International Journal of Mathematics Trends and Technology
Volume 48 | Number 5 | Year 2017 | Article Id. IJMTT-V48P548 | DOI : https://doi.org/10.14445/22315373/IJMTT-V48P548
In this paper a new definition of fuzzy ring and field with binary operations on the set of discrete fuzzy numbers are defined. Some properties related to these concepts are investigated.
[1] S.Abdullah.M.Aslam,T.A. Khan and M.Naeem, A new type of fuzzy normal subgroups and fuzzy cosets,Journal of Intelligent and Fuzzy Systems 25(2013),37-47.
[2] S.Abdullah.M.Aslam and K.Hila, A new generalization of fuzzy bi-ideals in semigroups its Applications in fuzzy finite state machines, Multiple-Valued Logic and Soft Computing 24 (2015),599-623.
[3] S.Abdullah,N-dimensional(;)Fuzzy Ideals of hemirings, International journal of Machine Learning and Cybernetics5 (2014),635-645.
[4]S.Abdullah.M.Aslam and H.Hedayathi,Interval valued intuitionstic fuzzy ideals in hemirings, Journal of Intelligent and fuzzy Systems 26 (2014),2873-2888.
[5] H.Aktaÿs and Cÿaćgman, Atype of fuzzy ring ,Arch Math Logic 46 (2007), 165-177.
[6] J.J. Buckley ,” Fuzzy complex numbers” Fuzzy Sets and Systems,33(1989), 333-345,1989.
[7]S.S.L.Chang , and L.A.Zadeh,” On fuzzy mapping and control ”, IEEE Trans Man Cybernet., 2(1972),30-34.
[8] Diamond.D and Kloeden, “Metric space of fuzzy sets”, Fuzzy Sets and Systems,100(1999), 63-71.
[9] K.A.Dib,N.Gaalhum and A.AM.Hassan,Fuzzy ring and fuzzy ideals,Fuzzy Math 4(2)(1996),245-261.
[10] Dubois and Prade .H “Operations on fuzzy numbers”,Internet J Systems,9(1978),613-626.
[11] D.Dubois and H.Prade,Fuzzy Sets Systems: Theory and Applications,1998.
[12] Goetschel R. andW.Voxman, “Elementry calculus”,Fuzzy Sets and Systems,18(1986),31-43.
[13] K.Hila and S.Abdullah,A study on intuitionistic fuzzy sets in semihypergroups, Journal of Intelligent and Fuzzy Systems 26(2014),1695-1710.
[14]G.J.Klir and B.Yuan,Fuzzy sets and Fuzzy Logic:theory and applications,Prentice-Hall PTR, Upper Saddlie River,1995.
[15]W.Liu,Fuzzy invariant subgroups and fuzzy ideals,Fuzzy Sets and Systems (1982),133-139.
[16] D.S.Malik and J.N. Mordeson,Fuzzy commutative Algebra, World Scientific Publishing, Singapore,1998.
[17] D.S.Malik and J.N.Mordeson, Fuzzy relations on rings and groups. Fuzzy Setsand Systems 43(1991),117-123.
[18] Y.C.Ren,Fuzzy Ideals and quotient rings,Fuzzy math 4(1985).19-26
[19] A.Rosenfield,Fuzzygroups,J Math Anal Appl35 (1971), 512-517
[20] VoxmanW ,”canonical representations of dicrete fuzzy numbers”, Fuzzy Sets and Systems 11(2001), 457-466.
[21] Wang Guixiang, Li Youming and Wen Chenglin, “On fuzzy n- cell numbers and n- dimension fuzzy vectors”, Fuzzy Sets and Systems, 158(2007), 71-84.
[22] WangGuixiang,Wu Cong and Chunhui Zhao, “Representation and Operations of Discrete Fuzzy Numbers”, Southeast Asian Bulletin of Mathematics, 28(2005),1003-1010.
[23] Wang Guixiang, and Wu Congxin, “ Fuzzy n-cell numbers and the differential of fuzzy n-cell number valuemappings”,Fuzzy Sets and Systems,130(2002), 367-381.
[24] X.Yuan and E.S.Lee, Fuzzy group based on fuzzy binary operational, Comput Math App 47 (2004), 631-641.
Thangaraj Beaula, B. Johnson, "Some Algebraic Concepts on Discrete Fuzzy Numbers," International Journal of Mathematics Trends and Technology (IJMTT), vol. 48, no. 5, pp. 321-329, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V48P548
PDF 
Abstract 
Keywords 
References 
Citation