RAJA. NOSHAD JAMIL - Academia.edu (original) (raw)

Papers by RAJA. NOSHAD JAMIL

Research paper thumbnail of Choosing Friends in Everyday Life by using Graph Theory

Journal of Combinatorial Mathematics and Combinatorial Computing, Mar 31, 2024

Research paper thumbnail of Intelligent System for Optimal Geometric Design Using Fuzzy Soft PDE

Mathematical Problems in Engineering, Apr 26, 2023

Research paper thumbnail of A Generalized Fuzzy Soft Set Based Recruiting Method

International Journal of Mathematics Trends and Technology, Sep 25, 2017

Decision making is very important to deal with many complex problems in various sectors involving... more Decision making is very important to deal with many complex problems in various sectors involving imprecise data and uncertainties. Generalized fuzzy soft matrix theory is a powerful tool for decision making. In this paper we defined some new types of generalized fuzzy soft matrices and gave a decision making method based on generalized fuzzy soft matrices.

Research paper thumbnail of New Horizons On Fuzzy Magic Graph

arXiv (Cornell University), Sep 1, 2015

In this paper, we define the concept of fuzzy magic graphs. A fuzzy graph = { , } is said to be a... more In this paper, we define the concept of fuzzy magic graphs. A fuzzy graph = { , } is said to be a fuzzy magic graph if there exist two injective functions : → [0; 1] and ∶ × → [0; 1] such that () < () + () () + () + () = () for all , ∈ (), where () ∈ [0; 1] is a fuzzy magic constant. Moreover, we investigate some families of fuzzy graphs like fuzzy paths, fuzzy stars and fuzzy cycles which are fuzzy magic graphs.

Research paper thumbnail of Analysis of fuzzified boundary value problems for MHD Couette and Poiseuille flow

Scientific Reports, May 19, 2022

In an uncertain atmosphere, the magnetohydrodynamics (MHD) flow in three principal flows of the t... more In an uncertain atmosphere, the magnetohydrodynamics (MHD) flow in three principal flows of the third grade fluid across two parallel plates is presented. Fuzzy differential equations are constructed by manipulating dimensionless differential equations. The prime purpose of the current article is to use a semi-analytical approach fuzzy-based Adomian decomposition method to achieve numerical results for nonlinear FDEs with fuzzy boundary conditions. Triangular fuzzy numbers are used in fuzzy BCs with help of α-cut approach. This strategy is linked to the membership function. In a graphic and tabular depiction, the effect of α and other constraints on fuzzy velocity profiles is explored. The current findings are in good agreement with their previous numerical and analytical results in a crisp environment.

Research paper thumbnail of Fuzzy Analysis for Thin-Film Flow of a Third-Grade Fluid Down an Inclined Plane

Mathematical Problems in Engineering

We examined the thin-film flow problem of a third-grade fluid on an inclined plane under a fuzzy ... more We examined the thin-film flow problem of a third-grade fluid on an inclined plane under a fuzzy environment. The highly nonlinear flow governing differential equations (DEs) with the boundary conditions are fuzzified using the triangular fuzzy numbers (TFNs) developed by α -cut α ∈ 0,1 . The fuzzy perturbation (FPM) method is adopted to calculate the fuzzified form of the governing equations as well as the fuzzified boundary conditions. For the validation, the present work is in good agreement as compared to existing work in the literature under the crisp form. For various values of the fluid parameter λ , inclined parameter γ and fuzzy parameter α -cut is presented in graphical form. The α -cut controls TFNs, and the variability of uncertainty is investigated using a triangular membership function (MF). Using TFNs, the middle (crisp), left, and right values of the fuzzy velocity profile are used for fuzzy linear regression analysis. The outcome of this study and the fuzzy velocity...

Research paper thumbnail of Total Face Irregularity Strength of Type (Alpha, Beta, Gamma) of Grid Graphs

We investigate new graph characteristics namely total (vertex, edge) face irregularity strength o... more We investigate new graph characteristics namely total (vertex, edge) face irregularity strength of gen- eralized plane grid graphs Gmn under k-labeling Phi of type (Alpha, Beta, Gamma). The minimum integer k for which a vertex-edge labelled graph has distinct face weights is called the total face irregularity strength of the graph and is denoted by tfs(Gmn). In this article, the graphs G = (V;E; F) under consideration are simple, finite, undirected and planar. We will estimate the exact tight lower bounds for the total face irregularity strength of some families of generalized plane grid graphs.

Research paper thumbnail of Study of Fuzzified Boundary Value Problems for MHD Couette and Poiseuille Flow of a Differential Type Fluid

In this work, discuss the magneto-hydro-dynamics (MHD) flow in three fundamental flaws of the thi... more In this work, discuss the magneto-hydro-dynamics (MHD) flow in three fundamental flaws of the third-grade fluid between two parallel plates in a fuzzy environment by the fuzzy Adomian decomposition method (ADM). We extend the work of Kamran and Siddique [19], using fuzzy differential equations (FDEs) and explain our approach with the help of membership function of triangular fuzzy numbers (TFNs). In the end, the effect of the fuzzy parameter (\(\alpha \in [0,\,1]\)), and other engineering parameters on fuzzy velocity profiles are investigating in graphically and tabular representation.

Research paper thumbnail of Aggregation operators based on some extension of fuzzy sets

Research paper thumbnail of Impact of generalized polytropic equation of state on charged anisotropic polytropes

The European Physical Journal C, 2020

In this paper, generalized polytropic equation of state is used to get new classes of polytropic ... more In this paper, generalized polytropic equation of state is used to get new classes of polytropic models from the solution of Einstein-Maxwell field equations for charged anisotropic fluid configuration. The models are developed for different values of polytropic index n=1,~\frac{1}{2},~2$$n=1,12,2. Masses and radii of eight different stars have been regained with the help of developed models. The speed of sound technique and graphical analysis of model parameters is used for the viability of developed models. The analysis of models indicates they are well behaved and physically viable.

Research paper thumbnail of New models of charged anisotropic polytropes with radiation density

The European Physical Journal Plus, 2020

In this manuscript, new classes of polytropic models have been developed by using polytropic equa... more In this manuscript, new classes of polytropic models have been developed by using polytropic equation of state (PEoS) for spherically symmetric gravitating sources in isotropic coordinates. The inner fluid configuration is charged anisotropic and models are developed for different values of polytropic index n=1,~\frac{1}{2},~2,~\frac{2}{3}$$n=1,12,2,23. Mass and radii of eight stars 4U 1820-30, Cen X-3, EXO 1785-248, SMC X-4, LMC X-4, SAX J1808.4-3658, 4U 1538-52 and Her X-1 have been regained with the help of developed models. The stability of models is discussed by using speed of sound technique and graphical analysis of model parameters. It is concluded that all models are well behaved and physically acceptable.

Research paper thumbnail of Method of Numerical Simulation of Stable Structures of Fluid Membranes and Vesicles

WSEAS TRANSACTIONS ON …, 2006

In this paper we study a methodology for the numerical simulation of stable structures of fluid m... more In this paper we study a methodology for the numerical simulation of stable structures of fluid membranes and vesicles in biological organisms. In particular, we discuss the effects of spontaneous curvature on vesicle cell membranes under the bending energy for given volume and surface area. The geometric modeling of the vesicle shapes are undertaken by means of surfaces generated as Partial Differential Equations (PDEs). We combine PDE based geometric modeling with numerical optimization in order to study the stable shapes adopted by the vesicle membranes. Thus, through the PDE method we generate a generic template of a vesicle membrane which is then efficiently parameterized. The parameterization is taken as a basis to set up a numerical optimization procedure which enables us to predict a series of vesicle shapes subject to given surface area and volume.

Research paper thumbnail of Study of Third-Grade Fluid under the Fuzzy Environment with Couette and Poiseuille Flows

Mathematical Problems in Engineering

In this work, fundamental flow problems, namely, Couette flow, fully developed plane Poiseuille fl... more In this work, fundamental flow problems, namely, Couette flow, fully developed plane Poiseuille flow, and plane Couette–Poiseuille flow of a third-grade non-Newtonian fluid between two horizontal parallel plates separated by a finite distance in a fuzzy environment are considered. The governing nonlinear differential equations (DEs) are converted into fuzzy differential equations (FDEs) and explain our approach with the help of the membership function (MF) of triangular fuzzy numbers (TFNs). Adomian decomposition method (ADM) is used to solve fundamental flow problems based on FDEs. In a crisp environment, the current findings are in good accord with their previous numerical and analytical results. Finally, the effect of the α -cut α ∈ 0,1 and other engineering constants on fuzzy velocity profile are invested in graphically and tabular forms. Also, the variability of the uncertainty is studied through the triangular MF.

Research paper thumbnail of Diminishing Choquet Hesitant 2-Tuple Linguistic Aggregation Operator for Multiple Attributes Group Decision Making

International Journal of Analysis and Applications

In this article, we develop a diminishing hesitant 2-tuple averaging operator (DH2TA) for hesitan... more In this article, we develop a diminishing hesitant 2-tuple averaging operator (DH2TA) for hesitant 2-tuple linguistic arguments. DH2TA work in the way that it aggregate all hesitant 2-tuple linguistic elements and during the aggregation process it also controls the hesitation in translation of the resultant aggregated linguistic term. We develop a scalar product for hesitant 2-tuple linguistic elements and based on the scalar product a weighted diminishing hesitant 2-tuple averaging operator (DWH2TA) is introduced. Moreover, combining Choquet integral with hesitant 2-tuple linguistic information, the diminishing Chouqet hesitant 2-tuple average operator (DCH2TA) is defined. The proposed operators higher reflect the correlations among the elements. After investigating the properties of these operators, a multiple attribute decision making method based on DCH2TA operator is proposed. Finally, an example is given to illustrate the significance and usefulness of proposed method.

Research paper thumbnail of Total Face Irregularity Strength of Grid and Wheel Graph under K-Labeling of Type (1, 1, 0)

In this study, we used grids and wheel graphs G � (V, E, F), which are simple, finite, plane, and... more In this study, we used grids and wheel graphs G � (V, E, F), which are simple, finite, plane, and undirected graphs with V as the vertex set, E as the edge set, and F as the face set. e article addresses the problem to find the face irregularity strength of some families of generalized plane graphs under k-labeling of type (α, β, c). In this labeling, a graph is assigning positive integers to graph vertices, graph edges, or graph faces. A minimum integer k for which a total label of all verteices and edges of a plane graph has distinct face weights is called k-labeling of a graph. e integer k is named as total face irregularity strength of the graph and denoted as tfs(G). We also discussed a special case of total face irregularity strength of plane graphs under k-labeling of type (1, 1, 0). e results will be verified by using figures and examples.

Research paper thumbnail of Induced hesitant 2-tuple linguistic aggregation operators with application in group decision making 1

In this article, hesitant 2-tuple linguistic arguments are used to evaluate the group decision ma... more In this article, hesitant 2-tuple linguistic arguments are used to evaluate the group decision making problems which have inter dependent or inter active attributes. Operational laws are developed for hesitant 2-tuple linguistic elements and based on these operational laws hesitant 2tuple weighted averaging operator and generalized hesitant 2tuple averaging operator are proposed. Combining Choquet integral with hesitant 2-tuple linguistic information, some new aggregation operators are defined, including the hesitant 2-tuple correlated averaging operator, the hesitant 2-tuple correlated geometric operator and the generalized hesitant 2-tuple correlated averaging operator. These proposed operators successfully manage the correlations among the elements. After investigating the properties of these operators, a multiple attribute decision making method based on these operators, is suggested. Finally, an example is given to illustrate the practicality and feasibility of proposed method.

Research paper thumbnail of Total Face Irregularity Strength of type (α, β, γ) of Grid Graphs

In this article, all graphs G = (V,E, F ) under consideration are simple, finite, plane and undir... more In this article, all graphs G = (V,E, F ) under consideration are simple, finite, plane and undirected. The minimum integer k for which a vertex-edge labelled graph has distinct face weights is called the total face irregularity strength of the graph and is denoted by tfs(Gn ). We will describe new graph characteristics namely total (vertex, edge) face irregularity strength of generalized plane grid graphs Gn under k−labeling of type (α, β, γ) and investigate the exact value for the total face irregularity strength of some families of generalized plane grid graphs. Results are verified by the help of an example.

Research paper thumbnail of Numerical Study of MHD Third-Grade Fluid Flow through an Inclined Channel with Ohmic Heating under Fuzzy Environment

Mathematical Problems in Engineering

The uncertainties or fuzziness occurs due to insufficient knowledge, experimental error, operatin... more The uncertainties or fuzziness occurs due to insufficient knowledge, experimental error, operating conditions, and parameters that give the imprecise information. In this article, we discuss the combined effects of the gravitational and magnetic parameters for both crisp and fuzzy cases in the three basic flow problems (namely, Couette flow, Poiseuille flow, and Couette–Poiseuille flow) of a third-grade fluid over an inclined channel with heat transfer. The dimensionless governing equations with the boundary conditions are converted into coupled fuzzy differential equations (FDEs). The fuzzified forms of the governing equations along with the boundary conditions are solved by employing the numerical technique bvp4c built in MATLAB for both cases, which is very efficient and has a less computational cost. In the first case, proposed problems are analyzed in a crisp environment, while in the second case, they are discussed in a fuzzy environment with the help of α -cut approach, which...

Research paper thumbnail of Total Face Irregularity Strength of Grid and Wheel Graph under K-Labeling of Type (1, 1, 0)

Journal of Mathematics

In this study, we used grids and wheel graphs G = V , E , F , which are simple, finite, plane, an... more In this study, we used grids and wheel graphs G = V , E , F , which are simple, finite, plane, and undirected graphs with V as the vertex set, E as the edge set, and F as the face set. The article addresses the problem to find the face irregularity strength of some families of generalized plane graphs under k -labeling of type α , β , γ . In this labeling, a graph is assigning positive integers to graph vertices, graph edges, or graph faces. A minimum integer k for which a total label of all verteices and edges of a plane graph has distinct face weights is called k -labeling of a graph. The integer k is named as total face irregularity strength of the graph and denoted as tfs G . We also discussed a special case of total face irregularity strength of plane graphs under k -labeling of type (1, 1, 0). The results will be verified by using figures and examples.

Research paper thumbnail of Optimization of Complex Geometry Using Tenth Order Partial Differential Equation

Scientific Inquiry and Review

This paper presents an efficient and intuitive technique of shape parameterization for design opt... more This paper presents an efficient and intuitive technique of shape parameterization for design optimization using a partial differential equation (PDE) of order ten. It shows how the choice of two introduced parameters can enable one to parameterize complex geometries. With the use of PDE based formulation, it is shown in this paper how the shape can be defined and manipulated on the basis of parameterization and the boundary value approaches by which complex shapes can be created. Further the boundary conditions which are used in it are a boundary and an intermediate curves for defining the shape. This technique allows complex shapes to be parameterized intuitively using a very small set of design parameters. Hence, Practical design optimization of problems becomes more achievable by applying PDE based approach of shape parameterization by incorporating standard numerical optimization techniques [1,2].

Research paper thumbnail of Choosing Friends in Everyday Life by using Graph Theory

Journal of Combinatorial Mathematics and Combinatorial Computing, Mar 31, 2024

Research paper thumbnail of Intelligent System for Optimal Geometric Design Using Fuzzy Soft PDE

Mathematical Problems in Engineering, Apr 26, 2023

Research paper thumbnail of A Generalized Fuzzy Soft Set Based Recruiting Method

International Journal of Mathematics Trends and Technology, Sep 25, 2017

Decision making is very important to deal with many complex problems in various sectors involving... more Decision making is very important to deal with many complex problems in various sectors involving imprecise data and uncertainties. Generalized fuzzy soft matrix theory is a powerful tool for decision making. In this paper we defined some new types of generalized fuzzy soft matrices and gave a decision making method based on generalized fuzzy soft matrices.

Research paper thumbnail of New Horizons On Fuzzy Magic Graph

arXiv (Cornell University), Sep 1, 2015

In this paper, we define the concept of fuzzy magic graphs. A fuzzy graph = { , } is said to be a... more In this paper, we define the concept of fuzzy magic graphs. A fuzzy graph = { , } is said to be a fuzzy magic graph if there exist two injective functions : → [0; 1] and ∶ × → [0; 1] such that () < () + () () + () + () = () for all , ∈ (), where () ∈ [0; 1] is a fuzzy magic constant. Moreover, we investigate some families of fuzzy graphs like fuzzy paths, fuzzy stars and fuzzy cycles which are fuzzy magic graphs.

Research paper thumbnail of Analysis of fuzzified boundary value problems for MHD Couette and Poiseuille flow

Scientific Reports, May 19, 2022

In an uncertain atmosphere, the magnetohydrodynamics (MHD) flow in three principal flows of the t... more In an uncertain atmosphere, the magnetohydrodynamics (MHD) flow in three principal flows of the third grade fluid across two parallel plates is presented. Fuzzy differential equations are constructed by manipulating dimensionless differential equations. The prime purpose of the current article is to use a semi-analytical approach fuzzy-based Adomian decomposition method to achieve numerical results for nonlinear FDEs with fuzzy boundary conditions. Triangular fuzzy numbers are used in fuzzy BCs with help of α-cut approach. This strategy is linked to the membership function. In a graphic and tabular depiction, the effect of α and other constraints on fuzzy velocity profiles is explored. The current findings are in good agreement with their previous numerical and analytical results in a crisp environment.

Research paper thumbnail of Fuzzy Analysis for Thin-Film Flow of a Third-Grade Fluid Down an Inclined Plane

Mathematical Problems in Engineering

We examined the thin-film flow problem of a third-grade fluid on an inclined plane under a fuzzy ... more We examined the thin-film flow problem of a third-grade fluid on an inclined plane under a fuzzy environment. The highly nonlinear flow governing differential equations (DEs) with the boundary conditions are fuzzified using the triangular fuzzy numbers (TFNs) developed by α -cut α ∈ 0,1 . The fuzzy perturbation (FPM) method is adopted to calculate the fuzzified form of the governing equations as well as the fuzzified boundary conditions. For the validation, the present work is in good agreement as compared to existing work in the literature under the crisp form. For various values of the fluid parameter λ , inclined parameter γ and fuzzy parameter α -cut is presented in graphical form. The α -cut controls TFNs, and the variability of uncertainty is investigated using a triangular membership function (MF). Using TFNs, the middle (crisp), left, and right values of the fuzzy velocity profile are used for fuzzy linear regression analysis. The outcome of this study and the fuzzy velocity...

Research paper thumbnail of Total Face Irregularity Strength of Type (Alpha, Beta, Gamma) of Grid Graphs

We investigate new graph characteristics namely total (vertex, edge) face irregularity strength o... more We investigate new graph characteristics namely total (vertex, edge) face irregularity strength of gen- eralized plane grid graphs Gmn under k-labeling Phi of type (Alpha, Beta, Gamma). The minimum integer k for which a vertex-edge labelled graph has distinct face weights is called the total face irregularity strength of the graph and is denoted by tfs(Gmn). In this article, the graphs G = (V;E; F) under consideration are simple, finite, undirected and planar. We will estimate the exact tight lower bounds for the total face irregularity strength of some families of generalized plane grid graphs.

Research paper thumbnail of Study of Fuzzified Boundary Value Problems for MHD Couette and Poiseuille Flow of a Differential Type Fluid

In this work, discuss the magneto-hydro-dynamics (MHD) flow in three fundamental flaws of the thi... more In this work, discuss the magneto-hydro-dynamics (MHD) flow in three fundamental flaws of the third-grade fluid between two parallel plates in a fuzzy environment by the fuzzy Adomian decomposition method (ADM). We extend the work of Kamran and Siddique [19], using fuzzy differential equations (FDEs) and explain our approach with the help of membership function of triangular fuzzy numbers (TFNs). In the end, the effect of the fuzzy parameter (\(\alpha \in [0,\,1]\)), and other engineering parameters on fuzzy velocity profiles are investigating in graphically and tabular representation.

Research paper thumbnail of Aggregation operators based on some extension of fuzzy sets

Research paper thumbnail of Impact of generalized polytropic equation of state on charged anisotropic polytropes

The European Physical Journal C, 2020

In this paper, generalized polytropic equation of state is used to get new classes of polytropic ... more In this paper, generalized polytropic equation of state is used to get new classes of polytropic models from the solution of Einstein-Maxwell field equations for charged anisotropic fluid configuration. The models are developed for different values of polytropic index n=1,~\frac{1}{2},~2$$n=1,12,2. Masses and radii of eight different stars have been regained with the help of developed models. The speed of sound technique and graphical analysis of model parameters is used for the viability of developed models. The analysis of models indicates they are well behaved and physically viable.

Research paper thumbnail of New models of charged anisotropic polytropes with radiation density

The European Physical Journal Plus, 2020

In this manuscript, new classes of polytropic models have been developed by using polytropic equa... more In this manuscript, new classes of polytropic models have been developed by using polytropic equation of state (PEoS) for spherically symmetric gravitating sources in isotropic coordinates. The inner fluid configuration is charged anisotropic and models are developed for different values of polytropic index n=1,~\frac{1}{2},~2,~\frac{2}{3}$$n=1,12,2,23. Mass and radii of eight stars 4U 1820-30, Cen X-3, EXO 1785-248, SMC X-4, LMC X-4, SAX J1808.4-3658, 4U 1538-52 and Her X-1 have been regained with the help of developed models. The stability of models is discussed by using speed of sound technique and graphical analysis of model parameters. It is concluded that all models are well behaved and physically acceptable.

Research paper thumbnail of Method of Numerical Simulation of Stable Structures of Fluid Membranes and Vesicles

WSEAS TRANSACTIONS ON …, 2006

In this paper we study a methodology for the numerical simulation of stable structures of fluid m... more In this paper we study a methodology for the numerical simulation of stable structures of fluid membranes and vesicles in biological organisms. In particular, we discuss the effects of spontaneous curvature on vesicle cell membranes under the bending energy for given volume and surface area. The geometric modeling of the vesicle shapes are undertaken by means of surfaces generated as Partial Differential Equations (PDEs). We combine PDE based geometric modeling with numerical optimization in order to study the stable shapes adopted by the vesicle membranes. Thus, through the PDE method we generate a generic template of a vesicle membrane which is then efficiently parameterized. The parameterization is taken as a basis to set up a numerical optimization procedure which enables us to predict a series of vesicle shapes subject to given surface area and volume.

Research paper thumbnail of Study of Third-Grade Fluid under the Fuzzy Environment with Couette and Poiseuille Flows

Mathematical Problems in Engineering

In this work, fundamental flow problems, namely, Couette flow, fully developed plane Poiseuille fl... more In this work, fundamental flow problems, namely, Couette flow, fully developed plane Poiseuille flow, and plane Couette–Poiseuille flow of a third-grade non-Newtonian fluid between two horizontal parallel plates separated by a finite distance in a fuzzy environment are considered. The governing nonlinear differential equations (DEs) are converted into fuzzy differential equations (FDEs) and explain our approach with the help of the membership function (MF) of triangular fuzzy numbers (TFNs). Adomian decomposition method (ADM) is used to solve fundamental flow problems based on FDEs. In a crisp environment, the current findings are in good accord with their previous numerical and analytical results. Finally, the effect of the α -cut α ∈ 0,1 and other engineering constants on fuzzy velocity profile are invested in graphically and tabular forms. Also, the variability of the uncertainty is studied through the triangular MF.

Research paper thumbnail of Diminishing Choquet Hesitant 2-Tuple Linguistic Aggregation Operator for Multiple Attributes Group Decision Making

International Journal of Analysis and Applications

In this article, we develop a diminishing hesitant 2-tuple averaging operator (DH2TA) for hesitan... more In this article, we develop a diminishing hesitant 2-tuple averaging operator (DH2TA) for hesitant 2-tuple linguistic arguments. DH2TA work in the way that it aggregate all hesitant 2-tuple linguistic elements and during the aggregation process it also controls the hesitation in translation of the resultant aggregated linguistic term. We develop a scalar product for hesitant 2-tuple linguistic elements and based on the scalar product a weighted diminishing hesitant 2-tuple averaging operator (DWH2TA) is introduced. Moreover, combining Choquet integral with hesitant 2-tuple linguistic information, the diminishing Chouqet hesitant 2-tuple average operator (DCH2TA) is defined. The proposed operators higher reflect the correlations among the elements. After investigating the properties of these operators, a multiple attribute decision making method based on DCH2TA operator is proposed. Finally, an example is given to illustrate the significance and usefulness of proposed method.

Research paper thumbnail of Total Face Irregularity Strength of Grid and Wheel Graph under K-Labeling of Type (1, 1, 0)

In this study, we used grids and wheel graphs G � (V, E, F), which are simple, finite, plane, and... more In this study, we used grids and wheel graphs G � (V, E, F), which are simple, finite, plane, and undirected graphs with V as the vertex set, E as the edge set, and F as the face set. e article addresses the problem to find the face irregularity strength of some families of generalized plane graphs under k-labeling of type (α, β, c). In this labeling, a graph is assigning positive integers to graph vertices, graph edges, or graph faces. A minimum integer k for which a total label of all verteices and edges of a plane graph has distinct face weights is called k-labeling of a graph. e integer k is named as total face irregularity strength of the graph and denoted as tfs(G). We also discussed a special case of total face irregularity strength of plane graphs under k-labeling of type (1, 1, 0). e results will be verified by using figures and examples.

Research paper thumbnail of Induced hesitant 2-tuple linguistic aggregation operators with application in group decision making 1

In this article, hesitant 2-tuple linguistic arguments are used to evaluate the group decision ma... more In this article, hesitant 2-tuple linguistic arguments are used to evaluate the group decision making problems which have inter dependent or inter active attributes. Operational laws are developed for hesitant 2-tuple linguistic elements and based on these operational laws hesitant 2tuple weighted averaging operator and generalized hesitant 2tuple averaging operator are proposed. Combining Choquet integral with hesitant 2-tuple linguistic information, some new aggregation operators are defined, including the hesitant 2-tuple correlated averaging operator, the hesitant 2-tuple correlated geometric operator and the generalized hesitant 2-tuple correlated averaging operator. These proposed operators successfully manage the correlations among the elements. After investigating the properties of these operators, a multiple attribute decision making method based on these operators, is suggested. Finally, an example is given to illustrate the practicality and feasibility of proposed method.

Research paper thumbnail of Total Face Irregularity Strength of type (α, β, γ) of Grid Graphs

In this article, all graphs G = (V,E, F ) under consideration are simple, finite, plane and undir... more In this article, all graphs G = (V,E, F ) under consideration are simple, finite, plane and undirected. The minimum integer k for which a vertex-edge labelled graph has distinct face weights is called the total face irregularity strength of the graph and is denoted by tfs(Gn ). We will describe new graph characteristics namely total (vertex, edge) face irregularity strength of generalized plane grid graphs Gn under k−labeling of type (α, β, γ) and investigate the exact value for the total face irregularity strength of some families of generalized plane grid graphs. Results are verified by the help of an example.

Research paper thumbnail of Numerical Study of MHD Third-Grade Fluid Flow through an Inclined Channel with Ohmic Heating under Fuzzy Environment

Mathematical Problems in Engineering

The uncertainties or fuzziness occurs due to insufficient knowledge, experimental error, operatin... more The uncertainties or fuzziness occurs due to insufficient knowledge, experimental error, operating conditions, and parameters that give the imprecise information. In this article, we discuss the combined effects of the gravitational and magnetic parameters for both crisp and fuzzy cases in the three basic flow problems (namely, Couette flow, Poiseuille flow, and Couette–Poiseuille flow) of a third-grade fluid over an inclined channel with heat transfer. The dimensionless governing equations with the boundary conditions are converted into coupled fuzzy differential equations (FDEs). The fuzzified forms of the governing equations along with the boundary conditions are solved by employing the numerical technique bvp4c built in MATLAB for both cases, which is very efficient and has a less computational cost. In the first case, proposed problems are analyzed in a crisp environment, while in the second case, they are discussed in a fuzzy environment with the help of α -cut approach, which...

Research paper thumbnail of Total Face Irregularity Strength of Grid and Wheel Graph under K-Labeling of Type (1, 1, 0)

Journal of Mathematics

In this study, we used grids and wheel graphs G = V , E , F , which are simple, finite, plane, an... more In this study, we used grids and wheel graphs G = V , E , F , which are simple, finite, plane, and undirected graphs with V as the vertex set, E as the edge set, and F as the face set. The article addresses the problem to find the face irregularity strength of some families of generalized plane graphs under k -labeling of type α , β , γ . In this labeling, a graph is assigning positive integers to graph vertices, graph edges, or graph faces. A minimum integer k for which a total label of all verteices and edges of a plane graph has distinct face weights is called k -labeling of a graph. The integer k is named as total face irregularity strength of the graph and denoted as tfs G . We also discussed a special case of total face irregularity strength of plane graphs under k -labeling of type (1, 1, 0). The results will be verified by using figures and examples.

Research paper thumbnail of Optimization of Complex Geometry Using Tenth Order Partial Differential Equation

Scientific Inquiry and Review

This paper presents an efficient and intuitive technique of shape parameterization for design opt... more This paper presents an efficient and intuitive technique of shape parameterization for design optimization using a partial differential equation (PDE) of order ten. It shows how the choice of two introduced parameters can enable one to parameterize complex geometries. With the use of PDE based formulation, it is shown in this paper how the shape can be defined and manipulated on the basis of parameterization and the boundary value approaches by which complex shapes can be created. Further the boundary conditions which are used in it are a boundary and an intermediate curves for defining the shape. This technique allows complex shapes to be parameterized intuitively using a very small set of design parameters. Hence, Practical design optimization of problems becomes more achievable by applying PDE based approach of shape parameterization by incorporating standard numerical optimization techniques [1,2].