Multiset relations and multigroups under tn-norm

Subject Areas : Statistics

Hossein Naraghi ¹ , Saeed Mirvakili ² , Peyman Ghiasvand ³

1 - Department of Mathematics, Payame Noor University, Tehran, Iran
2 - Department of Mathematics, Payame Noor University, Tehran, Iran
3 - Department of Mathematics, Payame Noor University, Tehran, Iran

Received: 2020-10-02 Accepted : 2020-12-07 Published : 2021-07-23

Keywords: چندمجموعه, tn-نرم, گروه, چندگروه, رابطه‌ی چندمجموعه‌ای,

Abstract :

Multi Set Relations and Multi Groups under Tn-norm(ABSTRACT)In this paper , first we introduce the properties and theorems of the multi groups . After , we describe the results of the isomorphisms in multi groups , We show that how a multi group can be generated another non constant multi group under a proper binary operator, , call it t n norm . In fact, under an arbitrary t n norm to a multi group, we obtain the other multi group and examine their interactions . We use this process to generate a non constant multi group of a multi set relation under an arbitrary t n norm . We also present at the end an application of the concepts presented for generating usage encryption .K E Y W O R D S : Group , Multi set , Multi set relation , Multi group , T n norm .

References:

[1] J. A. Awolola and A.M. Ibrahim, Some results on multigroups, Quasi. Related Systems 24(2): 169- 177(2016)

[2] W.D. Blizard, Multiset theory, Notre Dame J. of Formal Logic, 30:36- 66(1989)

[3] W.D. Blizard, The development of multiset theory, Modern Logic, 1: 319-352(1991)

[4] C. Brink, Multisets and the Algebra of Relevance Logic. The Journal of Non-Classical Logic, (1): 1-21 (1988)

[5] M. Dresher and O. Ore, Theory of multigroups, American J. Math., 60: 705-733(1938)

[6] A.M. Ibrahim and P.A. Ejegwa, A survey on the concept of multigroup theory, J. Nigerian Asso. Mathl. Physics 38: 75- 89(2016)

[7] L. Mao, Topological multigroups and multifields, Int. J. Math. Combin., 1: 8-17(2009)

[8] R. K. Meyer, and M. A. McRobbie, On multisets and relevant implication I and II. Australasian Journal of Philosophy, 60: 107-139(1982)

[9] S. K. Nazmul, P. Majumdar and S.K. Samantha, On Multisets and Multigroups, Annals of Fuzzy Mathematics and Informatics, 6(3): 643-656(2013)

[10] W. Penowitz, Projective geometries as multigroups, American J. Math., 65: 235-256:(1943)

[11] B.M. Schein, Multigroups, J. Algebra 111: 114-132(1987)

[12] D. Singh, A.M. Ibrahim, T. Yohanna, and J.N. Singh, An overview of the applications of multisets, Novi Sad J. Math. 37(2): 73-92 (2007)

[13] G. Silvia, J. Pantovic and V. Gradimir, Binary relations and algebras on multisets. Publications de L’Institute Mathematique, Nouvelle serie, tome 95(109): 111-117(2014)

[14] D. Singh, A Note on the Development of Multiset Theory. Modern Logic, 4: 405-406(1994)

[15] D. Singh, A. M. Ibrahim, T. Yohanna and J.N. Singh, An Overview of Applications of Multisets. Novi Sad Journal of Mathematics, 37(2): 73-92(2007)

[16] D. Singh, A. M. Ibrahim, T. Yohanna and J.N. Singh, A Systemization of Fundamentals of Multiset. Lecturas Matematicas, 29:33-48(2008)

[17] A. Syropoulous, Mathematics of multisets, Springer-Verlag Berlin Heidelberg (2001)

[18] Y. Tella and S. Daniel, A study of group theory in the context of multiset theory, Int. J. Sci. Tech. 2(8): 609-615(2013)

[19] Y. Tella and S. Daniel, Symmetric groups under multiset perspective, IOSR J. Math. 7 (5), 47-52(2013)

[20] N.J. Wildberger, A new look at multisets, School of Mathematics, UNSW Sydney 2052, Australia, (2003)

[21] نظام الدین فقیه، سیستم­های پویا: اصول و تعین هویت، شابک 7-806-459-964-978، (1393)

[22] نظام الدین فقیه، مبانی شبیه­سازی سیستم­ها، شابک 964-6810-06-3، (1378)