in the network heterogeneity study, which have implications in networks found across biology, ecology and economy; so special concepts of irregular VGSs with several key properties were explained. Today one of the most important applications of decision making is in medical science for diagnosing the patient's disease. Hence, we recommend an application of VGS in medical diagnosis. [ABSTRACT FROM AUTHOR]