### Uncertain Relations on a Finite Set and their Properties

Received: 9 September 2014     Accepted: 13 October 2014     Published: 20 October 2014
Abstract

There exists some relationships which are difficult to be simply measured by “yes” or “no" in practice, and there must be a certain amount to indicate the extent of this relationship between the two elements. In this paper, the property of the uncertain relations is examined by the uncertainty theory. Firstly it offers the definition of uncertain relation and the concept of property index of the uncertain relation based on uncertain theory; secondly it gives the calculation method of the property index of the uncertain relation; finally, a simple example is presented to illustrate the method.

Keywords

Uncertain Relation, Property Index, Uncertainty Theory

References
 [1] Bernard Kolman, Robert C.Busby, Sharon Cutler Ross, Discrete Mathematical Structures, Fifth Edition, Pearson Education, Inc.,2004. [2] Kenneth H. Rosen, Discrete Mathematics and Its Applications, Sixth Edition, The McGraw-Hill Companies, Inc.,2007. [3] SU Y.F.,The Random Structure of Relation and Applications. Acta Analysis Functional is Applicata 5（2003）,351-355. [4] Regenwetter M., Marley A.A.J., Random Relations, Random Utilities, and Random Functions, Journal of Mathematical Psychology, 45(2001), 864-912. [5] Zadeh L.A. Fuzzy sets. Information and Control, 8（1965）,338～353. [6] Ovchinnikov S., Aggregating transitive fuzzy binary relations. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 1992, 3: 47～55. [7] Beliakov G., Definition of general aggregation operators through similarity relations. Fuzzy Sets and Systems,2000, 114: 437～453. [8] Liu B., Uncertainty Theory, 2nd ed., Springer-Verlag, Berlin, 2007. [9] Liu B., Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer-Verlag, Berlin, 2010. [10] Liu B., Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems,vol.2, no.1, 3-16, 2008. [11] Liu B, Uncertain Set Theory and Uncertain Inference Rule with Application to Uncertain Control, Journal of Uncertain Systems, Vol. 4, No. 2, 83-98, 2010. [12] Liu B., Theory and Practice of Uncertain Programming, 2nd ed., Springer-Verlag, Berlin,2009. [13] Gao XL, Gao Y., Connectedness Index of Uncertainty Graphs, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol.21, no.1, 127-137, 2013. [14] Gao X.L. Tree Index of Uncertain Graph. Technical Report,2012. http://orsc.edu.cn/online/120707.pdf. [15] Gao X.L. Cycle Index of Uncertain Graph. Information: an International Interdisciplinary Journal, vol.16,no.2A, 1131-1138,2013. [16] Gao X., Some properties of continuous uncertain measure, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol.17, no.3, 419-426, 2009. [17] Gao X., Gao Y. and Ralescu D., On Liu’s Inference Rule for Uncertain Systems, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol.18, no.1, 1-11,2010. [18] You C., Some convergence theorems of uncertain sequences, Mathematical and Computer Modelling, vol.49, no.3-4, 482-487, 2009. [19] Liu B, Uncertainty Theory, 5thed.,http://orsc.edu.cn/liu/ut.pdf. [20] Liu, B., Some research problems in uncertainty theory, Journal of Uncertain Systems, Vol.3, No.1, 3-10,2009. [21] Li, M.X., Judgment methods on the properties of relation in discrete mathematics, College Mathematics,Vol.26, No.5,203-206,2010.
• APA Style

Xiulian Gao. (2014). Uncertain Relations on a Finite Set and their Properties. Pure and Applied Mathematics Journal, 3(6-1), 13-19. https://doi.org/10.11648/j.pamj.s.2014030601.13

ACS Style

Xiulian Gao. Uncertain Relations on a Finite Set and their Properties. Pure Appl. Math. J. 2014, 3(6-1), 13-19. doi: 10.11648/j.pamj.s.2014030601.13

AMA Style

Xiulian Gao. Uncertain Relations on a Finite Set and their Properties. Pure Appl Math J. 2014;3(6-1):13-19. doi: 10.11648/j.pamj.s.2014030601.13

• @article{10.11648/j.pamj.s.2014030601.13,
author = {Xiulian Gao},
title = {Uncertain Relations on a Finite Set and their Properties},
journal = {Pure and Applied Mathematics Journal},
volume = {3},
number = {6-1},
pages = {13-19},
doi = {10.11648/j.pamj.s.2014030601.13},
url = {https://doi.org/10.11648/j.pamj.s.2014030601.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2014030601.13},
abstract = {There exists some relationships which are difficult to be simply measured by “yes” or “no" in practice, and there must be a certain amount to indicate the extent of this relationship between the two elements. In this paper, the property of the uncertain relations is examined by the uncertainty theory. Firstly it offers the definition of uncertain relation and the concept of property index of the uncertain relation based on uncertain theory; secondly it gives the calculation method of the property index of the uncertain relation; finally, a simple example is presented to illustrate the method.},
year = {2014}
}

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T1  - Uncertain Relations on a Finite Set and their Properties
AU  - Xiulian Gao
Y1  - 2014/10/20
PY  - 2014
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DO  - 10.11648/j.pamj.s.2014030601.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
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EP  - 19
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.s.2014030601.13
AB  - There exists some relationships which are difficult to be simply measured by “yes” or “no" in practice, and there must be a certain amount to indicate the extent of this relationship between the two elements. In this paper, the property of the uncertain relations is examined by the uncertainty theory. Firstly it offers the definition of uncertain relation and the concept of property index of the uncertain relation based on uncertain theory; secondly it gives the calculation method of the property index of the uncertain relation; finally, a simple example is presented to illustrate the method.
VL  - 3
IS  - 6-1
ER  -
Author Information
• College of Mathematical Sciences, Dezhou University, Dezhou, Shandong 253023, P. R. China

• Sections