Department of Mathematics
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Item INNOVATIVE EXPERT SYSTEM FOR CORONARY HEART DISEASE DIAGNOSIS UTILIZING SOFT SETS(IEEE, 2024-10) Jackson, S; Sasikala, D; Deepa, MIn the recent past, there has been a development of a vast array of theories seeking to explain deal with uncertainties. As a branch of artificial intelligence, medical systems supported with mathematical equations have shown great results in disease diagnosis. Soft set theory is a relatively novel field developed by Molodstov that shows a great deal of potential. In this paper, the “Soft Expert System Framework Incorporating Soft Set Theory and Fuzzy Set Theory” is proposed with the aim of providing a new mathematical tool for handling vagueness in diagnosis. We undertook the development of the Soft Expert System (SES) using medical dataset that contains patient records in order to predict coronary artery disease. In this study, the fuzzy set and soft set were utilized to assess the likelihood of the disease based on the variables including age, blood sugar, high density lipoprotein (HDL), low density lipoprotein (LDL), glycated hemoglobin (HbA1C), uric acid, and blood pressure. The methodology includes key procedures: The generic structure includes Data input, Fuzzyfication, Conversion of Fuzzy sets to soft sets, Reduction of parameters in soft sets, Formulation of soft rules and Data output. This system assumes the role of assisting medical practitioners to improve on their diagnostic abilities and will also ensure that the process takes less time as it would in the normal course.Item A NEW PERSPECTIVE OF NEUTROSOPHIC HYPERCONNECTED SPACES(University of New Mexico, 2022) Sasikala, D; Deepa, MThe focus of this article is to introduce a new class of sets namely neutrosophic semi j-open and neu- trosophic semi j-closed sets in neutrosophic topological space. Using this, we present the new spaces neutrosophic hyperconnected and neutrosophic semi j-hyperconnected. Also we explore the characteristics of neutrosophic semi j-open sets, neutrosophic semi j-closed set, neutrosophic hyperconnectedness. Finally we examine the properties of neutrosophic semi j-hyperconnectedness with some existing sets.Item AN ELEMENTARY APPROACH ON HYPERCONNECTED SPACES(Turkish Journal of Computer and Mathematics Education, 2021-04-20) Sasikalaa, D; Deepa, MThis paper aims to establish a new notion of hyperconnected spaces namely semi j hyperconnected spaces by using semi j open sets. The relation between the existing spaces are also discussed. We also investigate some elementary properties of semi j hyperconnected spaces.Item A NOTE ON CONNECTEDNESS IN TOPOLOGICAL SPACES(Advances in Mathematics: Scientific Journal, 2020) Sasikala, D; Deepa, MIn this paper, we introduce two new types of connectedness namely j-connectedness and 1 2 j-connectedness in a topological space. Also, we discuss some of their basic properties and analyze the characterization using theorems.Item CHARACTERIZATION OF J-OPEN SETS IN MINIMAL STRUCTURE SPACES(Malaya Journal of Matematik, 2020-07-04) Deepa, M; Surekha, S SThe aim of this paper is to introduce the notion of m-j open sets in minimal structure spaces together with its corresponding interior and closure operators. Furthermore, we investigated the basic properties of the sets and studied their relationship with other existing sets. Moreover, the minimal structure properties of j-border, j-frontier and j-exterior of the sets have been discussed.Item A STRUCTURE OF OPEN SETS IN QUAD TOPOLOGICAL SPACES(The International journal of analytical and experimental modal analysis, 2019-11) Sasikala, D; Deepa, MThe main aim of this paper is to present a new set, namely quad j-open set in quad topological space. We discuss the basic properties of quad j-open sets using quad j-interior and quad j-closure. In Addition we study the relationships among quad j-closed, quad b- closed and quad j-regular open in quad topological space.Item SOFT ˆ - GENERALIZED CLOSED SETS AND SOFT ˆ - GENERALIZED OPEN SETS IN SOFT TOPOLOGICAL SPACES(International Journal of Innovative Research in Science, Engineering and Technology, 2015-11) Parvathy, C.R; Deepa, MIn this paper a new class of soft sets called Soft- generalized closed sets and Soft ˆ- generalized open sets in Soft Topological spaces are introduced and studied. This new class is defined over an initial universe and with a fixed set of parameters. Some basic properties of this new class of soft sets are investigated. This new class of Soft - generalized closed sets and Softˆ- generalized open sets widening the scope of Soft Topological spaces and its applications.Item VOLUME MINIMIZATION OF A CLOSED COIL HELICAL SPRING USING ALO, GWO, DA, FA, FPA, WOA, CSO. BA, PSO AND GSA(Horizon Research Publishing, 2021-04-18) Rejula Mercy, J; Elizabeth Amudhini Stephen, SSprings are important members often used in machines to exert force, absorb energy and provide flexibility. In mechanical systems, wherever flexibility or relatively a large load under the given circumstances is required, some form of spring is used. In this paper, non-traditional optimization algorithms, namely, Ant Lion Optimizer, Grey Wolf Optimizer, Dragonfly optimization algorithm, Firefly algorithm, Flower Pollination Algorithm, Whale Optimization Algorithm, Cat Swarm Optimization, Bat Algorithm, Particle Swarm Optimization, Gravitational Search Algorithm are proposed to get the global optimal solution for the closed coil helical spring design problem. The problem has three design variables and eight inequality constraints and three bounds. The mathematical formulation of the objective function U is to minimize the volume of closed coil helical spring subject to constraints. The design variables considered are Wire diameter d, Mean coil diameter D, Number of active coils N of the spring. The proposed methods are tested and the performance is evaluated. Ten non-traditional optimization methods are used to find the minimum volume. The problem is computed in the MATLAB environment. The experimental results show that Particle Swarm Optimization outperforms other methods. The results show that PSO gives better results in terms of consistency and minimum value in terms of time and volume of a closed coil helical spring compared to other methods. When compared to other Optimization methods, PSO has few advantages like simplicity and efficiency. In the future, PSO could be extended to solve other mechanical element problems.Item SOLUTION TO A SYSTEM OF NON-LINEAR FUZZY DIFFERENTIAL EQUATION WITH GENERALIZED HUKUHARA DERIVATIVE VIA FIXED POINT THEOREM(DergiPark, 2023) Basil, S; Antony, SIn this manuscript, we define a new class of control functions classified as ascendant functions. Consequently, we investigate a fuzzy coupled fixed point result, that is different from one available in the literature, using the notion of simulation function; we present a non-trivial example to validate the result. As an inference, we use the result to analyze the existence of a solution for a non-linear system of fuzzy initial value problem involving generalized Hukuhara derivative.Item A CONTEMPORARY POSTULATES ON RESOLVABLE SETS AND FUNCTIONS(University of New Mexico, 2023) Deepa, M; Sasikala, D; Said, BIn this article, a new class of sets namely neutrosophic resolvable sets in neutrosophic topological space have been introduced. We present the neutrosophic resolvable functions between neutrosophic topological spaces by neutrosophic resolvables sets. Also we examine the characteristics of neutrosophic resolvable sets and neutrosophic resolvable functions with the existing sets.