Abstract: The decision making problems mostly involve optimization of conflicting multiple objectives. Multi-objective optimization essentially investigates trade-off between the objectives. Classical optimization and its several branches have sound theoretical foundations and are featured by a vast collection of sophisticated algorithms and softwares. It has become an indispensable tool for powerful modelling and decision making in a wide range of applications in management science, industry and engineering field. Although, it is not always possible to properly represent the real world situations with classical mathematics, due to the presence of uncertain events. Most often, the recorded or collected data are inherently imprecise or inexact. The data may be affected by measurement errors or by random events. Sometimes the data may be roughly estimated or it is more appropriate to assume that the data belongs to some uncertain set or interval. There are two major causes behind this imperfection or uncertainty of the information—imprecision and randomness. In finding optimal solution for an optimization problem in uncertain environment, decision maker (DM) seeks a set of decision or design variables that yields the best performing system. But the realistic optimization problems, especially those stemming from engineering or industrial design or other complex multidisciplinary systems, are characterized by the existence of multiple criteria with some complicated additional constraints. According to the characteristic of the constraint set, multi-criteria optimization problems (MCDM) can be categorized into two parts: multi-attribute decision making (MADM) and multi-objective decision making (MODM) problems. I would like to stress upon the situation when the feasible space in MODM is continuous or piecewise continuous in nature. More emphasize will be given on the techniques of capturing hazy Pareto frontier. This haziness can be viewed as a fuzzy curve consisting of a set of fuzzy points. I intend to discuss a few applications of it in realistic decision situations as well.
Bio: Dr. Debjani Chakraborty has been a faculty member of Indian Institute of Technology, Kharagpur since 1997 in School of Management and Department of Mathematics respectively. Dr. Chakraborty received B.Sc. (Mathematics Hons.) in 1987 from University of Calcutta and M.Sc. (1989), Ph.D. (1995) from IIT Kharagpur with CSIR fellowship. She is the recipient of the prestigious Young Scientist Award 1997 in Mathematics from Indian Science Congress Association for her contributions to multi-objective optimization in imprecise and uncertain environment. She has also been awarded the Young Scientist Scheme from Dept. of Science & Technology, Govt. of India in 1997 as an individual scientist. She is a nominated member of the Indian National Science Academy of Science, Allahabad. Her current areas of research include theory and applications of fuzzy logic in optimization, fuzzy geometry, and fuzzy logic in medical science and technology. She has authored more than 120 papers among which more than 75 are in peer-reviewed journals. She has also delivered e-learning through online web and video lecture series on Optimization under NPTEL and MOOC programmes.