A study on multi-rational numbers forming a multi-field

International Journal of Mathematics Trends and Technology (IJMTT)
© 2020 by IJMTT Journal
Volume-66 Issue-5
Year of Publication : 2020
Authors : Debjyoti Chatterjee, S. K. Samanta


MLA Style:Debjyoti Chatterjee, S. K. Samanta  "A study on multi-rational numbers forming a multi-field" International Journal of Mathematics Trends and Technology 66.5 (2020):107-123. 

APA Style: Debjyoti Chatterjee, S. K. Samanta.(2020). A study on multi-rational numbers forming a multi-field International Journal of Mathematics Trends and Technology, 107-123.

In an attempt to develop multi number system, in this paper, we introduce a concept of multi-rational number system which forms a multi-field. It is also shown that the multi-rational number system is an extension of multi-integer system.

[1] S. Alkhazdah, A. R. Salleh and N. Hassan, Soft multiset theory, Appl. Math. Sci., 5 (72) (2011).
[2] L. Anderson, Combinatorics of finite sets, Clarendon Press, Oxford, 1987.
[3] K. T. Atanassov, Intuionistic fuzzy sets, Fuzzy sets and Systems, 20(1986) 87-96.
[4] Wayne D. Blizart, Multiset theory, Notre Dame Journal of formal logic, 30 (1) (1989) 36-66.
[5] K. Chakraborty, R. Biswas and S. Nanda, on Yager’s theory of bags and fuzzy bags, Compt. Artificial Intelligence, 18 (1) (1999) 1-17.
[6] Debjyoti Chatterjee and S.K. Samanta, An axiomatic development of multi-natural numbers, International Journal of Mathematics Trends and Technology (IJMTT), 48 (2) (2017) 136-146.
[7] Debjyoti Chatterjee and S.K. Samanta, A study on multi-integers forming a multi-integral domain, Annals of Fuzzy Mathematics and Informatics, Volume 15, No. 2. (April 2018) pp. 149-167.
[8] G. F. Clements, On multiset k-families, Discrete Mathematics, 69 (2) (1988) 153-164.
[9] A. Bronselaer, D. V. Birtosm and G. D. Tre, A framework for multiset merging, Fuzzy Sets and Systems, 191 (2012) 1-20.
[10] N. G. De Bruijin, Denumerations of rooted trees and multisets, Discrete Appl. Math., 6 (1) (1983) 25-33.
[11] N. Dershowith and Z. Manna, Proving termination with multiset orderings, Comm. ACM, 22 (1979) 465-476.
[12] K. P. Girish and S. J. John, Multiset topologies induced by multiset relations, Information Sciences, 188 (0) (2012) 298-313.
[13] K. P. Girish and S. J. John, On multiset topologies, Theory and Applications of Mathematics and Computer Science, 2 (1) (2012) 37-52.
[14] A. Hallez, A. Bronselaer and G. D. Tre, Comparison of sets and multisets, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems, 17 (Suppl. 1) (2009) 153-172.
[15] J. L. Hickman, A note on the concept of multiset, Bull. Austral. Math. Soc., 22 (2) (1980) 211-217.
[16] S. P. Jena, S. K. Ghosh and B. K. Tripathy, On the theory of Bags and lists, Information Sciences, 132 (14) (2001) 241-254.
[17] D. E. Knuth, The art of computer programming, Volume 2 p. 636 – Seminumerical Algorithms, Second Edition – Wesley, Reading, Mass., 1981.
[18] B. Li, W. Peizhang and L. Xihui, Fuzzy bags with set-valued statistics, Comput. Math. Appl., 15 (1988) 3-39.
[19] P. Majumdar and S. K. Samanta, Soft multisets, J. Math. Comput. Sci, 2 (6) (2012) 1700-1711.
[20] S. Miyamoto, Operations for real-valued bags and bag relations, in ISEA-EUSFLAT, (2009) 612-617.
[21] Sk. Nazmul, P. Majumdar and S. K. Samanta, On multisets and multigroups, Ann. Fuzzy Math. Inform., 6 (3) (2013) 643-656.
[22] G. Paun and M. J. Perez-Jimenez, Membrane computing: brief introduction, recent results and applications, Bio Systems, 85 (2006) 11-22.
[23] T. K. Shinoj and Sunil Jacob John, Intuitionistic fuzzy multisets and its application in medical diagnosis, World Academy of Science, Engineering and Technology, 6 (2012) 01-28.
[24] D. Sing, A. M. Ibrahim, T. Yohanna and J. N. Singh, An overview of the applications of multisets, NOVI SAD J. MATH., 37 (3) (2007) 73-92.
[25] R. R. Yagar, On the theory of bags, Int. General Syst., 13 (1986) 23-37.

Multiset, Multi-natural number, Multi-integer, Multi-rational number, Multi-ring, Multi-integral domain, Multi-field.