MULTI-FUZZY SET RELATIONAL STRUCTURES
Keywords:
Relations, Sets, power multi-fuzzy, partial order
Abstract
In this paper, the concepts of multi-fuzzy set relational structures were introduced and some of their properties were presented. Relations were established on both the class of multi-fuzzy sets and on the power multi-fuzzy set of a given multi-fuzzy set. It is demonstrated that as relation on the latter turn out to be a linear order, relations on the former were only partial orders. Some related results were also presented.
References
Blizard, W. (1989). Multiset theory, Notre Dame Journal of formal logic, 30, 36–66.
Blizard, W. (1991). The development of multiset theory. Modern Logic, 1, 319-352.
Grefen, P. W. P. J. and de By, R. A. (1994). A multiset extended relational algebra: A formal approach to a practical issue. In: 10th International Conference on Data Engineering (ICDE), Houston, TX, USA, 80-88.
Girish, K. P. and Sunil, J. J. (2009). General relations between partially ordered multisets and their chains and antichains, Mathematical Communications, 14 (2) 193-205.
Hickman, J. L. (1980). A Note on the concept of Multiset. A bulletin of the Australian Mathematical society, 22, 211 – 217.
Isah, A. I. (2019). Soft multiset in a new perspective, Annals of Fuzzy Mathematics and Informatics, 18 (3) 309-315.
Klir, G. J. and Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, NJ.
Molodtsov, D. (1999). Soft set theory-First results, Computers Mathematics with Applications, 37 (4/5) 19-31.
Pawlak, Z. (1982). Rough Set, International Journal of computer and Information Science, 11 (5) 341-356.
Singh, D., Ibrahim, A, M., Yohanna, T. and Singh, J. N. (2007). An Overview of the Applications of Multisets. Novi Sad Journal of Mathematics, 2(37) 73–92.
Singh, D. and Isah, A. I. (2014). Prefixes, Suffixes and Substrings in a Multilanguage: A Perspective, Applied Mathematical Sciences, 8 (127) 6325 – 6339.
Singh, D., Alkali, A. J. and Isah, A. I. (2014). Some applications of α-cuts in fuzzy multiset theory, Journal of Emerging Trends in Computing and Information Sciences 5 (4) 328- 335.
Singh, D., Alkali, A. J. and Isah, A. I. (2015). An extension of the properties of inverse α-cuts to fuzzy multisets, Annals of Fuzzy Mathematics and Informatics, 9 (6) 917-923.
Singh, D. and Isah, A. I. (2016). Mathematics of multisets: a unified approach, Afrika Matematika, Springer, 27, 1139–1146.
Syropoulos, A. (2006). Fuzzifying P systems, The Computer Journal, 49 (5) 619-628.
Yager, R. R. (1986). On the theory of bags, International Journal of General Systems 13, 23–37.
Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8, 338-353.
Blizard, W. (1991). The development of multiset theory. Modern Logic, 1, 319-352.
Grefen, P. W. P. J. and de By, R. A. (1994). A multiset extended relational algebra: A formal approach to a practical issue. In: 10th International Conference on Data Engineering (ICDE), Houston, TX, USA, 80-88.
Girish, K. P. and Sunil, J. J. (2009). General relations between partially ordered multisets and their chains and antichains, Mathematical Communications, 14 (2) 193-205.
Hickman, J. L. (1980). A Note on the concept of Multiset. A bulletin of the Australian Mathematical society, 22, 211 – 217.
Isah, A. I. (2019). Soft multiset in a new perspective, Annals of Fuzzy Mathematics and Informatics, 18 (3) 309-315.
Klir, G. J. and Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, NJ.
Molodtsov, D. (1999). Soft set theory-First results, Computers Mathematics with Applications, 37 (4/5) 19-31.
Pawlak, Z. (1982). Rough Set, International Journal of computer and Information Science, 11 (5) 341-356.
Singh, D., Ibrahim, A, M., Yohanna, T. and Singh, J. N. (2007). An Overview of the Applications of Multisets. Novi Sad Journal of Mathematics, 2(37) 73–92.
Singh, D. and Isah, A. I. (2014). Prefixes, Suffixes and Substrings in a Multilanguage: A Perspective, Applied Mathematical Sciences, 8 (127) 6325 – 6339.
Singh, D., Alkali, A. J. and Isah, A. I. (2014). Some applications of α-cuts in fuzzy multiset theory, Journal of Emerging Trends in Computing and Information Sciences 5 (4) 328- 335.
Singh, D., Alkali, A. J. and Isah, A. I. (2015). An extension of the properties of inverse α-cuts to fuzzy multisets, Annals of Fuzzy Mathematics and Informatics, 9 (6) 917-923.
Singh, D. and Isah, A. I. (2016). Mathematics of multisets: a unified approach, Afrika Matematika, Springer, 27, 1139–1146.
Syropoulos, A. (2006). Fuzzifying P systems, The Computer Journal, 49 (5) 619-628.
Yager, R. R. (1986). On the theory of bags, International Journal of General Systems 13, 23–37.
Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8, 338-353.
Published
2020-04-17
How to Cite
IsahA. I. (2020). MULTI-FUZZY SET RELATIONAL STRUCTURES. FUDMA JOURNAL OF SCIENCES, 4(1), 662 - 667. Retrieved from https://fjs.fudutsinma.edu.ng/index.php/fjs/article/view/96
Section
Research Articles
Copyright (c) 2020 FUDMA JOURNAL OF SCIENCES
FUDMA Journal of Sciences
