Multi-criteria Decision Making Methods with Bipolar Fuzzy Sets

MUHAMMAD AKRAM is Professor at the Department of Mathematics, University of the Punjab, Lahore, Pakistan. He earned his Ph.D. in fuzzy mathematics from the Government College University, Lahore, Pakistan. His research interests include numerical algorithms, fuzzy graphs, fuzzy algebras, and fuzzy decision support systems. He has published 10 monographs and¿¿485¿research articles in international peer-reviewed journals.¿¿According to reports from Stanford University for years 2020, 2021 and 2022, Dr. Akram is ranked in the¿top 2% of scientists for years 2020, 2021 and 2022 in the world¿in¿artificial¿intelligence and¿image¿processing.¿He has been on the editorial of¿15¿international academic journals and reviewer/referee for¿155¿international journals, including¿Mathematical Reviews¿(USA) and Zentralblatt MATH (Germany). Under his supervision,¿17¿Ph.D. students have completed their research and he is currently guiding five more towards the same. SHUMAIZA is a research scholar at the University of Punjab, Lahore, Pakistan, from where she also has earned her M.Phil. degree in Mathematics. She has won the HEC indigenous scholarship for her Ph.D. program and has published 15 research articles in renowned international peer-reviewed journals. Her area of research is fuzzy systems. JOSÉ CARLOS R. ALCANTUD is Full Professor at the Department of Economics and Economic History, University of Salamanca, Spain, since 2010, and has been heading the BORDA Research Unit since 2015. He received his Ph.D. in Mathematics in 1996 from the University of Santiago de Compostela, Spain and M.Sc. in Mathematics in 1991 from the University of Valencia, Spain. His research interests include social choice theory, mathematical economics, and fuzzy theory and decision support systems. He has published over 200 papers on these topics and has supervised 3Ph.D. students on their research.