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Rakesh Bajaj

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Papers by Rakesh Bajaj

Modified EDAS method for MCDM in robotic agrifarming with picture fuzzy soft Dombi aggregation operators

Soft Computing

On Cohesive Fuzzy Sets, Operations and Properties with Applications in Electromagnetic Signals and Solar Activities

Symmetry

In the present communication, a new concept of a cohesive fuzzy set (CHFS) has been proposed as a... more In the present communication, a new concept of a cohesive fuzzy set (CHFS) has been proposed as a synchronized generalization of complex fuzzy sets and hesitant fuzzy sets in a systematic way. The novelty of the introduced notion lies in the selection of the best alternative among the available multiple favorable situations, where the possibility of its range is in the extended unit circle of the complex plane. We study the relationship between the CHFS and the complex intuitionistic fuzzy set (CIFS), along with validation of the obtained results. On the basis of the proposed notion, various properties, operations, and identities have been established with their necessary proof. The applications of CHFS in the process of filtering the signals for obtaining the reference signal using the necessary Fourier cosine transform or inverse Fourier cosine transform and identifying the maximum number of sunspots in a particular interval of solar activity have been suitably discussed with illu...

On Renewable Energy Source Selection Methodologies Utilizing Picture Fuzzy Hypersoft Information with Choice and Value Matrices

Scientia Iranica

In a decision-making problem, the uncertainty component of refusal and abstain along with the sub... more In a decision-making problem, the uncertainty component of refusal and abstain along with the sub-parametrization features in the information are not catered by intuitionistic fuzzy/Pythagorean fuzzy sets. In the present communication, we first introduce the novel notion of picture fuzzy hypersoft matrix along with various important binary operations and properties. The inclusion of the novel notion of picture fuzzy hypersoft matrices allows the decision makers to define their preference in a more general sub-parameterized linguistic form for the evaluation of available alternatives. The proposition concentrates on presenting a robust decision-making framework for identifying the optimal and most suitable renewable energy source. In this regard, the revised definition of picture fuzzy hypersoft choice matrix/weighted choice matrix (PFHSCM/PFHSWCM), value matrix, and total score matrix have been presented. Further, two algorithms of decision-making for the selection of the best renewable energy sources have been provided along with appropriate illustrations and ranking descriptions.

On Exponential Interval Valued Intuitionistic Fuzzy Entropy of Order a and type ß and its Applications in Decision Making

International Journal of Computer Applications, 2014

On Some Reliability Properties of Mean Inactivity Time under Weighing

International Journal of Computer Applications, 2011

In the present communication, we discuss some reliability properties of mean inactivity time orde... more In the present communication, we discuss some reliability properties of mean inactivity time order and study the preservation of mean inactivity time under some weight function. Weighted Distribution methods arise in the context of research related to reliability, data gathering, ecology, inference, modeling, bio-medicine and several other areas. In general, weighted distributions have wide role for the analysis of life time data.

Reliability Properties of Series and Parallel Systems from Bivariate Exponential Models

Communications in Statistics - Theory and Methods, 2002

... Manuel Franco a * &amp; Juana María Vivo b pages 2349-2360. ... These concepts of reliabi... more

T-spherical Fuzzy Soft Matrices with Applications in Decision-Making and Selection Process

In the present communication, we have introduced the notion of T -spherical fuzzy soft matrix (TS... more In the present communication, we have introduced the notion of T -spherical fuzzy soft matrix (TSFSM) and studied various types of associated binary operations and properties. In literature, it has been observed that the concept of soft matrix plays a vital role in many engineering applications as well as to cater different socio-economic and financial sector problems. As per the definition of T -spherical fuzzy set, the proposed notion would have an additional capability to address the impreciseness of the information close enough to human opinion mathematically. Further, on the basis of the structure of proposed TSFSM and using the concept of choice matrix along with its weighted form, a new algorithm for the decision-making process has been outlined. Next, utilizing the score/utility matrix, we present another algorithm for the selection process. For the sake of understanding of the proposed methodologies, illustrative examples have also been presented. Some comparative remarks f...

Complex Neutrosophic Matrix with Some Algebraic Operations and Matrix Norm Convergence

In this article, a new concept of the Complex Neutrosophic Matrix is introduced to solve differen... more In this article, a new concept of the Complex Neutrosophic Matrix is introduced to solve different problems related to uncertainties. Based on the proposed matrix, we have provided various algebraic operations like addition, subtraction, union many others which will be of great help in estabalishing the fundamental concepts. The results obtained through the above operations will be consequently utilized in solving the higher-dimensional problems due to their matrix properties. This novel concept lays the foundation of various research solutions in the field of the complex neutrosophic matrix, which are yet to be considered by researchers.The matrix norm convergence of the proposed matrix has also beenstudied for the necessary foundation of the complex neutrosophic matrix. Also, the future studies of the proposed concept have been proposed.

Mechanical response of nets of graphical objects

Stochastic Comparisons of Heterogeneous Samples with Homogeneous Exponential Samples

World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 2012

In the present communication, stochastic comparison of a series (parallel) system having heteroge... more In the present communication, stochastic comparison of a series (parallel) system having heterogeneous components with random lifetimes and series (parallel) system having homogeneous exponential components with random lifetimes has been studied. Further, conditions under which such a comparison is possible has been established. Keywords—Exponential distribution, Order statistics, Star ordering, Stochastic ordering.

Study of Output Convergence Pattern of BRIC Economies: Application of Fuzzy Mathematics

The IUP Journal of Applied Economics, 2009

: The present paper tests the projected convergence pattern of per capita GDP of Brazil, Russia, ... more

On Laplacian energy of picture fuzzy graphs in site selection problem

J. Intell. Fuzzy Syst., 2021

In the present work, the adjacency matrix, the energy and the Laplacian energy for a picture fuzz... more In the present work, the adjacency matrix, the energy and the Laplacian energy for a picture fuzzy graph/directed graph have been introduced along with their lower and the upper bounds. Further, in the selection problem of decision making, a methodology for the ranking of the available alternatives has been presented by utilizing the picture fuzzy graph and its energy/Laplacian energy. For the shake of demonstrating the implementation of the introduced methodology, the task of site selection for the hydropower plant has been carried out as an application. The originality of the introduced approach, comparative remarks, advantageous features and limitations have also been studied in contrast with intuitionistic fuzzy and Pythagorean fuzzy information.

On Measures of Similarity for Neutrosophic Sets with Applications in Classification and Evaluation Processes

In the last decades, different researchers have considerably incorporated the notion of neutrosop... more In the last decades, different researchers have considerably incorporated the notion of neutrosophic sets, their properties and different measures for managing the uncertainty, impreciseness and vagueness in the information. It may be noted that neutrosophic set is a popular defined procedures for solving the classification problem and evaluation problem of decisionmaking. Numerical examples for the classification problem and the decision-making problem have also been presented and compared the obtained results with the well established existing approaches.

Reliability Analysis of k-out-of-n : G System Using Triangular Intuitionistic Fuzzy Numbers

World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 2014

In the present paper, we analyze the vague reliability of k-out-of-n : G system (particularly, se... more In the present paper, we analyze the vague reliability of k-out-of-n : G system (particularly, series and parallel system) with independent and non-identically distributed components, where the reliability of the components are unknown. The reliability of each component has been estimated using statistical confidence interval approach. Then we converted these statistical confidence interval into triangular intuitionistic fuzzy numbers. Based on these triangular intuitionistic fuzzy numbers, the reliability of the k-out-of-n : G system has been calculated. Further, in order to implement the proposed methodology and to analyze the results of k-out-of-n : G system, a numerical example has been provided. Keywords—Vague set, vague reliability, triangular intuitionistic fuzzy number, k-out-of-n : G system, series and parallel system.

On Solution of Interval Valued Intuitionistic Fuzzy Assignment Problem Using Similarity Measure and Score Function

The primary objective of the paper is to propose a new method for solving assignment problem unde... more The primary objective of the paper is to propose a new method for solving assignment problem under uncertain situation. In the classical assignment problem (AP), zpqdenotes the cost for assigning the qth job to the pth person which is deterministic in nature. Here in some uncertain situation, we have assigned a cost in the form of composite relative degree Fpq instead of pq z and this replaced cost is in the maximization form. In this paper, it has been solved and validated by the two proposed algorithms, a new mathematical formulation of IVIF assignment problem has been presented where the cost has been considered to be an IVIFN and the membership of elements in the set can be explained by positive and negative evidences. To determine the composite relative degree of similarity of IVIFS the concept of similarity measure and the score function is used for validating the solution which is obtained by Composite relative similarity degree method. Further, hypothetical numeric illusion ...

On Parametric Divergence Measure of Neutrosophic Sets with its Application in Decision-making Models

In various decision-making models the divergence measure is found to be a useful information meas... more In various decision-making models the divergence measure is found to be a useful information measure in handling impreciseness and uncertainty among the qualitative and quantitative factors of the decision-making process. In the proposed work, a novel parametric divergence measure for neutrosophic sets has been proposed along with its various properties. On the basis of the proposed parametric divergence measure, we have outlined some methodologies along with its implementing procedural steps for classification problem (pattern recognition problem, medical diagnosis problem) and multi criteria decision making problem. Also, numerical examples for the application problems have been provided for illustration of the proposed methodologies. Comparative remarks along with necessary observations and advantages have also been presented in view of the existing appraoches.

Implementation of Intuitionistic Fuzzy Approach in Maximizing Net Present Value

The applicability of Net Present Value (NPV) in an investment project is becoming more and more p... more The applicability of Net Present Value (NPV) in an investment project is becoming more and more popular in the field of engineering economics. The classical NPV methodology involves only the precise and accurate data of the investment project. In the present communication, we give a new mathematical model for NPV which uses the concept of intuitionistic fuzzy set theory. The proposed model is based on triangular intuitionistic fuzzy number, which may be known as Intuitionistic Fuzzy Net Present Value (IFNPV). The model has been applied to an example and the results are presented. Keywords—Net Present Value, Intuitionistic Fuzzy Set, Investment Projects.

Technique for Reducing Dimensionality of Data in Decision-Making Utilizing Neutrosophic Soft Matrices

The decision-making problems in which there are large numbers of qualitative and quantitative fac... more The decision-making problems in which there are large numbers of qualitative and quantitative factors involved, the technique of dimensionality reduction plays an important role for simplicity and wider applicability. The impreciseness in the information about these factors are being considered in the neutrosophic perception with the parameters degree of truth-membership, degree of indeterminacy (neutral) and degree of falsity for a better span of the information. In the present communication, we first propose a technique for finding the threshold value for the information provided in the form of neutrosophic soft matrix. Further, utilizing the proposed definitions of the object-oriented neutrosophic soft matrix and the parameter-oriented neutrosophic soft matrix, we present a new algorithm for the dimensionality reduction process. The proposed algorithm has also been applied in an illustrative example of decision-making problem. Further, a comparative analysis in contrast with the ...

Synthesis and characterization of some transition metal picrate complexes with isonicotinic acid hydrazide

On Some New Statistical Correlation Measures for T -spherical Fuzzy Sets and Applications in Soft Computing

Modified EDAS method for MCDM in robotic agrifarming with picture fuzzy soft Dombi aggregation operators

Soft Computing

On Cohesive Fuzzy Sets, Operations and Properties with Applications in Electromagnetic Signals and Solar Activities

Symmetry

In the present communication, a new concept of a cohesive fuzzy set (CHFS) has been proposed as a... more In the present communication, a new concept of a cohesive fuzzy set (CHFS) has been proposed as a synchronized generalization of complex fuzzy sets and hesitant fuzzy sets in a systematic way. The novelty of the introduced notion lies in the selection of the best alternative among the available multiple favorable situations, where the possibility of its range is in the extended unit circle of the complex plane. We study the relationship between the CHFS and the complex intuitionistic fuzzy set (CIFS), along with validation of the obtained results. On the basis of the proposed notion, various properties, operations, and identities have been established with their necessary proof. The applications of CHFS in the process of filtering the signals for obtaining the reference signal using the necessary Fourier cosine transform or inverse Fourier cosine transform and identifying the maximum number of sunspots in a particular interval of solar activity have been suitably discussed with illu...

On Renewable Energy Source Selection Methodologies Utilizing Picture Fuzzy Hypersoft Information with Choice and Value Matrices

Scientia Iranica

In a decision-making problem, the uncertainty component of refusal and abstain along with the sub... more In a decision-making problem, the uncertainty component of refusal and abstain along with the sub-parametrization features in the information are not catered by intuitionistic fuzzy/Pythagorean fuzzy sets. In the present communication, we first introduce the novel notion of picture fuzzy hypersoft matrix along with various important binary operations and properties. The inclusion of the novel notion of picture fuzzy hypersoft matrices allows the decision makers to define their preference in a more general sub-parameterized linguistic form for the evaluation of available alternatives. The proposition concentrates on presenting a robust decision-making framework for identifying the optimal and most suitable renewable energy source. In this regard, the revised definition of picture fuzzy hypersoft choice matrix/weighted choice matrix (PFHSCM/PFHSWCM), value matrix, and total score matrix have been presented. Further, two algorithms of decision-making for the selection of the best renewable energy sources have been provided along with appropriate illustrations and ranking descriptions.

On Exponential Interval Valued Intuitionistic Fuzzy Entropy of Order a and type ß and its Applications in Decision Making

International Journal of Computer Applications, 2014

On Some Reliability Properties of Mean Inactivity Time under Weighing

International Journal of Computer Applications, 2011

In the present communication, we discuss some reliability properties of mean inactivity time orde... more In the present communication, we discuss some reliability properties of mean inactivity time order and study the preservation of mean inactivity time under some weight function. Weighted Distribution methods arise in the context of research related to reliability, data gathering, ecology, inference, modeling, bio-medicine and several other areas. In general, weighted distributions have wide role for the analysis of life time data.

Reliability Properties of Series and Parallel Systems from Bivariate Exponential Models

Communications in Statistics - Theory and Methods, 2002

... Manuel Franco a * &amp; Juana María Vivo b pages 2349-2360. ... These concepts of reliabi... more

T-spherical Fuzzy Soft Matrices with Applications in Decision-Making and Selection Process

In the present communication, we have introduced the notion of T -spherical fuzzy soft matrix (TS... more In the present communication, we have introduced the notion of T -spherical fuzzy soft matrix (TSFSM) and studied various types of associated binary operations and properties. In literature, it has been observed that the concept of soft matrix plays a vital role in many engineering applications as well as to cater different socio-economic and financial sector problems. As per the definition of T -spherical fuzzy set, the proposed notion would have an additional capability to address the impreciseness of the information close enough to human opinion mathematically. Further, on the basis of the structure of proposed TSFSM and using the concept of choice matrix along with its weighted form, a new algorithm for the decision-making process has been outlined. Next, utilizing the score/utility matrix, we present another algorithm for the selection process. For the sake of understanding of the proposed methodologies, illustrative examples have also been presented. Some comparative remarks f...

Complex Neutrosophic Matrix with Some Algebraic Operations and Matrix Norm Convergence

In this article, a new concept of the Complex Neutrosophic Matrix is introduced to solve differen... more In this article, a new concept of the Complex Neutrosophic Matrix is introduced to solve different problems related to uncertainties. Based on the proposed matrix, we have provided various algebraic operations like addition, subtraction, union many others which will be of great help in estabalishing the fundamental concepts. The results obtained through the above operations will be consequently utilized in solving the higher-dimensional problems due to their matrix properties. This novel concept lays the foundation of various research solutions in the field of the complex neutrosophic matrix, which are yet to be considered by researchers.The matrix norm convergence of the proposed matrix has also beenstudied for the necessary foundation of the complex neutrosophic matrix. Also, the future studies of the proposed concept have been proposed.

Mechanical response of nets of graphical objects

Stochastic Comparisons of Heterogeneous Samples with Homogeneous Exponential Samples

World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 2012

In the present communication, stochastic comparison of a series (parallel) system having heteroge... more In the present communication, stochastic comparison of a series (parallel) system having heterogeneous components with random lifetimes and series (parallel) system having homogeneous exponential components with random lifetimes has been studied. Further, conditions under which such a comparison is possible has been established. Keywords—Exponential distribution, Order statistics, Star ordering, Stochastic ordering.

Study of Output Convergence Pattern of BRIC Economies: Application of Fuzzy Mathematics

The IUP Journal of Applied Economics, 2009

: The present paper tests the projected convergence pattern of per capita GDP of Brazil, Russia, ... more

On Laplacian energy of picture fuzzy graphs in site selection problem

J. Intell. Fuzzy Syst., 2021

In the present work, the adjacency matrix, the energy and the Laplacian energy for a picture fuzz... more In the present work, the adjacency matrix, the energy and the Laplacian energy for a picture fuzzy graph/directed graph have been introduced along with their lower and the upper bounds. Further, in the selection problem of decision making, a methodology for the ranking of the available alternatives has been presented by utilizing the picture fuzzy graph and its energy/Laplacian energy. For the shake of demonstrating the implementation of the introduced methodology, the task of site selection for the hydropower plant has been carried out as an application. The originality of the introduced approach, comparative remarks, advantageous features and limitations have also been studied in contrast with intuitionistic fuzzy and Pythagorean fuzzy information.

On Measures of Similarity for Neutrosophic Sets with Applications in Classification and Evaluation Processes

In the last decades, different researchers have considerably incorporated the notion of neutrosop... more In the last decades, different researchers have considerably incorporated the notion of neutrosophic sets, their properties and different measures for managing the uncertainty, impreciseness and vagueness in the information. It may be noted that neutrosophic set is a popular defined procedures for solving the classification problem and evaluation problem of decisionmaking. Numerical examples for the classification problem and the decision-making problem have also been presented and compared the obtained results with the well established existing approaches.

Reliability Analysis of k-out-of-n : G System Using Triangular Intuitionistic Fuzzy Numbers

World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 2014

In the present paper, we analyze the vague reliability of k-out-of-n : G system (particularly, se... more In the present paper, we analyze the vague reliability of k-out-of-n : G system (particularly, series and parallel system) with independent and non-identically distributed components, where the reliability of the components are unknown. The reliability of each component has been estimated using statistical confidence interval approach. Then we converted these statistical confidence interval into triangular intuitionistic fuzzy numbers. Based on these triangular intuitionistic fuzzy numbers, the reliability of the k-out-of-n : G system has been calculated. Further, in order to implement the proposed methodology and to analyze the results of k-out-of-n : G system, a numerical example has been provided. Keywords—Vague set, vague reliability, triangular intuitionistic fuzzy number, k-out-of-n : G system, series and parallel system.

On Solution of Interval Valued Intuitionistic Fuzzy Assignment Problem Using Similarity Measure and Score Function

The primary objective of the paper is to propose a new method for solving assignment problem unde... more The primary objective of the paper is to propose a new method for solving assignment problem under uncertain situation. In the classical assignment problem (AP), zpqdenotes the cost for assigning the qth job to the pth person which is deterministic in nature. Here in some uncertain situation, we have assigned a cost in the form of composite relative degree Fpq instead of pq z and this replaced cost is in the maximization form. In this paper, it has been solved and validated by the two proposed algorithms, a new mathematical formulation of IVIF assignment problem has been presented where the cost has been considered to be an IVIFN and the membership of elements in the set can be explained by positive and negative evidences. To determine the composite relative degree of similarity of IVIFS the concept of similarity measure and the score function is used for validating the solution which is obtained by Composite relative similarity degree method. Further, hypothetical numeric illusion ...

On Parametric Divergence Measure of Neutrosophic Sets with its Application in Decision-making Models

In various decision-making models the divergence measure is found to be a useful information meas... more In various decision-making models the divergence measure is found to be a useful information measure in handling impreciseness and uncertainty among the qualitative and quantitative factors of the decision-making process. In the proposed work, a novel parametric divergence measure for neutrosophic sets has been proposed along with its various properties. On the basis of the proposed parametric divergence measure, we have outlined some methodologies along with its implementing procedural steps for classification problem (pattern recognition problem, medical diagnosis problem) and multi criteria decision making problem. Also, numerical examples for the application problems have been provided for illustration of the proposed methodologies. Comparative remarks along with necessary observations and advantages have also been presented in view of the existing appraoches.

Implementation of Intuitionistic Fuzzy Approach in Maximizing Net Present Value

The applicability of Net Present Value (NPV) in an investment project is becoming more and more p... more The applicability of Net Present Value (NPV) in an investment project is becoming more and more popular in the field of engineering economics. The classical NPV methodology involves only the precise and accurate data of the investment project. In the present communication, we give a new mathematical model for NPV which uses the concept of intuitionistic fuzzy set theory. The proposed model is based on triangular intuitionistic fuzzy number, which may be known as Intuitionistic Fuzzy Net Present Value (IFNPV). The model has been applied to an example and the results are presented. Keywords—Net Present Value, Intuitionistic Fuzzy Set, Investment Projects.

Technique for Reducing Dimensionality of Data in Decision-Making Utilizing Neutrosophic Soft Matrices

The decision-making problems in which there are large numbers of qualitative and quantitative fac... more The decision-making problems in which there are large numbers of qualitative and quantitative factors involved, the technique of dimensionality reduction plays an important role for simplicity and wider applicability. The impreciseness in the information about these factors are being considered in the neutrosophic perception with the parameters degree of truth-membership, degree of indeterminacy (neutral) and degree of falsity for a better span of the information. In the present communication, we first propose a technique for finding the threshold value for the information provided in the form of neutrosophic soft matrix. Further, utilizing the proposed definitions of the object-oriented neutrosophic soft matrix and the parameter-oriented neutrosophic soft matrix, we present a new algorithm for the dimensionality reduction process. The proposed algorithm has also been applied in an illustrative example of decision-making problem. Further, a comparative analysis in contrast with the ...

Synthesis and characterization of some transition metal picrate complexes with isonicotinic acid hydrazide

On Some New Statistical Correlation Measures for T -spherical Fuzzy Sets and Applications in Soft Computing