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

Bulletin 195

the main top ic of invest igat ion. At f i rst fuzzy models of technical e lements had been considered. Fo l lowing this, fuzzy a lgor i thms for s t ructure synthe- sis were developed. Problems of fuzzy dec is ion-making were tackled s imu l taneous ly w i th par t ia l ly po lyopt imiza t ion tasks. Now the man ipu la t ion of experts ' knowledge is being invest igated, wh ich in part leads to fuzzy equat ion systems. Ano the r f ield of interest was focused on the control of p lant and large product ion systems. This is c losely connected wi th fuzzy logic contro l lers and thei r appl icat ion to industr ia l processes. Ano ther kind of prob lem to be solved are those of an economic nature, e.g. model l ing of economic parameters and evaluat ions, wh ich often can be taken account of by fuzzy s tatements in a more conven ient way than by cr isp methods.

Data analys is is a fur ther f ield of invest igat ion (being present in the above problems). Especial ly the evaluat ion of the qual i ty of data wi th respect to a g iven model leads to impor tan t quest ions of fuzzy regression in a broader sense. Numer ica l real izat ion of the developed methods plays an impor tant part for appl icat ion. Hence, it is essential that effort be concentrated to solve such prob lems and to create user or iented software.

Literature

[1] M. Dohnal and K. Hartmann, A fuzzy definitional algorithm and synthesis problems, C.A.C.E., Montreux (April 1979).

[2] M. Franke, W. Franke and M. Vitek, Unsch~irfe betriebswirtschaftlicher informationen und erh6hte Effektivit~t der Informationsverarbeitung, Wiss. Zeitschrift d. THLM 27 (3) (1985) 1-10.

[3] S. G6tze, Struktursynthese auf der Grundlage der unscharfen Modellierung, THLM 1980 (Unpubl. WP).

[4] M. Wagenknecht and K. Hartmann, On fuzzy rank-ordering in polyoptimization, Fuzzy Sets and Systems 11 (1983) 253-264.

[5] M. Wagenknecht and K. Hartmann, On the construction of fuzzy eigen solutions in given regions, Fuzzy Sets and Systems 20 (1986) 55-65.

[6] M. Wagenknecht and K. Hartmann, Fuzzy modelling with tolerances, Fuzzy Sets and Systems 20 (1986) 325-332.

[7] M. Wagenknecht and K. Hartmann, On the solution of direct and inverse problems for fuzzy equation systems with tolerances, Fuzzy Sets and Systems, to appear.

[8] W. Wei6, H.-J. H~rig and J. Sch0tte, Anwendung der unscharfen Systembeschreibung for die mikrorechnergestOtzte Steuerung eines Hochtemperaturprozesses, MSR 26 (4) (1983) 213-216.

[9] G. Zeising, M. Wagenknecht and K. Hartmann, Synthesis of distillation trains with heat integration by a combined fuzzy and graphical approach, Fuzzy Sets and Systems 12 (1984) 103-115.

[10] G. Zeising, M. Wagenknecht and K. Hartmann, Ein unscharfer Algorithmus zur Synthese von W~rmeObertragersystemen, Wiss. Zeitschrift THLM 27 (1) (1984) 62-69.

K. Har tmann Akademie der Wissenschaften der DDR Institut for chemische Technologie Rudower Chaussee 5, 1199 Berlin