Graph theory has put forward a mathematical foundation for modelling and fine tuning communication and transportation networks. Centers and path centers serve as effective tools for optimizing traffic flow and efficiently allocating resources. The present article examines the concepts of eccentricity, center and path center of a fuzzy graph based on & micro;-distance. The major contribution of this article is an algorithm to find the path center and center of trees in fuzzy context. Many characteristics of center and path center of fuzzy graphs are explored and illustrated. Furthermore, eccentricities of adjacent nodes in a fuzzy graph and eccentricities of end nodes of effective arcs and strongly & micro;-related nodes are investigated.
The work is devoted to the control of the technological process of obtaining polypropylene by alkalizing, washing and drying the propane propylene fraction (PPF). As a scientific innovation in the presented work, the following should be noted: 1) For the first time, a dynamic expert system has been created for the technological process of obtaining polypropylene by the above-mentioned method; 2) A dynamic database has been developed that provides storage and use of fractographic data used in the management of the technological process of obtaining polypropylene; 3) Appropriate instrumentation have been selected and their activities in the system have been provided for the full automatic implementation of the processes of production, primary processing and maintenance of the regime parameters of the technological process; 4) Algorithms for the initial processing of setting values of parameters for the management of the technological process have been developed; a complex of relevant programs for questioning and processing of transmitters has been created. To ensure the security of the database developed by me in SQL Server, it is first necessary to create users and assign them appropriate access privileges, including management, data editing, device addition, and other related operation.
The main purpose of this article is to introduce the notion of d(v)-point in a vector metric space which is a generalization of the notion of d-point in metric spaces and extend Weston's characterization of metric completeness to vector metric spaces in terms of d(v)-point. In fact, we have utilized the concepts of lower semicontinuity and uniform continuity in this new framework to establish the main result. Finally, we established relations among minimal points, d(v)-points and fixed points in this new setting. As an application of this study, we obtained the analogue of Banach Contraction Principle in vector metric spaces.
Explained variation measures are very popular in regression models. They explain the amount of variation in the dependent variable by the explanatory variables. In some situations, a small sample size is available in comparison to the number of explanatory variables. In this case, explained variation measures may become significantly inflated. In order to tackle this problem, adjusted explained variation measures are used. In this work, we propose adjusted explained variation measures depend on the deviance for zero-inflated Poisson regression model (ZIPRM). We compare the performance of the suggested measures with that of the unadjusted explained variation measures for the ZIPRM using a Monte Carlo simulation experiment and real datasets.
In this paper, we introduce the concept of fuzzy general disjointness property along with its notation. Our results indicate that a fuzzy section semi-complemented lattice possesses the fuzzy atomic covering property if it meets the criteria for the fuzzy atomic disjointness property. Furthermore, we establish that if a fuzzy section semicomplemented lattice satisfies the fuzzy disjointness property, then it is both fuzzy 1modular and a fuzzy Birkhoff lattice.
