A Review Based on Various Applications to Find a Consistent Pairwise Comparison Matrix

Authors

  • Shalu Kaushik Department of Applied Science (Mathematics), Gurukula Kangri (Deemed to be University), Haridwar, India
  • Sangeeta Pant Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Lavale, Pune, India
  • Lokesh Kumar Joshi Department of Applied Science (Mathematics), Gurukula Kangri (Deemed to be University), Haridwar, India
  • Anuj Kumar School of Computer Science Engineering & Applications, D. Y. Patil International University (DYPIU), Akrudi, Pune, India
  • Mangey Ram Department of Mathematics, Computer Science and Engineering, Graphic Era Deemed to be University, Dehradun, India

DOI:

https://doi.org/10.13052/jrss0974-8024.1713

Keywords:

Pairwise comparison matrix, analytic hierarchy process, consistency ratio, consistency index, repairing of pairwise comparison matrix

Abstract

Multi-criteria decision-making (MCDM) is a crucial process that provides a systematic approach to resolving numerous challenging problems encountered in everyday life. An effective method for addressing such MCDM challenges is the Analytic Hierarchy Process (AHP). Within AHP, the resolution of these problems relies on the Pairwise Comparison Matrix (PCM), a pivotal component of the decision-making framework. A fundamental aspect of AHP lies in ensuring the consistency of the comparison matrix to validate the logical perspective of the respondents. An inconsistent matrix undermines its utility as a reference for decision-making, underscoring the significance of achieving consistency in the PCM as a pivotal stage in the decision-making process. In this discourse, we delve into various methodologies aimed at deriving a refined and consistent PCM capable of replacing the original inconsistent version. To facilitate comprehension, we categorize the references based on proposed approaches and specific focal points.

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Author Biographies

Shalu Kaushik, Department of Applied Science (Mathematics), Gurukula Kangri (Deemed to be University), Haridwar, India

Shalu Kaushik earned a B.sc degree from the R. K. (PG) College, Shamli, Uttar Pradesh, India and M.sc degree from V. V. (PG) College Shamli, Uttar Pradesh, India. She is a promising young researcher serving as a Research Scholar at the Department of Applied Sciences (Mathematics) within the Gurukula Kangri (Deemed to be University), Haridwar, India. Her research focuses on Multi-Criteria Decision Making, Analytic Hierarchy Process and Pair-Wise Comparison Matrix.

Sangeeta Pant, Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Lavale, Pune, India

Sangeeta Pant received the Ph.D. degree from the G. B. Pant University of Agriculture and Technology, Pantnagar, India. She is currently an Associate Professor with Symbiosis International (Deemed University), Pune, India. Before this, she was associated with the Department of Mathematics, School of Engineering and Computing, Dev Bhoomi Uttarakhand University, Dehradun, as an Associate Professor. She was also an Assistant Professor (SG) with the University of Petroleum and Energy Studies (UPES), Dehradun, India. She has published around 65 research articles in journals/ books of national and international repute in her area of interest. She has been actively involved in various other research related activities, such as editing/reviewing for various reputable journals and organizing/participating in conferences. Her research interests include numerical optimization, artificial intelligence, nature-inspired algorithms, and MCDM.

Lokesh Kumar Joshi, Department of Applied Science (Mathematics), Gurukula Kangri (Deemed to be University), Haridwar, India

Lokesh Kumar Joshi received his Master’s and Ph.D. degree in Mathematics from G. B. Pant University of Agriculture and Technology, Pantnagar, India. He has been working as an Assistant Professor in Gurukula Kangri (Deemed to be University), Haridwar, India. His current area of interest is Fuzzy Sets, Fixed Point Theorems and Applications.

Anuj Kumar, School of Computer Science Engineering & Applications, D. Y. Patil International University (DYPIU), Akrudi, Pune, India

Anuj Kumar received the master’s and Ph.D. degrees in mathematics from the G. B. Pant University of Agriculture and Technology, Pantnagar, India. He is currently a Professor with D. Y. Patil International University, Pune, India. Before this position, he was associated with the University of Petroleum and Energy Studies (UPES), Dehradun, India, as an Associate Professor. He was an Assistant Professor in mathematics with ICFAI University, Dehradun. He has published more than 70 research articles in journals of national and international repute. His research interests include MCDM, reliability analysis, optimization, and artificial intelligence. He is also an Associate Editor of the International Journal of Mathematical, Engineering, and Management Sciences. He is a regular reviewer for various reputable journals from, Elsevier, IEEE, Springer, Taylor & Francis, and Emerald.

Mangey Ram, Department of Mathematics, Computer Science and Engineering, Graphic Era Deemed to be University, Dehradun, India

Mangey Ram received the Ph.D. degree major in Mathematics and minor in Computer Science from G. B. Pant University of Agriculture and Technology, Pantnagar, India in 2008. He has been a Faculty Member for around thirteen years and has taught several core courses in pure and applied mathematics at undergraduate, postgraduate, and doctorate levels. He is currently the Research Professor at Graphic Era (Deemed to be University), Dehradun, India & Visiting Professor at Peter the Great St. Petersburg Polytechnic University, Saint Petersburg, Russia. Before joining the Graphic Era, he was a Deputy Manager (Probationary Officer) with Syndicate Bank for a short period. He is Editor-in-Chief of International Journal of Mathematical, Engineering and Management Sciences; Journal of Reliability and Statistical Studies; Journal of Graphic Era University; Series Editor of six Book Series with Elsevier, CRC Press-A Taylor and Frances Group, Walter De Gruyter Publisher Germany, River Publisher and the Guest Editor & Associate Editor with various journals. He has published 300 plus publications (journal articles/books/book chapters/conference articles) in IEEE, Taylor & Francis, Springer Nature, Elsevier, Emerald, World Scientific and many other national and international journals and conferences. Also, he has published more than 55 books (authored/edited) with international publishers like Elsevier, Springer Nature, CRC Press-A Taylor and Frances Group, Walter De Gruyter Publisher Germany, River Publisher. His fields of research are reliability theory and applied mathematics. Dr. Ram is a Senior Member of the IEEE, Senior Life Member of Operational Research Society of India, Society for Reliability Engineering, Quality and Operations Management in India, Indian Society of Industrial and Applied Mathematics, He has been a member of the organizing committee of a number of international and national conferences, seminars, and workshops. He has been conferred with “Young Scientist Award” by the Uttarakhand State Council for Science and Technology, Dehradun, in 2009. He has been awarded the “Best Faculty Award” in 2011; “Research Excellence Award” in 2015; “Outstanding Researcher Award” in 2018 for his significant contribution in academics and research at Graphic Era Deemed to be University, Dehradun, India. Recently, he has been received the “Excellence in Research of the Year-2021 Award” by the Honourable Chief Minister of Uttarakhand State, India.

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Published

2024-06-05

How to Cite

Kaushik, S., Pant, S., Joshi, L. K., Kumar, A., & Ram, M. (2024). A Review Based on Various Applications to Find a Consistent Pairwise Comparison Matrix. Journal of Reliability and Statistical Studies, 17(01), 45–76. https://doi.org/10.13052/jrss0974-8024.1713

Issue

2024: Vol 17 Iss 1

Section

Advances in Reliability Studies