Deduction of Fuzzy Autocatalytic Set to Omega Algebra and Transformation Semigroup

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.

Authors:

• Liew Siaw Yee
• Tahir Ahmad

Keywords:

• Fuzzy autocatalytic set
• omega algebra
• semigroup
• transformation semigroup.

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 Unpublished PhD Thesis.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.