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ABOUT THE AUTHORS

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Preface

Preface

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Range of FRM, 168 RSFRM model, 172-3

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SBAM model, 186-8 SCFAM model, 193-5 SDBAM model, 182-3 SDFAM model, 195-7 SDSBAM model, 184-6 SDSFRM model, 173-4 SFAM model, 167, 197-9 SFCM model, 241-2 SFRM model, 167, 174-6 Signal functions, 179 Simple FCM, 238 Simple FRM, 169 Simple matrices, 7-8 SRBAM model, 182-4 SRFAM model, 192-3 Submatrix, 8-9 Super diagonal matrix, 15 Super fuzzy column matrix, 79 Super fuzzy column vector, 76-7 Super fuzzy matrices, 80-1 Supermatrix, 7-10 Symmetric partitioning, 12 Symmetric simple matrix, 13-4

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Transpose of a fuzzy supermatrix, 86-7 Type I super column vector, 17 Type II column super vectors, 18-9 Type III super vector, 20-1

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Dr.W.B.Vasantha Kandasamy is an Associate Professor in the Department of Mathematics, Indian Institute of Technology Madras, Chennai. In the past decade she has guided 11 Ph.D. scholars in the different fields of non-associative algebras, algebraic coding theory, transportation theory, fuzzy groups, and applications of fuzzy theory of the problems faced in chemical industries and cement industries.

She has to her credit 640 research papers. She has guided over 57 M.Sc. and M.Tech. projects. She has worked in collaboration projects with the Indian Space Research Organization and with the Tamil Nadu State AIDS Control Society. This is her 32nd book.

On India's 60th Independence Day, Dr.Vasantha was conferred the Kalpana Chawla Award for Courage and Daring Enterprise by the State Government of Tamil Nadu in recognition of her sustained fight for social justice in the Indian Institute of Technology (IIT) Madras and for her contribution to mathematics. (The award, instituted in the memory of Indian-American astronaut Kalpana Chawla who died aboard Space Shuttle Columbia). The award carried a cash prize of five lakh rupees (the highest prize-money for any Indian award) and a gold medal. She can be contacted at vasanthakandasamy@gmail.com You can visit her on the web at: http://mat.iitm.ac.in/~wbv or: http://www.vasantha.net

Dr. Florentin Smarandache is an Associate Professor of Mathematics at the University of New Mexico in USA. He published over 75 books and 100 articles and notes in mathematics, physics, philosophy, psychology, literature, rebus. In mathematics his research is in number theory, non-Euclidean geometry, synthetic geometry, algebraic structures, statistics, neutrosophic logic and set (generalizations of fuzzy logic and set respectively), neutrosophic probability (generalization of classical and imprecise probability). Also, small contributions to nuclear and particle physics, information fusion, neutrosophy (a generalization of dialectics), law of sensations and stimuli, etc. He can be contacted at smarand@unm.edu

Rev. Fr. K. Amal, SJ is presently pursuing his Ph.D. in Mathematics in the Madurai Kamaraj University, Tamil Nadu, India. Having completed his bachelor's degree in mathematics at the St. Joseph’s

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College, Trichy, he entered the Society of Jesus in July 1977. In 1985, he completed his master's degree in mathematics in Loyola College, Chennai and his master's degree in sociology in 1992. Ordained in 1988, he started his service as a parish priest in Mallihapuram, a Dalit parish, in the Chengelpet district. He later served the All India Catholic University Federation (AICUF ), a student movement, for 15 long years till 2003; in the latter seven-and-a-half years he occupied the position of National Director, AICUF. During his tenure, the movement witnessed newer areas of operation and scaled greater heights in its expansion and animation works, particularly with Dalit and Tribal students. Transferred to the Indian Social Institute, Bangalore, in 2004, as its Superior, he was invited to be the Director of Works of the Human Rights Desk and the Training Unit. Besides this, he has been an Advisor to the Asia-Pacific Chapter of the International Movement of Catholic Students (IMCS) since June 2003.

In this capacity he had traveled far and wide in the Asia Pacific region and elsewhere too. He has organized, participated, animated and served as a resource person in many workshops, seminars and meetings. He can be contacted at kamalsj@gmail.com

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ISBN-10: 1-59973-027-8 ISBN-13: 978-1-59973-027-1 EAN: 9781599730271

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