...d group loop 1 SMARANDACHE FUZZY ALGEBRA W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Techn... ... group loop 1 SMARANDACHE FUZZY ALGEBRA W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technolo... ...group loop 1 SMARANDACHE FUZZY ALGEBRA W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology Madras... ... Indian Institute of Technology Madras Chennai – 600 036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv ... ...tion by: Copyright 2003 by American Research Press and W. B. Vasantha Kandasamy Rehoboth, Box 141 NM 87322, USA Many books c... ..., λ) , x λ + y ν = (x + y) min (λ, v) , d µ o x λ + c K o y v = (dx + cy) min{µ , λ, k, v}. Proof: Left for the reader to refer [75]. The... ...y for all x ∈ V, (K o A)(x) = sup{min {K(c), A(y)}c ∈ P ⊂ R , y ∈ V, x = cy P is a subfield in R relative to which V is defined}. DEFINITION 4.... ...49. JACOBSON, Nathan, Basic Algebra I, Freeman, New York, 1974. 50. JUN, Young Bae, NEGGERS, J. and KIM, Hee Sik, Normal L-fuzzy ideals in semiring... ...c groups, J. Fuzzy Math., 3, 465-470 (1995). 56. KIM, Kyung Ho, and JUN, Young Bae, Normal fuzzy R-subgroups in near- rings, Fuzzy Sets and Systems,...