- Email: [email protected]
Research on fuzzy algebra in Changchun
362
Bulletin
cently, some results are obtained related to the notions of fuzzy sublattices and fuzzy ideals of a lattice. Few research students under my supervision are also working on fuzzy congruences in a semigroup or group. Those who are interested in collaborations in these areas are welcome, and they can correspond on the address given below. Dr. Naseem Ajmal B-85, Pandara Road New Delhi - 110003, India
Research on Statistics with Fuzzy Data at Vienna and some Cooperations Beginning with a paper "Is it necessary to develop a Fuzzy Bayesian Inference", published in 1987 there, a small group at Vienna started to work on statistical inference for non-precise data. Beginning by myself, Dr. S. FrLihwirth-Schnatter from Vienna joined our department of Statistics at the University of Technology and later a refugee from Romania, Dr. S. Niculescu, worked for some months at our department. Two joint papers in FSS originate from this time. Several other papers were published in different journals and proceedings volumes. Dr. Fr~,ihwirth-Schnatter got a position in the Department of Statistics at the Vienna University of Economics and Dr. Niculescu is now working at the National Water Research Institute, Burlington, Canada. In the past several masters theses in the field of statistics for fuzzy data were completed. Presently, Dr. W. Gurker from our department is working on calibration with non-precise data and also a doctoral thesis related to these problems is written. A Chinese student completed a doctoral theisis "Formal Description of Uncertainty in Decision Support and Information Systems". Besides the mentioned cooperations we have contact with Prof. R. Kruse from Braunschweig in Germany and one doctoral student is presently working at the Computer Science and Engineering Department with Professor A. Kandel from the University of South Florida, Tampa. In August 1993 our department organizes an international symposium on "Statistics with Non-precise Data" at Innsbruck in Tyrol. One of the invited speakers there will be Professor H. Bandemer from the Bergakademie Freiberg, a leading expert in fuzzy data analysis in the German speaking region. In Austria there are several scientists working on fuzzy set theory and applications. Some of them are Professor W, Janko, Wien, Dozent E.P, Klement, Linz, Dozent K.-P. Adlassnig, Wien, Dr. A. Geyer-Schulz, Wien, and probably others. In the winter semester of 1992 I was on sabbatical writing a booklet on "Statistics with Non-precise Data". Prof. Reinhard Viertl University of Technology 1040 Wien Austria
Research on Fuzzy Algebra in Changchun We became interested in the theory of fuzzy set and started to do some research in 1980. Liu Xuhua's (Dept. of Computer and Science, Jilin University) chief works are on the fuzzy Boolean algebra and artificial intelligence. Li Xianggao (Dept. of Mathematics, the Jilin mechanic college) mainly studies the fuzzy relational equations and the characteristic values of fuzzy matrixes. The main interests of Gu Wenxiang (Dept. of Mathematics, Northeast Normal University), Lu Tu (Dept. of Mathematics, the Changchun teacher's college) and Chen Degang (Dept. of Mathematics, Northeast Normal University) are in the following fields: (1) The theory of fuzzy groups; (2) Fuzzy algebra; (3) Fuzzy linear spaces; (4) Fuzzy rings and fuzzy ideals; (5) Fuzzy mapping. We have obtained some results in the past ten years. The papers published recently have been listed in the references. At the present, we are interested in some other problems and we will expend a lot of energy on them.
References [1] Gu Wenxiang and Lu Tu, The isotonic fuzzy algebraic Systems, Fuzzy Systems and Mathematics 2 (1991) 92-94. [2J Gu Wenxiang, Relations among groups Gin(I), G, and S,, Northeastern Math. J. 2 (1990) 174-176. [3] Gu Wenxiang, R-fuzzy groups, T-fuzzy groups and pointwise fuzzy groups, J. of Northeast Normal University 3 (1990) 37-40. [4] Gu Wenxiang and Lu Tu, Fuzzy linear spaces, Fuzzy Sets and Systems 49 (1992) 377-380. [5] Gu Wenxiang and Lu Tu, Fuzzy algebras over fuzzy fields redefined, Fuzzy Sets and Systems 53 (1992) 105-107. [6] Gu Wenxiang and Lu Tu, The properties of fuzzy divisible groups, Fuzzy Sets and Systems (1993), to appear. Gu Wenxiang Northeast Normal University Ghangchun, Jilin 130024, P.R. China
From Fu Guoyao, Nanjing Following my recent publication [4] in this journal I would like to introduce recent advances in this subject. Up to now the complexity (i.e. amount of work done by the algorithm) of any algorithm for computing the transitive closure of a fuzzy similarity matrix is o(n 3) at least, and in discrete mathematics it is known that for a Boolean m a t r i x - a particular kind of fuzzy matrix, the complexity of any feasible algorithm for computing the transitive closure is o(n 3) at least as well. Hence we may ask the question whether any and every algorithm for computing the transitive closure, must have complexity of at least o(n3)? I think it should be answered negatively, as I have recently designed an algorithm, whose
Bulletin
cently, some results are obtained related to the notions of fuzzy sublattices and fuzzy ideals of a lattice. Few research students under my supervision are also working on fuzzy congruences in a semigroup or group. Those who are interested in collaborations in these areas are welcome, and they can correspond on the address given below. Dr. Naseem Ajmal B-85, Pandara Road New Delhi - 110003, India
Research on Statistics with Fuzzy Data at Vienna and some Cooperations Beginning with a paper "Is it necessary to develop a Fuzzy Bayesian Inference", published in 1987 there, a small group at Vienna started to work on statistical inference for non-precise data. Beginning by myself, Dr. S. FrLihwirth-Schnatter from Vienna joined our department of Statistics at the University of Technology and later a refugee from Romania, Dr. S. Niculescu, worked for some months at our department. Two joint papers in FSS originate from this time. Several other papers were published in different journals and proceedings volumes. Dr. Fr~,ihwirth-Schnatter got a position in the Department of Statistics at the Vienna University of Economics and Dr. Niculescu is now working at the National Water Research Institute, Burlington, Canada. In the past several masters theses in the field of statistics for fuzzy data were completed. Presently, Dr. W. Gurker from our department is working on calibration with non-precise data and also a doctoral thesis related to these problems is written. A Chinese student completed a doctoral theisis "Formal Description of Uncertainty in Decision Support and Information Systems". Besides the mentioned cooperations we have contact with Prof. R. Kruse from Braunschweig in Germany and one doctoral student is presently working at the Computer Science and Engineering Department with Professor A. Kandel from the University of South Florida, Tampa. In August 1993 our department organizes an international symposium on "Statistics with Non-precise Data" at Innsbruck in Tyrol. One of the invited speakers there will be Professor H. Bandemer from the Bergakademie Freiberg, a leading expert in fuzzy data analysis in the German speaking region. In Austria there are several scientists working on fuzzy set theory and applications. Some of them are Professor W, Janko, Wien, Dozent E.P, Klement, Linz, Dozent K.-P. Adlassnig, Wien, Dr. A. Geyer-Schulz, Wien, and probably others. In the winter semester of 1992 I was on sabbatical writing a booklet on "Statistics with Non-precise Data". Prof. Reinhard Viertl University of Technology 1040 Wien Austria
Research on Fuzzy Algebra in Changchun We became interested in the theory of fuzzy set and started to do some research in 1980. Liu Xuhua's (Dept. of Computer and Science, Jilin University) chief works are on the fuzzy Boolean algebra and artificial intelligence. Li Xianggao (Dept. of Mathematics, the Jilin mechanic college) mainly studies the fuzzy relational equations and the characteristic values of fuzzy matrixes. The main interests of Gu Wenxiang (Dept. of Mathematics, Northeast Normal University), Lu Tu (Dept. of Mathematics, the Changchun teacher's college) and Chen Degang (Dept. of Mathematics, Northeast Normal University) are in the following fields: (1) The theory of fuzzy groups; (2) Fuzzy algebra; (3) Fuzzy linear spaces; (4) Fuzzy rings and fuzzy ideals; (5) Fuzzy mapping. We have obtained some results in the past ten years. The papers published recently have been listed in the references. At the present, we are interested in some other problems and we will expend a lot of energy on them.
References [1] Gu Wenxiang and Lu Tu, The isotonic fuzzy algebraic Systems, Fuzzy Systems and Mathematics 2 (1991) 92-94. [2J Gu Wenxiang, Relations among groups Gin(I), G, and S,, Northeastern Math. J. 2 (1990) 174-176. [3] Gu Wenxiang, R-fuzzy groups, T-fuzzy groups and pointwise fuzzy groups, J. of Northeast Normal University 3 (1990) 37-40. [4] Gu Wenxiang and Lu Tu, Fuzzy linear spaces, Fuzzy Sets and Systems 49 (1992) 377-380. [5] Gu Wenxiang and Lu Tu, Fuzzy algebras over fuzzy fields redefined, Fuzzy Sets and Systems 53 (1992) 105-107. [6] Gu Wenxiang and Lu Tu, The properties of fuzzy divisible groups, Fuzzy Sets and Systems (1993), to appear. Gu Wenxiang Northeast Normal University Ghangchun, Jilin 130024, P.R. China
From Fu Guoyao, Nanjing Following my recent publication [4] in this journal I would like to introduce recent advances in this subject. Up to now the complexity (i.e. amount of work done by the algorithm) of any algorithm for computing the transitive closure of a fuzzy similarity matrix is o(n 3) at least, and in discrete mathematics it is known that for a Boolean m a t r i x - a particular kind of fuzzy matrix, the complexity of any feasible algorithm for computing the transitive closure is o(n 3) at least as well. Hence we may ask the question whether any and every algorithm for computing the transitive closure, must have complexity of at least o(n3)? I think it should be answered negatively, as I have recently designed an algorithm, whose