Fuzzy autocatalytic set (FACS) as fuzzy vector space


  • Rossiana Edhelyn Universiti Teknologi Malaysia
  • Tahir Ahmad Universiti Teknologi Malaysia




FACS, Adjacency Matrix, Euclidean Distance Matrix, Fuzzy Vector Space


Dynamic model of clinical waste incineration process in Malacca has been successfully developed using Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph Type 3. FACS combines the concept of fuzzy graph and autocatalytic set and has been proven to yield more precise results than using crisp graph. Next, the graph of its process has been transformed from non-coordinated FACS to coordinated FACS in Euclidean space. Some mathematical structures related to the transformation are adjacency, transition and Laplacian matrices of FACS. Furthermore, it is found that FACS to be primitive, irreducible and aperiodic. The set of adjacency matrices of FACS of Fuzzy Graph Type 3 is predicted to be seen as fuzzy vector space, and the set of Euclidean distance matrices represent coordinated FACS is also expected to be fuzzy vector space as well. As a recently developed theory, FACS has great capabilities in generating new mathematical theories and structures that would enrich the theory itself. this study is made to attempt the formulation of new algebraic structure in FACS which is fuzzy vector space.


Tahir A., Sabariah B., and Khairil A. A. “Modeling a clinical waste incineration process using fuzzy autocatalytic set.” Journal of Mathematical Chemistry (2010), 47(4),1263-1273.

M. Blue et al., “Applications of Fuzzy Logic to Graph Theory.” Los Alamost National Laboratory (1997). LA-UR-96-4792

A. Rosenfeld. In Fuzzy Graph, ed. By. L.A. Zadeh et al. “Fuzzy set and their applications to cognitive and decision process.” New York (1975) : Academic Press.

R. T. Yeh, S. Y. Bang. in Fuzzy Relations,” Fuzzy Graphs and Their applications to Clustering Analysis.”, 1975.

S. Jain, S. Krishna, “Graph Theory and the Evolution of Autocatalytic Networks, 2002.

Sabariah B., Modeling of Clinical Waste Incineration Process using Novel Fuzzy Autocatalytic Set: A Manifestation of Mathematical Thinking.”PhD Thesis (2005), UTM.

S. Jain, S. Khrisna. 1998. “Autocatalytic sets and the growth of complexity in an evolutionary model.” Phys. Rev. Lett. 81, 5684-5687

Sumarni A.B., “On the Structure of Fuzzy Autocatalytic Set of Fuzzy Graph Type-3.” PhD Thesis (2013), UTM.

S. Panayappan,”Fuzzy Linear Operator on Vector Spaces of Fuzzy Matrices”, Int. J. Contemp. Math. Sciences, Vol. 5, 2010, no. 13, 609-613