Dr. P. Senthil Kumar

@amity.edu

Associate Professor (Mathematics)
Amity School of Engineering and Technology of Amity University, Bengaluru, Karnataka, INDIA.

Dr. P. Senthil Kumar


                                    Download Compact PDF  
https://researchid.co/sensoft
Dr. P. Senthil Kumar is an Associate Professor (Mathematics) at the Amity School of Engineering and Technology of Amity University, Bengaluru, Karnataka, India. His research interests include operations research, fuzzy optimization, intuitionistic fuzzy optimization, numerical analysis, and graph theory. He has published his research papers in referred journal publishers like Springer and Inderscience. He also presented his research in the ELSEVIER conference proceedings. He is the author of the PSK method for solving transportation problems.

EDUCATION

2012 - 2017
PG and Research Department of Mathematics, Ph.D
Jamal Mohamed College, Tiruchirappalli, INDIA.
2011 - 2012
Directorate of Distance Education (Mathematics), PGDAOR
Annamalai University, Annamalai Nagar, INDIA.
2010 - 2011
Centre for Distance Education (Computer Science), PGDCA
Bharathidasan University, Tiruchirappalli, INDIA.
2009 - 2010
PG and Research Department of Mathematics, M.Phil.
Jamal Mohamed College, Tiruchirappalli, INDIA.
2008 - 2009
Mathematics, B.Ed
Tamilnadu Teacher Education University, Chennai, INDIA.
2006 - 2008
PG and Research Department of Mathematics, M.Sc
Jamal Mohamed College, Tiruchirappalli, INDIA.
2003 - 2006
PG and Research Department of Mathematics, B.Sc
Jamal Mohamed College, Tiruchirappalli, INDIA.

RESEARCH, TEACHING, or OTHER INTERESTS

Mathematics, Management Science and Operations Research, Statistics, Probability and Uncertainty, Software
16

Scopus Publications

1502

Scholar Citations

24

Scholar h-index

35

Scholar i10-index

Scopus Publications

  • An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems
    P. Senthil Kumar
    International Journal of System Assurance Engineering and Management, 2024
  • AI-driven decision support system for intuitionistic fuzzy assignment problems
    P. Senthil Kumar
    Using Traditional Design Methods to Enhance AI Driven Decision Making, 2024
    The assignment problem (AP) is a well-known optimization problem that deals with the allocation of 'n' jobs to 'n' machines on a 1-to-1 basis. It minimizes the cost/time or maximizes the profit/production of the problem. Generally, the profit, sale, cost, and time are all called the parameters of the AP (in a traditional AP, out of these parameters, exactly one parameter will be considered a parameter of the problem). These are not at all crisp numbers due to several uncontrollable factors, which are in the form of uncertainty and hesitation. So, to solve the AP in this environment, the author proposes the software and ranking method-based PSK (P. Senthil Kumar) method. Here, plenty of theorems related to intuitionistic fuzzy assignment problems (IFAPs) are proposed and proved by the PSK. To show the superiority of his method, he presents 4 IFAPs. The computer programs for the proposed problems are presented precisely, and the results are verified with Matlab, RGui, etc. In addition, comparative results, discussion, merits and demerits of his method, and future studies are given.
  • The theory and applications of the software-based PSK method for solving intuitionistic fuzzy solid transportation problems
    P. Senthil Kumar
    Perspectives and Considerations on the Evolution of Smart Systems, 2023
    It proposes the PSK (P. Senthil Kumar) method for solving intuitionistic fuzzy solid transportation problems (IFSTPs). In our daily life, uncertainty comes in many ways, e.g., the transportation cost (TC) is not a fixed one, it varies from time to time due to market conditions (i.e., the price of diesel is depending on the cost of crude oil), mode of the transportation, etc. So, to deal with the TP having uncertainty and hesitation in TC, in this chapter, the author divided IFSTP into 4 categories and solved type II- IFSTP by using TIFNs. The model of type II- IFSTP and its relevant CSTP both are presented. The PSK method is presented clearly with the proof of some theorems and corollary. To illustrate the PSK method with proposed models, the numerical experiment and its related graphs are presented. Real-life problems are identified and solved by the PSK method with MATLAB and LINGO software. Analysis, discussion, merits, and demerits of the PSK method are all presented. A valid conclusion and recommendations are given. Finally, some of the future research areas are also suggested.
  • The PSK method: A new and efficient approach to solving fuzzy transportation problems
    P. Senthil Kumar
    Transport and Logistics Planning and Optimization, 2023
    We have several logics to obtain the fuzzy optimal solution for fuzzy transportation problems (FTPs). But there is no logic to solve transportation problem (TP) under four different uncertain environments using a particular method in the literature. So, the author divided the TP under four different environments and formulates the problems and utilizes the fuzzy numbers to solve them. A method, namely PSK (P. Senthil Kumar) method, to find the fuzzy optimal solutions to the FTPs is proposed. Applications of the PSK method compared to other existing methods are demonstrated with four different numerical examples. To illustrate the PSK method, different types of FTPs are solved by using the PSK method with the help of software, for example, Lingo, Matlab, Tora, RGui, and RStudio, and the obtained results are compared, analyzed, and discussed. Conclusions on the study and recommendations for future research are also given.
  • Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set
    P. Senthil Kumar
    International Journal of System Assurance Engineering and Management, 2020
  • Developing a new approach to solve solid assignment problems under intuitionistic fuzzy environment
    P. Senthil Kumar
    International Journal of Fuzzy System Applications, 2020
    When people solve real-life SAP they tend to face the uncertainty state as well as hesitation due to many uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this article, the author tried to categorise the SAP under uncertain environment. He formulates the IFSAP and utilizes the TIFN to deal with uncertainty and hesitation. The SAP has uncertainty and hesitation in cost/time/profit/production is known as FIFSAP. The PSK (P. Senthil Kumar) method for finding an optimal solution for FIFAP is extended to solve the FIFSAP and the optimal objective value of FIFSAP is obtained in terms of TIFN. The main advantage of this method is that the optimal solution/assignment of FIFSAP is obtained without using the Hungarian method and intuitionistic fuzzy reduction method. Moreover, the proposed method is computationally very simple and easy to understand. The numerical example is presented to demonstrate computing procedure. The results affirm efficiency of the proposed method.
  • Intuitionistic fuzzy zero point method for solving type-2 intuitionistic fuzzy transportation problem
    P. Senthil Kumar
    International Journal of Operational Research, 2020
  • Intuitionistic fuzzy solid assignment problems: a software-based approach
    P. Senthil Kumar
    International Journal of System Assurance Engineering and Management, 2019
  • PSK Method for Solving Mixed and Type-4 Intuitionistic Fuzzy Solid Transportation Problems
    P. Senthil Kumar
    International Journal of Operations Research and Information Systems, 2019
    In this article, the author categorises the solid transportation problem (STP) under uncertain environments. He formulates the mixed and fully intuitionistic fuzzy solid transportation problems (FIFSTPs) and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The PSK (P. Senthil Kumar) method for finding an intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem (FIFTP) is extended to solve the mixed and type-4 IFSTP and the optimal objective value of mixed and type-4 IFSTP is obtained in terms of triangular intuitionistic fuzzy number (TIFN). The main advantage of this method is that the optimal solution of mixed and type-4 IFSTP is obtained without using the basic feasible solution and the method of testing optimality. Moreover, the proposed method is computationally very simple and easy to understand. Finally, the procedure for the proposed method is illustrated with the help of numerical examples which is followed by graphical representation of the finding.
  • PSK method for solving intuitionistic fuzzy solid transportation problems
    P.Senthil Kumar
    International Journal of Fuzzy System Applications, 2018
    This article proposes a method for solving intuitionistic fuzzy solid transportation problems (IFSTPs) in which only the transportation costs are represented in terms of intuitionistic fuzzy numbers (IFNs). The remaining parameters, namely: supply, demand and conveyance capacity, are all considered into crisp numbers. This type of STP is called a type-2 IFSTP. When solving the real life solid transportation problems (STPs) those tend to face the uncertainty state as well as hesitation due to many uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this article, the author tried to categorise the STPs under the uncertain environment. He formulates the intuitionistic fuzzy STPs and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The PSK (P.Senthil Kumar) method for finding an intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem (FIFTP) is extended to solve the type-2 IFSTP and the optimal objective value of type-2 IFSTP is obtained in terms of TIFN. The main advantage of this method is that the optimal solution of type-2 IFSTP is obtained without using the basic feasible solution and the method of testing optimality. Moreover, the proposed method is computationally very simple and easy to understand. A case study is presented to illustrate the procedure of the proposed method.
  • A note on ‘a new approach for solving intuitionistic fuzzy transportation problem of type-2’
    P. Senthil Kumar
    International Journal of Logistics Systems and Management, 2018
  • PSK method for solving type-1 and type-3 fuzzy transportation problems
    P. Senthil Kumar
    Fuzzy Systems Concepts Methodologies Tools and Applications, 2017
  • Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems
    P. Senthil Kumar, R. Jahir Hussain
    International Journal of System Assurance Engineering and Management, 2016
  • PSK method for solving type-1 and type-3 fuzzy transportation problems
    P. Senthil Kumar
    International Journal of Fuzzy System Applications, 2016
  • A systematic approach for solving mixed intuitionistic fuzzy transportation problems
    P.S. Kumar, R.J. Hussain
    International Journal of Pure and Applied Mathematics, 2014
  • Algorithmic approach for solving intuitionistic fuzzy transportation problem
    Applied Mathematical Sciences, 2012

RECENT SCHOLAR PUBLICATIONS

  • An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems
    PS Kumar
    International Journal of System Assurance Engineering and Management 15 (9 … , 2024
    2024
    Citations: 18
  • Algorithms and software packages for solving transportation problems with intuitionistic fuzzy numbers
    PS Kumar
    Operational research for renewable energy and sustainable environments, 1-55 , 2024
    2024
    Citations: 20
  • Theory and applications of the software-based PSK method for solving intuitionistic fuzzy solid assignment problems
    PS Kumar
    Applications of New Technology in Operations and Supply Chain Management … , 2024
    2024
    Citations: 10
  • AI-Driven Decision Support System for Intuitionistic Fuzzy Assignment Problems
    PS Kumar
    Using Traditional Design Methods to Enhance AI-Driven Decision Making, 352-398 , 2024
    2024
    Citations: 14
  • The theory and applications of the software-based PSK method for solving intuitionistic fuzzy solid transportation problems
    PS Kumar
    Perspectives and Considerations on the Evolution of Smart Systems, 137-186 , 2023
    2023
    Citations: 19
  • The PSK Method: A New and Efficient Approach to Solving Fuzzy Transportation Problems
    PS Kumar
    Transport and Logistics Planning and Optimization, 149-197 , 2023
    2023
    Citations: 30
  • Computationally simple and efficient method for solving real-life mixed intuitionistic fuzzy 3D assignment problems
    PS Kumar
    International Journal of Software Science and Computational Intelligence … , 2022
    2022
    Citations: 45
  • Finding the solution of balanced and unbalanced intuitionistic fuzzy transportation problems by using different methods with some software packages
    PS Kumar
    Handbook of Research on Applied AI for International Business and Marketing … , 2021
    2021
    Citations: 20
  • Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set
    PS Kumar
    International Journal of System Assurance Engineering and Management 11 (1 … , 2020
    2020
    Citations: 136
  • The PSK method for solving fully intuitionistic fuzzy assignment problems with some software tools
    PS Kumar
    Theoretical and Applied Mathematics in International Business, 149-202 , 2020
    2020
    Citations: 24
  • Intuitionistic fuzzy zero point method for solving type-2 intuitionistic fuzzy transportation problem
    PS Kumar
    International Journal of Operational Research 37 (3), 418-451 , 2020
    2020
    Citations: 77
  • Developing a new approach to solve solid assignment problems under intuitionistic fuzzy environment
    PS Kumar
    International Journal of Fuzzy System Applications (IJFSA) 9 (1), 1-34 , 2020
    2020
    Citations: 51
  • Intuitionistic fuzzy solid assignment problems: a software-based approach
    PS Kumar
    International Journal of System Assurance Engineering and Management 10 (4 … , 2019
    2019
    Citations: 57
  • PSK method for solving mixed and type-4 intuitionistic fuzzy solid transportation problems
    PS Kumar
    International Journal of Operations Research and Information Systems (IJORIS … , 2019
    2019
    Citations: 32
  • PSK method for solving intuitionistic fuzzy solid transportation problems
    PS Kumar
    International Journal of Fuzzy System Applications (IJFSA) 7 (4), 62-99 , 2018
    2018
    Citations: 45
  • Linear programming approach for solving balanced and unbalanced intuitionistic fuzzy transportation problems
    PS Kumar
    International Journal of Operations Research and Information Systems 9 (2 … , 2018
    2018
    Citations: 33
  • Search for an optimal solution to vague traffic problems using the PSK method
    PS Kumar
    Handbook of Research on Investigations in Artificial Life Research and … , 2018
    2018
    Citations: 23
  • A simple and efficient algorithm for solving type-1 intuitionistic fuzzy solid transportation problems
    PS Kumar
    International Journal of Operations Research and Information Systems 9 (3 … , 2018
    2018
    Citations: 24
  • A note on 'a new approach for solving intuitionistic fuzzy transportation problem of type-2'
    PS Kumar
    International Journal of Logistics Systems and Management (IJLSM) 29 (1 … , 2018
    2018
    Citations: 51
  • Book Chapter: PSK method for solving type-1 and type-3 fuzzy transportation problems
    PS Kumar
    Fuzzy Systems: Concepts, Methodologies, Tools, and Applications, 367-392 , 2017
    2017
    Citations: 63

MOST CITED SCHOLAR PUBLICATIONS

  • Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set
    PS Kumar
    International Journal of System Assurance Engineering and Management 11 (1 … , 2020
    2020
    Citations: 136
  • Algorithmic approach for solving intuitionistic fuzzy transportation problem
    RJ Hussain, PS Kumar
    Applied Mathematical Sciences 6 (80), 3981-3989 , 2012
    2012
    Citations: 114
  • Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems
    PS Kumar, RJ Hussain
    International Journal of System Assurance Engineering and Management 7 (1 … , 2016
    2016
    Citations: 97
  • A comparative study on transportation problem in fuzzy environment
    SI Mohideen, PS Kumar
    International Journal of Mathematics Research 2 (1), 151-158 , 2010
    2010
    Citations: 79
  • Intuitionistic fuzzy zero point method for solving type-2 intuitionistic fuzzy transportation problem
    PS Kumar
    International Journal of Operational Research 37 (3), 418-451 , 2020
    2020
    Citations: 77
  • A method for solving unbalanced intuitionistic fuzzy transportation problems
    PS Kumar, RJ Hussain
    Notes on Intuitionistic Fuzzy Sets 21 (3), 54-65 , 2015
    2015
    Citations: 70
  • Book Chapter: PSK method for solving type-1 and type-3 fuzzy transportation problems
    PS Kumar
    Fuzzy Systems: Concepts, Methodologies, Tools, and Applications, 367-392 , 2017
    2017
    Citations: 63
  • PSK method for solving type-1 and type-3 fuzzy transportation problems
    PS Kumar
    International Journal of Fuzzy System Applications 5 (4), 121-146 , 2016
    2016
    Citations: 63
  • A simple method for solving type-2 and type-4 fuzzy transportation problems
    PS Kumar
    International Journal of Fuzzy Logic and Intelligent Systems 16 (4), 225-237 , 2016
    2016
    Citations: 62
  • Intuitionistic fuzzy solid assignment problems: a software-based approach
    PS Kumar
    International Journal of System Assurance Engineering and Management 10 (4 … , 2019
    2019
    Citations: 57
  • Developing a new approach to solve solid assignment problems under intuitionistic fuzzy environment
    PS Kumar
    International Journal of Fuzzy System Applications (IJFSA) 9 (1), 1-34 , 2020
    2020
    Citations: 51
  • A note on 'a new approach for solving intuitionistic fuzzy transportation problem of type-2'
    PS Kumar
    International Journal of Logistics Systems and Management (IJLSM) 29 (1 … , 2018
    2018
    Citations: 51
  • A systematic approach for solving mixed intuitionistic fuzzy transportation problems
    PS Kumar, RJ Hussain
    International Journal of Pure and Applied Mathematics 92 (2), 181-190 , 2014
    2014
    Citations: 47
  • Computationally simple and efficient method for solving real-life mixed intuitionistic fuzzy 3D assignment problems
    PS Kumar
    International Journal of Software Science and Computational Intelligence … , 2022
    2022
    Citations: 45
  • PSK method for solving intuitionistic fuzzy solid transportation problems
    PS Kumar
    International Journal of Fuzzy System Applications (IJFSA) 7 (4), 62-99 , 2018
    2018
    Citations: 45
  • An optimal more-for-less solution of mixed constrains intuitionistic fuzzy transportation problems
    RJ Hussain, PS Kumar
    Int. J. Contemp. Math. Sciences 8 (12), 565-576 , 2013
    2013
    Citations: 43
  • Linear programming approach for solving balanced and unbalanced intuitionistic fuzzy transportation problems
    PS Kumar
    International Journal of Operations Research and Information Systems 9 (2 … , 2018
    2018
    Citations: 33
  • PSK method for solving mixed and type-4 intuitionistic fuzzy solid transportation problems
    PS Kumar
    International Journal of Operations Research and Information Systems (IJORIS … , 2019
    2019
    Citations: 32
  • A method for finding an optimal solution of an assignment problem under mixed intuitionistic fuzzy environment
    PS Kumar, RJ Hussain
    International Conference on Mathematical Sciences (ICMS-2014), 417-421 , 2014
    2014
    Citations: 32
  • A method for solving balanced intuitionistic fuzzy assignment problem
    PS Kumar, RJ Hussain
    International Journal of Engineering Research and Applications 4 (3), 897-903 , 2014
    2014
    Citations: 31