Fuzzy-petri-net reasoning supervisory controller and estimating states of markov chain models

Abstract

Abstract. Markov chain models are efficient tools for representing stochastic discrete event processes with wide applications in decision and control. A novel approach to fuzzy-Petri-net reasoning generated solution to initial or another state in Markov-chain models is proposed. Reasoning is performed by a fuzzy-Petri-net supervisory controller employing a fuzzy-rule production system design and a fuzzyPetri-net reasoning algorithm, which has been developed and implemented in C++. The reasoning algorithm implements calculation of the degrees of fulfilment for all the rules and their appropriate assignment to places of Petri net representation structure. The reasoning process involves firing active transitions and calculating degrees of fulfilment for the output places, which represent propositions in the knowledge base, and determining of fuzzy-distributions for output variables as well as their defuzzified values. Finally, these values are transferred to assign the state of Markov-chain decision model in terms of transition probabilities.

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“…see Zadeh, 1996Zadeh, , 2006Yager, 2004Yager, , 2006Kosko, 1993;Dimirovski, 2005Dimirovski, , 2008) the synergy of computational power available and of systems and control theory enabled new ways to systems engineering methodologies due to model developments exploiting combined qualitative (linguistic) information in addition to the quantitative (numerical) information as an alternative representation of non-linear and uncertain dynamical processes. The emerged soft-computing modelling techniques have particularly contributed to this paradigm of combined qualitative-quantitative information processing, which is generally intrinsic to all social systems.…”

A forward concurrent reasoning approach for rule-based systems using fuzzy colored Petri nets

“…Due to the graphic display and dynamic fuzzy reasoning, Fuzzy Petri nets (FPN) have been widely used in modeling [1][2] , inference [3][4][5] , diagnosis [3][4][6][7] , and learning [8][9] . Nevertheless, with the increase of the scale and complexity of a rule-based system, the reasoning efficient and reliability as well as modeling ability have become intractable issues.…”