On Generalized Inverses of Fuzzy Matrices

Abstract

As there exist fuzzy matrices that do not have generalized inverses, it is useful to find those fuzzy matrices that admit generalized inverses. Some useful results on idempotent fuzzy matrices are established. Characterizations are obtained for fuzzy matrices having different types of generalized inverses. An algorithm for computing a generalized inverse of a given matrix (if it exits) is also provided and illustrated using numerical examples.

Indexing terms:

• Fuzzy matrix
• Generalized inverse

Additional information

Notes on contributors

Dwijesh Dutta Majumder

Dwijesh Dutta Majumder, received MSc (Tech) from Calcutta University (1955) PhD in Digital Computer's memory technology from the same University (1962). In 1955, he joined the Electronic Computer Division of Indian Statistical Institute. From 1972 to 1992 he was head of the Electronics and Communication Sciences Unit in ISI. From 1992 till 1997 he was Emeritus Scientist of CSIR along with his continuing position of Professor Emeritus. He is also the founder-Secretary-Director of Institute of Cybernetics Systems & Information Technology (ICS&IT) and Chairman, Centre for Advanced Computing (C-FAC) at Salt Lake Electronics Complex since 1997. He has published more than 450 research papers and six books in the field of memory technology, pattern recognition, image analysis, computer vision, artificial intelligence, neural modelling, cybernetics and knowledge based computing and their applications to science, society and industries. Dr Majumder was three times Professor-in-charge of Physical & Earth Sciences Division of ISI, Joint Secretary in-charge of Budget, Finance and Adminisration of ISI and founder Chairman of the National Centre of Knowledge Based Computing. He is a fellow of IAPR, INSA, INAE, IASc, IETE and is a member of the Governing Boards of International Association of Pattern Recognition (IAPR), the World Organisation of Cybernetics Systems and the International Fuzzy Systems Association. He is the recepient of the following awards and distinctions-UN Fellowship to work as visiting scientist at the University of Michigan, Ann Arbor, USA, 1964; Sir J C Bose Award of IETE in 1969 for some innovative design and the fundamental contribution in Memory Technology; International Norbert Wiener Award 1977 from World Organisation of Systems and Cybernetics and KYBERNETES for his unified theory of cybernetics & systems; R L Wadhwa Gold Medal of IETE in 1982 for highest contribution in Electronics sciences in the preceeding ten years in India; Computer Society of India Award 1983 for his outstanding and pioneering contributions in computer science and technology; Michael Madhusudhan Award in Calcutta as a scientist of the year 1984; Sir C V Raman Award from Acoustical Society of India 1985 for his pioneering work on acoustic—phonetics studies of Indian classical music; Best Production Award in the 7th World Book Fair, Dusseldroff, 1986 for his book “Fuzzy Mathematical Approach to Pattern Rcognition”, John Wiley & Sons (Halsted Press) N Y 1986; Prasanta Chandra Mahalanobis Gold Medal of INSA, 1993 for pioneering contributions in Applied Sciences & Technology, Jawaharlal Nehru Birth Centenary Lecture and Award of INSA, 1994 on 2-D and 3-D shape analysis and recognition for pattern recognition & computer vision system; K S Krishnan Memorial Award of the IETE 1991 for the best system oriented paper of the year; Shri Om Prakash Bhasin Award for 1996 for pioneering contributions, in Science & Technology.

Professor Dutta Majumder, is a member of the Editorial Board of several international journals, participated in large number of national/International conferences. Professor Dutta Majumder's current research interests include multimodal image/data fusion and mind-body problem and consciousness studies.

P S S N V P Rao

P S S N V P Rao, presently Dean of Studies of Indian Statistical Institute, obtained his MSc degree in Statistics from Andhra University. He received his MTech in Computer Science and PhD degrees from Indian Statistical Institute. He held visiting positions at Institute of Statistics, Belgrade, University of Dar-es-Saalaam, Tanzania and Technical University of Munich, West Germany during 1976–83. He has about 20 research papers published in different international and national journals in the fields of Mathematics, Statistics and Computer Science.