Prof. P. Senthil Kumar, the chapter author of the book, the
Handbook of Research on Applied AI for International Business and Marketing Applications (ISBN: 9781799850779), has received a 20 h-index within 13 years of his research experience in this field because it is a trendy area (
As Jorge E. Hirsch, the creator of the h-index describes it, the index h is “the number of papers with citation number ≥h”). In particular, the author has published many research articles without co-authors. According to Hirsch, a person with 20 years of research experience with an h-index of 20 is considered good, 40 is great, and 60 is remarkable.
Prof. Kumar has introduced a new method, i.e., the PSK method, for solving the transportation problem in uncertain environments and also proved the supporting theorems, especially the PSK theorem. Prof. Krassimir Atanassov (Bulgarian mathematician) introduced intuitionistic fuzzy sets in 1983. Later, he presented ideas for intuitionistic fuzzy equations, inequalities and optimization. It is formulated the problem how to use the apparatus of the intuitionistic fuzzy sets for the needs of optimization. Hence, the author's paper gives a particular answer to this problem.
Today, we are delighted to welcome Prof. P. Senthil Kumar, who will share his valuable insights regarding his chapter, "
Finding the Solution of Balanced and Unbalanced Intuitionistic Fuzzy Transportation Problems by Using Different Methods With Some Software Packages."
Contributing Author Question & Answer
What was the driving force or motivation for starting your project/chapter?
Prof. Kumar: The concept of the intuitionistic fuzzy set was introduced by Atanassov. Burillo and colleagues defined intuitionistic fuzzy numbers. Annie Varghese and Sunny Kuriakose developed a crisp equivalent for each intuitionistic fuzzy number using its membership and non-membership functions. In the fuzzy transportation problem, Pandian and Natarajan proposed the Zero Point method. So, the works of Atanassov (1983), Burillo et al. (1994), Annie Varghese and Sunny Kuriakose (2012) and Pandian et al. (2010) were instrumental for this research work. In general, transport costs are not a fixed real number. It may change due to a variety of reasons, including market conditions and fluctuations in the prices of fuel, diesel, and natural gas. So, in order to deal with transportation issues in an uncertain environment, we need a specific strategy. As a result, the author presented two distinct approaches, method-1 and method-2.
What specific problems does your chapter address?
Prof. Kumar: The chapter discusses two problems: Balanced intuitionistic fuzzy transportation and unbalanced intuitionistic fuzzy transportation. The intuitionistic fuzzy transportation problem is basically a transportation problem in which all or some of the input values are intuitionistic fuzzy values. If the sum of the supply/intuitionistic fuzzy supply is equal to the sum of the demand/ intuitionistic fuzzy demand, then the problem is called the balanced intuitionistic fuzzy transportation problem. Otherwise, it is called an unbalanced intuitionistic fuzzy transportation problem.
For example, PSK Enterprise has 3 factories such as A, B, and C that manufacture the same product of refrigerators in 3 different places Vellore, Nilgiris and Sivagangai respectively. The proprietor would like to transport refrigerators from 3 different factories to 3 different cities/districts namely, Pudukkottai (D), Theni (E) and Salem (F). All the factories are connected to all the districts by roads and the refrigerators are all transported by Lorries or trucks. The supply and demand of the refrigerators are all well known crisp numbers. But the transportation cost is not known exactly due to the variations in rates of diesel or gas or petrol, traffic jams, nature of the road, weather in hilly areas, et cetera. Thus, the crisp supply, crisp demand and uncertain transportation cost (i.e., intuitionistic fuzzy transportation cost) per unit (rupees in hundreds) for refrigerators from 3-different factories to 3-different districts are given in the following table from the past experience.
The objective of the problem is to determine the optimal allocation to minimize the intuitionistic fuzzy transportation cost.
How does the book provide a solution to these problems?
Prof. Kumar: Method 1 solves issues using the linear programming technique, whereas Method 2 solves problems using the proposed new method, which is based on the MODI (Modified Distribution Method) approach/software (e.g., Matlab). The proposed chapter also verifies the optimal solutions with Matlab and TORA and presents computer code for them.
How long have you been working in a related field to the topic coverage?
Prof. Kumar: I have been working in this field for more than a decade. I began my research career in 2010 in fuzzy transportation problems and also published a paper titled 'A comparative study on transportation problem in fuzzy environment'. In 2012, I published a paper titled 'Algorithmic approach for solving intuitionistic fuzzy transportation problem', which is an extension of the fuzzy transportation problem. In 2013 and 2014, I published two papers, namely, An optimal more-for-less solution of mixed constraints intuitionistic fuzzy transportation problems and a New algorithm for solving mixed intuitionistic fuzzy assignment problem. In 2015 and 2016, I introduced a very simple and easy method for solving both fuzzy and intuitionistic fuzzy transportation problems, namely, the PSK method. From 2017 to 2020, I published several papers dealing with different types of fuzzy and intuitionistic fuzzy transportation problems, including the PSK theorem. Recently, I published a chapter titled 'Finding the solution of balanced and unbalanced intuitionistic fuzzy transportation problems by using different methods with some software packages', in the Handbook of Research on Applied AI for International Business and Marketing Applications.
What special organizations, or other professional affiliations give you experience in the areas covered by this book?
Prof. Kumar: Generally, uncertainty exists in many ways in an organization or industry. For example, consider the transportation problems. The cost is one of the parameters of the transportation problem. In general, this transportation cost is not a fixed crisp number; it may vary due to variations in the rates of gasoline or diesel. So, we need an efficient technique to minimize transportation costs in an uncertain environment. The proposed chapter gives alternative ideas to solve this issue. The author teaches this technique to students from 2021 until now. It gives optimal solutions with the software but without using the initial basic feasible solutions. The author has worked in many prestigious institutions, especially Jamal Mohamed College, which is in the top 100 NIRF (National Institutional Ranking Framework) rankings in India in 2023. The author also hopes that this book chapter will be helpful for academicians, business executives, practitioners, and PhD students because of its special features and solving real-life problems.
See Prof. P. Senthil Kumar's Other Chapters in IGI Global Publications
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