European Journal of Pure and Applied Mathematics, Oct 29, 2023
In this paper, we introduce collection of intuitionistic fuzzy sets as a developing and expanding... more In this paper, we introduce collection of intuitionistic fuzzy sets as a developing and expanding intuitionistic fuzzy theory. A collection of intuitionistic fuzzy sets is a set whose members of the universe set are intuitionistic fuzzy sets. We present intersection and union operation in the collection of of intuitionistic fuzzy sets and show that the operations hold commutative, assosiative, idempotent, and De Morgan's laws properties.
Let H= (T,S), be a finite simple graph, T(H)= T and S(H)= S, respectively, are the sets of vertic... more Let H= (T,S), be a finite simple graph, T(H)= T and S(H)= S, respectively, are the sets of vertices and edges on H. Let :T∪S→1,2,• • • ,k, be a total k-labeling on H and w (x), be a weight of x∈T while using labeling, which is evaluated based on the total number of all vertices labels in the neighborhood x and its incident edges. If every x∈T has a different weight, then is a distance vertex irregular total k-labeling (DVITL). Total distance vertex irregularity strength of H (tdis(H) is defined as the least k for which H has a DVITL. Our research investigates the DVITL of the path (P r) and cycle (C r) graphs. We establish a lower bound and then calculate the precise value of tdis(P r) and tdis(C r).
Developing environmentally friendly transportation that is affordable, secure, and simple to use ... more Developing environmentally friendly transportation that is affordable, secure, and simple to use is what is meant by sustainable transportation development. One of the best strategies to reduce the usage of private vehicles is to restructure the routes of public transportation. In order to reduce the uncertainty that might be present in the data, the problem of finding the transit route was solved using an intuitionistic fuzzy technique with interval values. The decision maker can develop a transportation route that reduces the number of private automobiles on the road in order to get to sustainable transportation as soon as possible by using intuitionistic fuzzy optimization. A straightforward case study produced a number of ideal routes to the nearby public facilities.
EJGTA : Electronic Journal of Graph Theory and Applications, Apr 8, 2023
A distance vertex irregular total k-labeling of a simple undirected graph G = G(V, E), is a funct... more A distance vertex irregular total k-labeling of a simple undirected graph G = G(V, E), is a function f : V (G) ∪ E(G) −→ {1, 2,. .. , k} such that for every pair vertices u, v ∈ V (G) and u ̸ = v, the weights of u and v are distinct. The weight of vertex v ∈ V (G) is defined to be the sum of the label of vertices in neighborhood of v and the label of all incident edges to v. The total distance vertex irregularity strength of G (denoted by tdis(G)) is the minimum of k for which G has a distance vertex irregular total k-labeling. In this paper, we present several results of the total distance vertex irregularity strength of some corona product graphs.
Intuitionistic Q-fuzzy set is one of the results of the development of the concept of fuzzy sets ... more Intuitionistic Q-fuzzy set is one of the results of the development of the concept of fuzzy sets by entering the degree of membership and nonmembership. In this paper, we would like to discuss the process of forming Cartesian product from intuitionistic Q-fuzzy ideal on ordered semigroup. Some of the properties of the Cartesian product are created and proven.
In this article, we present the structure of η-intuitionistic fuzzy ring. An η-intuitionistic fuz... more In this article, we present the structure of η-intuitionistic fuzzy ring. An η-intuitionistic fuzzy ring is a structure which is built with combinating the definition of fuzzy ring, intuitionistic fuzzy set, and η-intuitionistic fuzzy set. The η-intuitionistic fuzzy set is characterized by any value η∈[0,1], where the degree of membership μ_(A^η ) (k) is obtained based on the averaging operator of the degree of membership μ_A (k) and the value of η∈[0,1]. While the degree of non membership ν_(A^η ) (k) is obtained based on the averaging operator of the degree of non membership ν_A (k) and the value of 1-η∈[0,1]. In its development, new concepts were obtained, namely the η-intuitionistic fuzzy ideal and its properties related to the sum and product operation of η-intuitionistic fuzzy ideals. Furthermore, the η-intuitionistic fuzzy ideals concept can be developed into an η-intuitionistic fuzzy quotient ring, η-intuitionistic fuzzy homomorphism, and its properties on the next research.
HIV/AIDS disease continues to spread alarmingly despite the huge amounts of resources invested in... more HIV/AIDS disease continues to spread alarmingly despite the huge amounts of resources invested in fighting it. There is a need to integrate the series of control measures available to ensure a consistent reduction in the incidence of the disease pending the discovery of its cure. We present a deterministic model for controlling the spread of the disease using change in sexual habits and antiretroviral (ARV) therapy as control measures. We formulate a fixed time optimal control problem subject to the model dynamics with the goal of finding the optimal combination of the two control measures that will minimize the cost of the control efforts as well as the incidence of the disease. We estimate the model state initial conditions and parameter values from the demographic and HIV/AIDS data of South Africa. We use Pontryagin's maximum principle to derive the optimality system and solve the system numerically. Compared with the practice in most resource-limited settings where ARV treatment is given only to patients with fullblown AIDS, our simulation results suggest that starting the treatment as soon as the patients progress to the pre-AIDS stage of the disease coupled with appreciable change in the susceptible individuals' sexual habits reduces both the incidence and prevalence of the disease faster. In fact, the results predict that the implementation of the proposed strategy would drive new cases of the disease towards eradication in 10 years.
A deterministic mathematical model with public health education campaigns and antiretroviral ther... more A deterministic mathematical model with public health education campaigns and antiretroviral therapy as control variables are formulated and analyzed using sensitivity analysis and optimal control theory (Pontryagin's Maximum Principle). The sensitivity analysis shows that by increasing the public health education campaign for susceptible individuals and providing antiretroviral therapy to infected individuals in the symptomatic stage has an effect in reducing the spread of the HIV infection. The most sensitive parameter is the efficacy rate of the public health education campaign, followed by the contact rate of susceptibles with an infective in the asymptomatic stage, followed by the progression rate from the infected class into the pre-AIDS class. The least sensitive parameter is the natural death rate. The numerical simulation of both systems, i.e. with control and without control shows that the combination of the two strategies helps to make a significant reduction in the number of infectives in the asymptomatic stage, the number of individuals in the pre-AIDS stage, and the number of individuals with full-blown AIDS.
A modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and Mic... more A modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and Michaelis-Menten type prey harvesting is studied. The equilibrium points of the system are investigated. To see the stability of each equilibrium point, we perform some numerical simulations. Our numerical simulations show that the extinction of prey or survival of both prey and predator are conditionally stable.
The journal of experimental life science, Feb 27, 2018
In this paper, a fractional-order predator-prey model with prey refuge and additional food for pr... more In this paper, a fractional-order predator-prey model with prey refuge and additional food for predator is solved numerically. For that aim, the model is discretized using a piecewise constant arguments. The equilibrium points of the discrete fractional-order model are investigated. Numerical simulations are conducted to see the stability of each equilibrium point. The numerical simulations show that stability of the equilibrium points is dependent on the time step.
This paper presents an application of optimal control theory to assess the effectiveness of contr... more This paper presents an application of optimal control theory to assess the effectiveness of control measures on the spread of HIV in a population. This paper formulates and analyzes a deterministic mathematical model with use of condom, screening and therapy as control variables using optimal control theory and Pontryagin's Maximum Principle. It formulates the appropriate optimal control problem and investigate the necessary conditions for the disease control in order to determine the role of unaware infectives in the spread of HIV using of condom, screening of unaware infective and antiretroviral therapy are used as the control items. The optimality system is derived and solved numerically.
The number of claims plays an important role the profit achievement of health insurance companies... more The number of claims plays an important role the profit achievement of health insurance companies. Prediction of the number of claims could give the significant implications in the profit margins generated by the health insurance company. Therefore, the prediction of claim submission by insurance users in that year needs to be done by insurance companies. Machine learning methods promise the great solution for claim prediction of the health insurance users. There are several machine learning methods that can be used for claim prediction, such as the Naïve Bayes method, Decision Tree (DT), Artificial Neural Networks (ANN) and Support Vector Machine (SVM). The previous studies show that the SVM has some advantages over the other methods. However, the performance of the SVM is determined by some parameters. Parameter selection of SVM is normally done by trial and error so that the performance is less than optimal. Some optimization algorithms based heuristic optimization can be used to...
Graph theory is a branch of algebra that is growing rapidly both in concept and application studi... more Graph theory is a branch of algebra that is growing rapidly both in concept and application studies. This graph application can be used in chemistry, transportation, cryptographic problems, coding theory, design communication network, etc. There is currently a bridge between graphs and algebra, especially an algebraic structures, namely theory of graph algebra. One of researchs on graph algebra is a graph that formed by prime ring elements or called prime graph over ring R. The prime graph over commutative ring R (PG(R))) is a graph construction with set of vertices V(PG(R))=R and two vertices x and y are adjacent if satisfy xRy={0}, for x≠y. Girth is the shortest cycle length contains in PG(R) or can be written gr(PG(R)). Order in PG(R) denoted by |V(PG(R))| and size in PG(R) denoted by |E(PG(R))|. In this paper, we discussed prime graph over cartesian product over rings Z_m×Z_n and its complement. We focused only for m=p_1, n=p_2 and m=p_1, n=〖p_2〗^2, where p_1 and p_2 are prime n...
Let G be a finite, simple, and undirected graph with vertex set V G and edge set E G . A super ed... more Let G be a finite, simple, and undirected graph with vertex set V G and edge set E G . A super edge-magic labeling of G is a bijection f : V G ∪ E G ⟶ 1,2 , … , V G + E G such that f V G = 1,2 , … , V G and f u + f u v + f v is a constant for every edge u v ∈ E G . The super edge-magic labeling f of G is called consecutively super edge-magic if G is a bipartite graph with partite sets A and B such that f A = 1,2 , … , A and f B = A + 1 , A + 2 , … , V G . A graph that admits (consecutively) super edge-magic labeling is called a (consecutively) super edge-magic graph. The super edge-magic deficiency of G , denoted by μ s G , is either the minimum nonnegative integer n such that G ∪ n K 1 is super edge-magic or + ∞ if there exists no such n . The consecutively super edge-magic deficiency of a graph G is defined by a similar way. In this paper, we investigate the (consecutively) super edge-magic deficiency of subdivision of double stars. We show that, some of them have zero (consecutiv...
PROCEEDINGS OF THE 8TH SEAMS-UGM INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations, 2019
Let G = (V, E) be a finite and simple graph with vertex set V (G) and edge set E(G), having o rde... more Let G = (V, E) be a finite and simple graph with vertex set V (G) and edge set E(G), having o rder p and size q. A graph G is called super edge-magic if there exists a bijection f : V(G) ∪ E(G) −→ {1, 2, • • • , p + q} such that f (V(G)) = {1, 2, • • • , p} and f (u) + f (uv) + f (v) = k, for every edge uv ∈ E(G). The super edge-magic deficiency of a graph G, denoted by μ s (G), is either the minimum nonnegative integer n such that G ∪ nK 1 is super edge-magic or +∞ if there exists no such n. In this paper, we study the super edge-magic deficiency of forests where its components are subdivided stars or paths.
The purpose of this paper is to introduce one of the most important element closely connected wit... more The purpose of this paper is to introduce one of the most important element closely connected with the classical linear group namely projective special linear groups SL 2(K)/Z of degree 2 over a field K, where Z is the center of the special linear group SL 2(K) consists of all scalar matrices whose determinants 1. This element called projective transvection which is an element of the projective special linear group PSL 2(K) that is, a coset gZ where g is some element in SL 2(K). In the present study, we will extend our conception about the projective transvection, so we can say this element is generating set of PSL 2(K). For that reason, we need todescribe this element for obtaining more conception about PSL 2(K) especially to describe subgroups of PSL 2(K) that have been generated by projective transvection.
European Journal of Pure and Applied Mathematics, Oct 29, 2023
In this paper, we introduce collection of intuitionistic fuzzy sets as a developing and expanding... more In this paper, we introduce collection of intuitionistic fuzzy sets as a developing and expanding intuitionistic fuzzy theory. A collection of intuitionistic fuzzy sets is a set whose members of the universe set are intuitionistic fuzzy sets. We present intersection and union operation in the collection of of intuitionistic fuzzy sets and show that the operations hold commutative, assosiative, idempotent, and De Morgan's laws properties.
Let H= (T,S), be a finite simple graph, T(H)= T and S(H)= S, respectively, are the sets of vertic... more Let H= (T,S), be a finite simple graph, T(H)= T and S(H)= S, respectively, are the sets of vertices and edges on H. Let :T∪S→1,2,• • • ,k, be a total k-labeling on H and w (x), be a weight of x∈T while using labeling, which is evaluated based on the total number of all vertices labels in the neighborhood x and its incident edges. If every x∈T has a different weight, then is a distance vertex irregular total k-labeling (DVITL). Total distance vertex irregularity strength of H (tdis(H) is defined as the least k for which H has a DVITL. Our research investigates the DVITL of the path (P r) and cycle (C r) graphs. We establish a lower bound and then calculate the precise value of tdis(P r) and tdis(C r).
Developing environmentally friendly transportation that is affordable, secure, and simple to use ... more Developing environmentally friendly transportation that is affordable, secure, and simple to use is what is meant by sustainable transportation development. One of the best strategies to reduce the usage of private vehicles is to restructure the routes of public transportation. In order to reduce the uncertainty that might be present in the data, the problem of finding the transit route was solved using an intuitionistic fuzzy technique with interval values. The decision maker can develop a transportation route that reduces the number of private automobiles on the road in order to get to sustainable transportation as soon as possible by using intuitionistic fuzzy optimization. A straightforward case study produced a number of ideal routes to the nearby public facilities.
EJGTA : Electronic Journal of Graph Theory and Applications, Apr 8, 2023
A distance vertex irregular total k-labeling of a simple undirected graph G = G(V, E), is a funct... more A distance vertex irregular total k-labeling of a simple undirected graph G = G(V, E), is a function f : V (G) ∪ E(G) −→ {1, 2,. .. , k} such that for every pair vertices u, v ∈ V (G) and u ̸ = v, the weights of u and v are distinct. The weight of vertex v ∈ V (G) is defined to be the sum of the label of vertices in neighborhood of v and the label of all incident edges to v. The total distance vertex irregularity strength of G (denoted by tdis(G)) is the minimum of k for which G has a distance vertex irregular total k-labeling. In this paper, we present several results of the total distance vertex irregularity strength of some corona product graphs.
Intuitionistic Q-fuzzy set is one of the results of the development of the concept of fuzzy sets ... more Intuitionistic Q-fuzzy set is one of the results of the development of the concept of fuzzy sets by entering the degree of membership and nonmembership. In this paper, we would like to discuss the process of forming Cartesian product from intuitionistic Q-fuzzy ideal on ordered semigroup. Some of the properties of the Cartesian product are created and proven.
In this article, we present the structure of η-intuitionistic fuzzy ring. An η-intuitionistic fuz... more In this article, we present the structure of η-intuitionistic fuzzy ring. An η-intuitionistic fuzzy ring is a structure which is built with combinating the definition of fuzzy ring, intuitionistic fuzzy set, and η-intuitionistic fuzzy set. The η-intuitionistic fuzzy set is characterized by any value η∈[0,1], where the degree of membership μ_(A^η ) (k) is obtained based on the averaging operator of the degree of membership μ_A (k) and the value of η∈[0,1]. While the degree of non membership ν_(A^η ) (k) is obtained based on the averaging operator of the degree of non membership ν_A (k) and the value of 1-η∈[0,1]. In its development, new concepts were obtained, namely the η-intuitionistic fuzzy ideal and its properties related to the sum and product operation of η-intuitionistic fuzzy ideals. Furthermore, the η-intuitionistic fuzzy ideals concept can be developed into an η-intuitionistic fuzzy quotient ring, η-intuitionistic fuzzy homomorphism, and its properties on the next research.
HIV/AIDS disease continues to spread alarmingly despite the huge amounts of resources invested in... more HIV/AIDS disease continues to spread alarmingly despite the huge amounts of resources invested in fighting it. There is a need to integrate the series of control measures available to ensure a consistent reduction in the incidence of the disease pending the discovery of its cure. We present a deterministic model for controlling the spread of the disease using change in sexual habits and antiretroviral (ARV) therapy as control measures. We formulate a fixed time optimal control problem subject to the model dynamics with the goal of finding the optimal combination of the two control measures that will minimize the cost of the control efforts as well as the incidence of the disease. We estimate the model state initial conditions and parameter values from the demographic and HIV/AIDS data of South Africa. We use Pontryagin's maximum principle to derive the optimality system and solve the system numerically. Compared with the practice in most resource-limited settings where ARV treatment is given only to patients with fullblown AIDS, our simulation results suggest that starting the treatment as soon as the patients progress to the pre-AIDS stage of the disease coupled with appreciable change in the susceptible individuals' sexual habits reduces both the incidence and prevalence of the disease faster. In fact, the results predict that the implementation of the proposed strategy would drive new cases of the disease towards eradication in 10 years.
A deterministic mathematical model with public health education campaigns and antiretroviral ther... more A deterministic mathematical model with public health education campaigns and antiretroviral therapy as control variables are formulated and analyzed using sensitivity analysis and optimal control theory (Pontryagin's Maximum Principle). The sensitivity analysis shows that by increasing the public health education campaign for susceptible individuals and providing antiretroviral therapy to infected individuals in the symptomatic stage has an effect in reducing the spread of the HIV infection. The most sensitive parameter is the efficacy rate of the public health education campaign, followed by the contact rate of susceptibles with an infective in the asymptomatic stage, followed by the progression rate from the infected class into the pre-AIDS class. The least sensitive parameter is the natural death rate. The numerical simulation of both systems, i.e. with control and without control shows that the combination of the two strategies helps to make a significant reduction in the number of infectives in the asymptomatic stage, the number of individuals in the pre-AIDS stage, and the number of individuals with full-blown AIDS.
A modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and Mic... more A modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and Michaelis-Menten type prey harvesting is studied. The equilibrium points of the system are investigated. To see the stability of each equilibrium point, we perform some numerical simulations. Our numerical simulations show that the extinction of prey or survival of both prey and predator are conditionally stable.
The journal of experimental life science, Feb 27, 2018
In this paper, a fractional-order predator-prey model with prey refuge and additional food for pr... more In this paper, a fractional-order predator-prey model with prey refuge and additional food for predator is solved numerically. For that aim, the model is discretized using a piecewise constant arguments. The equilibrium points of the discrete fractional-order model are investigated. Numerical simulations are conducted to see the stability of each equilibrium point. The numerical simulations show that stability of the equilibrium points is dependent on the time step.
This paper presents an application of optimal control theory to assess the effectiveness of contr... more This paper presents an application of optimal control theory to assess the effectiveness of control measures on the spread of HIV in a population. This paper formulates and analyzes a deterministic mathematical model with use of condom, screening and therapy as control variables using optimal control theory and Pontryagin's Maximum Principle. It formulates the appropriate optimal control problem and investigate the necessary conditions for the disease control in order to determine the role of unaware infectives in the spread of HIV using of condom, screening of unaware infective and antiretroviral therapy are used as the control items. The optimality system is derived and solved numerically.
The number of claims plays an important role the profit achievement of health insurance companies... more The number of claims plays an important role the profit achievement of health insurance companies. Prediction of the number of claims could give the significant implications in the profit margins generated by the health insurance company. Therefore, the prediction of claim submission by insurance users in that year needs to be done by insurance companies. Machine learning methods promise the great solution for claim prediction of the health insurance users. There are several machine learning methods that can be used for claim prediction, such as the Naïve Bayes method, Decision Tree (DT), Artificial Neural Networks (ANN) and Support Vector Machine (SVM). The previous studies show that the SVM has some advantages over the other methods. However, the performance of the SVM is determined by some parameters. Parameter selection of SVM is normally done by trial and error so that the performance is less than optimal. Some optimization algorithms based heuristic optimization can be used to...
Graph theory is a branch of algebra that is growing rapidly both in concept and application studi... more Graph theory is a branch of algebra that is growing rapidly both in concept and application studies. This graph application can be used in chemistry, transportation, cryptographic problems, coding theory, design communication network, etc. There is currently a bridge between graphs and algebra, especially an algebraic structures, namely theory of graph algebra. One of researchs on graph algebra is a graph that formed by prime ring elements or called prime graph over ring R. The prime graph over commutative ring R (PG(R))) is a graph construction with set of vertices V(PG(R))=R and two vertices x and y are adjacent if satisfy xRy={0}, for x≠y. Girth is the shortest cycle length contains in PG(R) or can be written gr(PG(R)). Order in PG(R) denoted by |V(PG(R))| and size in PG(R) denoted by |E(PG(R))|. In this paper, we discussed prime graph over cartesian product over rings Z_m×Z_n and its complement. We focused only for m=p_1, n=p_2 and m=p_1, n=〖p_2〗^2, where p_1 and p_2 are prime n...
Let G be a finite, simple, and undirected graph with vertex set V G and edge set E G . A super ed... more Let G be a finite, simple, and undirected graph with vertex set V G and edge set E G . A super edge-magic labeling of G is a bijection f : V G ∪ E G ⟶ 1,2 , … , V G + E G such that f V G = 1,2 , … , V G and f u + f u v + f v is a constant for every edge u v ∈ E G . The super edge-magic labeling f of G is called consecutively super edge-magic if G is a bipartite graph with partite sets A and B such that f A = 1,2 , … , A and f B = A + 1 , A + 2 , … , V G . A graph that admits (consecutively) super edge-magic labeling is called a (consecutively) super edge-magic graph. The super edge-magic deficiency of G , denoted by μ s G , is either the minimum nonnegative integer n such that G ∪ n K 1 is super edge-magic or + ∞ if there exists no such n . The consecutively super edge-magic deficiency of a graph G is defined by a similar way. In this paper, we investigate the (consecutively) super edge-magic deficiency of subdivision of double stars. We show that, some of them have zero (consecutiv...
PROCEEDINGS OF THE 8TH SEAMS-UGM INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations, 2019
Let G = (V, E) be a finite and simple graph with vertex set V (G) and edge set E(G), having o rde... more Let G = (V, E) be a finite and simple graph with vertex set V (G) and edge set E(G), having o rder p and size q. A graph G is called super edge-magic if there exists a bijection f : V(G) ∪ E(G) −→ {1, 2, • • • , p + q} such that f (V(G)) = {1, 2, • • • , p} and f (u) + f (uv) + f (v) = k, for every edge uv ∈ E(G). The super edge-magic deficiency of a graph G, denoted by μ s (G), is either the minimum nonnegative integer n such that G ∪ nK 1 is super edge-magic or +∞ if there exists no such n. In this paper, we study the super edge-magic deficiency of forests where its components are subdivided stars or paths.
The purpose of this paper is to introduce one of the most important element closely connected wit... more The purpose of this paper is to introduce one of the most important element closely connected with the classical linear group namely projective special linear groups SL 2(K)/Z of degree 2 over a field K, where Z is the center of the special linear group SL 2(K) consists of all scalar matrices whose determinants 1. This element called projective transvection which is an element of the projective special linear group PSL 2(K) that is, a coset gZ where g is some element in SL 2(K). In the present study, we will extend our conception about the projective transvection, so we can say this element is generating set of PSL 2(K). For that reason, we need todescribe this element for obtaining more conception about PSL 2(K) especially to describe subgroups of PSL 2(K) that have been generated by projective transvection.
Uploads
Papers by Noor Hidayat