[1] Barry Mitchell, Theory of Categories, Academic Press, New York (1965) [2] Bernard Kolman, Robert C.Busby and Sharon Cutler Ross, Discrete

Transcription

1 [1] Barry Mitchell, Theory of Categories, Academic Press, New York (1965) [2] Bernard Kolman, Robert C.Busby and Sharon Cutler Ross, Discrete Mathematical Structures, PHI Learning, New Delhi (2009) [3] Birkhoff G., Lattice Theory, 3rd Edition, Coll.Publ.XXV, American Math.Soc. Providence, R.I., (1967) [4] Bodo Pareigis, Categories and Functors, Academic Press, New York (1973) [5] Das P.S., Fuzzy groups and level subgroups, J.Math.Anal. &Appl., 84, (1981) [6] Davey B.A. and Priestley, Introduction to Lattices and Order, Cambridge University Press, Cambridge (1990) [7] Eilenberg S. and MacLane S., General Theory of Natural Equivalences, Trans.Am.Math.Soc., 58, (1945) [8] George J.Klir and Bo Yuan, Fuzzy Sets and Fuzzy logic, PHI Learning, New Delhi (2009) [9] Goguen J. A., L-Fuzzy Sets, Journal of Mathematical Analysis and Applications, 18, (1967)

2 [10] Herstein I.N., Topics in Algebra, Second Edition, Vikas Publishing House, New Delhi (1984) [11] John B.Fraleigh, A First Course in Abstract Algebra, Third Edition, Narosa Publishing House, New Delhi(1986) [12] John N. Mordeson and D.S.Malik, Fuzzy Commutative Algebra, World Scientific, Singapore (1998) [13] Kenneth H. Rosen, Discrete Mathematics&Its Applications, 6th Edition, Tata McGraw-Hill, New Delhi (2007) [14] Purna Chandra Biswal, Discrete Mathematics and Graph Theory, PHI Learning, New Delhi (2009) [15] Rosenfeld A., Fuzzy Groups, J.Math.Anal. &Appl, 35, (1971) [16] Saunders MacLane, Categories for the Working Mathematician, Springer- Verlag, New York (1971) [17] Serge Lang, Algebra, Third Edition, Addison Wesley (1999) [18] Souriar Sebastian, A note on the paper of Biswas, Fuzzy Sets and Systems (1994) [19] Souriar Sebastian and S.Babusundar, On the chains of level subgroups of homomorphic images and pre-images of fuzzy groups, Banyan Journal of Mathematics, 1, 25-34(1994) [20] Souriar Sebastian and S.Babusundar, Existence of fuzzy subgroups of every level cardinality upto 0, Fuzzy Sets and Systems, 67, (1994) 109

3 [21] Souriar Sebastian and S.Babusundar, Commutative L-fuzzy subgroups, Fuzzy Sets and Systems, 68, (1994) [22] Souriar Sebastian and S.Babusundar, Generalisations of some results of Das, Fuzzy Sets and Systems, 71, (1995) [23] Souriar Sebastian and S.Babusundar, Fuzzy groups and group homomorphisms, Fuzzy Sets and Systems, 81, (1996) [24] Souriar Sebastian, A characterization of translation invariant properties of fuzzy groups, Alb.J. of Pure and App.Math., 1, (2002) [25] Souriar Sebastian, A new approach to Maschke s theorem, Alb.J.of Pure and App.Math., 2(1), (2003) [26] Souriar Sebastian, On RS integration with respect to MD functions, Alb.J.of Pure and App.Math., 2(2), (2003) [27] Souriar Sebastian, A rigorous proof of the fundamental theorem on fuzzy numbers, Alb.J. of Pure and App.Math., 3(1), (2004) [28] Souriar Sebastian, Sasigopalan, etc, Approximation studies on image enhancement using fuzzy techniques, Int.J. of Adv.Sci.& Tech., z 10, 11-26(2009) [29] Souriar Sebastian and Thampy Abraham, Fuzzification of Cayley s and Lagrange s theorems, J.Comp.&Math.Sci., 1(1), 41-46(2009) 110

4 [30] Souriar Sebastian, Sasigopalan, etc, Modified fuzzy basis function and function approximation, J.Comp.&Math.Sci., 1(2), (2010) [31] Souriar Sebastian and George Mathew, On a certain class of fuzzy ideals leading to discrete valuation rings, J.Comp. & Math.Sci., 1(6), (2010) [32] Souriar Sebastian and George Mathew, On valuation fuzzy ideals of rings, Ultra Scientist, 22(3), (2010) [33] Souriar Sebastian and Thampy Abraham, On injective fuzzy G-modules, Ultra Scientist, 22(3), (2010) [34] Souriar Sebastian and Thampy Abraham, On fuzzy representations of fuzzy G-modules, J.Comp.&Math.Sci., 1(5), (2010) [35] Souriar Sebastian and Thampy Abraham, A fundamental theorem of fuzzy representations, Alb.J.of Pure and App. Math., 9(2), (2010) [36] Souriar Sebastian and George Mathew, Local fuzzy ideals and P-fuzzy ideals, Alb.J. of Pure and App.Math.,9(2), (2010) [37] Souriar Sebastian and George Mathew, Equivalence of certain class of fuzzy ideals and real valuation rings, J.Comp.&Math. Sci., 2(1), 51-60(2011) [38] Souriar Sebastian and George Mathew, Fuzzy ideals of integral domains, Ultra Scientist, 23(1), (2011) 111

5 [39] Souriar Sebastian and George Mathew, P-fuzzy modules, Ultra Scientist, 23(2), (2011) [40] Souriar Sebastian and George Mathew, Multiples of fractionary fuzzy ideals of integral domains, J.Comp. & Math.Sci., 2(3), (2011) [41] Souriar Sebastian and George Mathew, Fuzzy decomposition of fuzzy ideals of PID, Ultra Scientist, 23(3) (2011) [42] Souriar Sebastian and George Mathew, Cyclic P-fuzzy modules over Dedekind domains, J.Comp.&Math.Sci., 2(5), (2011) [43] Souriar Sebastian, V.M.Mary etc., On fuzzy ideals and rings, J.Comp.&Math.Sci., 3(1), (2012) [44] Souriar Sebastian and Shery Fernandez, A fuzzy technique for traffic solution, J.Comp.&Math.Sci., 3(1), 37-46(2012) [45] Souriar Sebastian and James Philip, Similarity measure for intuitionistic fuzzy sets: An intuitionistic approach, J.Comp. & Math.Sci., 3(1), (2012) [46] Souriar Sebastian and James Philip, A method of medical diagnosis using intuitionistic fuzzy sets, Ultra Scientist, 24(1), (2012) [47] Souriar Sebastian and Shery Fernandez, On pseudo fuzzy complements of fuzzy sets and the existence of equilibrium and dual points, Ultra Scientist, 24(1), 87-90(2012) 112

6 [48] Souriar Sebastian and Prathish Abraham, Semi-simple fuzzy G-modules, J.Comp.Math.Sci., 3(4), (2012) [49] Souriar Sebastian,V.M.Mary etc., On Q-fuzzy prime ideals of Q-rings, Ultra Scientist, 24(2) (2012) [50] Souriar Sebastian and George Mathew, On level fuzzy and valuation fuzzy ideals of rings, J.Fuzzy Math., 20(3), (2012) [51] Souriar Sebastian,Alexander Mendez and Divya Mary Daise.S, On some categories of L-fuzzy groups, J.Comp. & Math.Sci., 3(6), (2012). [52] Souriar Sebastian,Alexander Mendez and Divya Mary Daise.S, On the maximal lattice of finite cyclic groups, J.Ult.Sci.Phy.Sci. (To appear) [53] Souriar Sebastian,Alexander Mendez and Divya Mary Daise.S, A method of construction of maximal lattice of infinite cyclic groups, J.Comp. & Math.Sci. (To appear). [54] Souriar Sebastian, Alexander Mendez and Divya Mary Daise.S, The Category L-FCyc, J.Ult.Sci.Phy.Sci.(To appear). [55] Souriar Sebastian,Alexander Mendez and Divya Mary Daise.S, On isomorphisms in the category L-FCyc (Communicated). [56] Souriar Sebastian, Alexander Mendez and Divya Mary Daise.S, On the initial, final and zero objects and zero morphisms in the category L-FCyc (Communicated). 113

7 [57] Souriar Sebastian, Alexander Mendez and Divya Mary Daise.S, Yoneda Lemma in L-FCyc (Communicated). [58] Vijay K Khanna, Lattices and Boolean Algebras, Vikas Publishing House, New Delhi(2005) [59] Zadeh L.A., Fuzzy Sets, Information Control, 8, (1965) 114