194 Bulletin

5. Research at the Indian Institute of Technology, Kharagpur

The Department of Mathematics of the Institute is actively engaged in teaching as well as research in various fields of Pure and Applied Mathematics, Operations Research being one of them.

Prof. J.R. Rao, Prof. S.B. Sinha and Dr. R.N. Tiwari along with their group of research students, who join for a short period for their Ph.D. degree and then leave the Institute, form the core of the Operations Research group in the Department of Mathematics.

At present the group is working in Multicriteria Decision Making (MCDM) problems using a fuzzy set theoretic approach. Some of these investiga- tions are already published or accepted for publication in the Journal of Fuzzy Sets and Systems. The research students associated with this group are D. Singh, S. Dharmar, B.K. Mohanty, (Miss) Nilima Roy and (Miss) K. Saraswati. Whereas the group consisting of Tiwari, Rao and Dharmar is trying to push ahead various aspects of goal programming using fuzzy set theory, the group Rao, Tiwari and Mohanty is trying to assimilate and revisit the problems of the decision making operator (gamma operator) used by Zimmermann, the preference structure of alternatives and criteria in MCDM and suitability of aspiration levels in goal programming, etc. The application of fuzzy set theory to these problems has helped to overcome the earlier shortcomings by way of refining the concept itself in some cases and by giving some additional measure which can be used as criterion (e.g., suitability of aspiration levels) in certain other cases. D. Singh's work is compiled in the form of his Ph.D. thesis on MCDM problems. Nilima Roy and K. Saraswati are working in certain aspects of MCDM problems using fuzzy set theory. One of our colleagues, Dr S. Nanda is working on pure mathematical aspects of the applications of fuzzy sets (e.g., application to functional analysis, topology, etc.).

References [1] R. N. Tiwari, S. Dharmar and J.R. Rao, Priority structure in fuzzy goal programming, Fuzzy

Sets and Systems 19 (1986) 251-259. [2] R.N. Tiwari, S. Dharmar and J.R. Rao, Fuzzy goal programming -An additive model, Fuzzy

Sets and Systems, to appear. [3] J.R. Rao, R.N. Tiwari and B.K. Mohanty, A method for finding numerical compensation for

fuzzy multicriteria decision problems, Fuzzy Sets and Systems, to appear. [4] J.R. Rao, R.N. Tiwari and B.K. Mohanty, A preference structure on aspiration levels in a

goal programming problem - A fuzzy approach, Fuzzy Sets and Systems, to appear. [5] D. Singh, Multiple criteria decision making: Preference modelling using fuzzy sets, Ph.D,

Thesis, Dept. of Mathematics, Indian Institute of Technology, Kharagpur (1983).

6. The Working Group on Fuzzy Sets at the Technical University "Carl Schorlemmer", Leuna-Merseburg, G.D.R.

At the Technical University Merseburg work on theory and application of fuzzy sets started up at the end of the seventies. Chemical engineering is