Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30184
Deduction of Fuzzy Autocatalytic Set to Omega Algebra and Transformation Semigroup

Authors: Liew Siaw Yee, Tahir Ahmad

Abstract:

In this paper, the Fuzzy Autocatalytic Set (FACS) is composed into Omega Algebra by embedding the membership value of fuzzy edge connectivity using the property of transitive affinity. Then, the Omega Algebra of FACS is a transformation semigroup which is a special class of semigroup is shown.

Keywords: Fuzzy autocatalytic set, omega algebra, semigroup, transformation semigroup.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1083221

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 891

References:


[1] Kauffman, S. A. (1971). Cellular Homeostasis, Epigenesist and Replication in Randomly Aggregated Macromolecular Systems. Journal of Cybernetics. 1:71-96.
[2] Rossler, O. E. (1971). A System Theoretic Model of Biogenesis. Z. Naturforchung. 26b: 741-746.
[3] Jain, S. and Krishan, S. (1998). Autocatalytic Sets and the Growth of Complexity in an Evolutionary model. Physical Review Letters. 81- 5684-5687.
[4] Tahir, A., Sabariah, B., and Kharil, A. A., (2006). "Fuzzy Autocatalytic Set In Modeling An Incineration Process" Journal Fuzzy Set and System (submitted; Manuscript Id. No:FSS-D-06-00458).
[5] Sabariah, B. (2006). Modeling of Clinical Waste Incinerator Process Using Novel Fuzzy Autocatalytic Set: Manifestation of Mathematical Thinking. Universiti Teknologi Malaysia. Unpublished PhD Thesis.
[6] Plotkin, B. I., Greenglaz, L. Ja., Gvaramija, A. A. (1992). Algebraic Structures in Automata and Databases Theory. Singapore: World Scientific.
[7] Jain, S. and Krishan, S. (1999). Emergence and the Growth of Complexity Networks in an Adaptive Systems. Computer Physics Communications. 121-122: 116-121.
[8] Ding, C., He, X., Xiong, H., Peng, H. and Holbrook, S. R. (2006). Transitive Closure and Metric Inequality of Weighted Graphs: Detecting Protein Interaction Modules Using Cliques. Int. J. Data Mining and Bioinformatics. 1(2): 162-177
[9] Eilenberg, S. (1976). Automata, languages, and machines. vol B. New York: Academic Press.