Length and order of fuzzy autocatalytic set of a pressurized water reactor

Abstract

The pressurized water reactor (PWR) is one type of nuclear power plant that generates electricity using heat from nuclear reactions which use steam produced from heated water to spin large turbines that generate electricity. The PWR contains two systems namely primary and secondary systems. The secondary system of a PWR in a previous study cannot give information regarding the catalytic interaction and relation amongst each and every parameter in the system and unable to present all the possible catalytic reactions between the variables in the system. In this research, several structures of Fuzzy Graph Type-3 of Fuzzy Autocatalytic Set (FACS) of a secondary system of a PWR, namely possible paths, fuzzy edge connectivity, length, detour distance, order, and size are explored. Omega algebra is used to determine all the possible paths for a FACS with respect to its fuzzy edge connectivity, length, and detour distance. An algorithm is developed and coded to find all the possible paths of the PWR. Furthermore, the algorithm is extended to obtain more characteristics of the FACS system. A sample data from a secondary system of a PWR is then applied to the algorithm to obtain a total of 317 possible cycle paths and 243 possible non-cycle paths at a maximum length of five. In addition, based on the patterns of non-cycle paths of FACS graphs, new characteristics of FACS are obtained and proven in the form of lemma, theorem and corollaries. In summary, the finding in this study can be used to characterize FACS of a PWR as well as other applications.