Fuzzy Sets and Systems 45 (1992) 397-401 397 North-Holland

Bulletin

Editorial

This edition of the Bulletin presents varied research reports and news from around the fuzzy world. My thanks to all the contributors. In the next Bulletin we hope to carry inter alia a review of Bart Kosko's remark- able book linking fuzzy sets and neural networks.

lan Graham November 1991

Working Group Fuzzy Sets

The German Society for Operations Research (DGOR) is planning to establish a new working group: Fuzzy Sets.

This group wants to support progress in theory and application of fuzzy set techniques. We wil l show how fuzzy set methods can be combined with classical models and algorithms from the field of operations research as well as with more advanced computer technologies like knowledge-based systems and neural nets.

Economical and technical applications are of special interest.

The goals of our work are a better f low of information between theory and practice, an improvement of the communication between researchers, and an exchange of experience between practitioners. Especially prac- titioners are encouraged to contribute to our work by giving hints to problems in practical applications of fuzzy set methods.

Participants of this working group should be members of DGOR.

Information:

Richard Weber Lehrstuhl for Unternehmensforschung RWTH Aachen Templergraben 64 Germany FAX: + 49-241-806189

Research at Delhi University

At Delhi University I am successful in forming a group of researchers who are working in the areas of fuzzy topology and fuzzy algebraic structures. The group includes Dr. V.N. Dixit, Dr. J.K. Kohli, S.K. Azad, Rajesh Kumar, Anand Swaroop, B.K. Tyagi and Ratna Dev Sharma besides many others who are interested in various aspects of fuzzy set theory.

The research in fuzzy topology was initiated in the year 1986, and a series of papers were written in the areas of fuzzy continuity and its weaker forms, thereby establishing a localized theory in the studies of these concepts. In separate papers, we have also investigated the concept of connectedness and local connectedness in fuzzy topology. We have introduced four notions of connectedness for an arbitrary fuzzy set; they all coin- cide when the fuzzy set in question is the whole fuzzy space. Based on the notions of ci-connectedness, four notions of local connectedness have been introduced and studied: Two of these notions are shown to be 'good extensions' in the sense of Lowen.

We have also introduced the concepts of overlapping and non-overlapping families of fuzzy sets, which are used to formulate the definition of covering dimension in fuzzy topological spaces. The notion of covering dimension is also shown to be a 'good extension' of its counter-part in general topology. Work in this direction is in progress.

In another direction, we have investigated regular fuzzy spaces due to Hutton. We have provided several characterizations of these spaces. In the process, we have introduced (%closure and 0-closure of a fuzzy set. We have also introduced the notion of fuzzy almost regular spaces and it has been shown that a fuzzy space is fuzzy almost regular if and only if, for every fuzzy set, its (%closure coincides with it 0-closure. Moreover, we have established the inter-relationship of the notions of regular fuzzy spaces, fuzzy almost regular spaces and fuzzy semi-regular spaces. The notion of fuzzy Urysohn space is introduced and discussed.

Recently, we are involved in the development of the theory of fuzzy nets. We have also established various applications of this important concept. Consequently, the notion of closed fuzzy graph is introduced and discussed in one of our papers. In a different paper, motivated by the= concept of N-compactness and fuzzy nets, we have introduced the concepts of local N- compactness, countable compactness and sequencial compactness in fuzzy topological spaces. A pleasing feature of these notions is that all of them are 'good extensions' in the sense of Lowen.

The progress of research in fuzzy groups and fuzzy rings is also at a very brisk rate. Recently, under my guidance a thesis entitled "Fuzzy Algebraic Structures" has been submitted and the degree of Doctor of Phil- osphy has been awarded to Rajesh Kumar, under my supervision (jointly with Dr. V. N. Dixit). The thesis basically deals with some aspects of fuzzy groups, such as union of fuzzy subgroups, fuzzy subgroup generated by a fuzzy set and fuzzy Sylow subgroups. Moreover, a systematic development of the notion of fuzzy rings has been made in the thesis. Several concepts in the realm

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