Knowledge representation and reasoning with industrial application using interval-valued intuitionistic fuzzy Petri nets and extended TOPSIS

Fuzzy Petri nets (FPNs) have many successes in various applications as an important modeling technique for knowledge representation and reasoning. However, in the real world, the following conditions may make it difficult to precisely model knowledge based on current FPNs, including the cognitive nonconformity, fuzziness and uncertainty of experiential cognition of experts. In an effort to overcome the shortcomings of current FPNs, the interval-valued intuitionistic FPNs (IVIFPNs) are proposed based on interval-valued intuitionistic fuzzy sets (IVIFSs), IVIFSs hybrid averaging (IVIFSsHA) operator and extended TOPSIS (ETOPSIS). Combining with IVIFSsHA operator, an inference algorithm based on matrix operation is proposed to improve the efficiency of computing final truth values. In addition, an optimal alternative is determined based on the proposed ETOPSIS, in which intuitionistic information and fuzzy information can be considered simultaneously based on the proposed information collaborative entropy. Finally, a comparison test is presented to show the effectiveness of ETOPSIS. Moreover, a novel model for the identification of aluminum electrolysis cell condition is proposed based on IVIFPNs and ETOPSIS, and the application result shows that the proposed methods are efficient to deal with cognitive nonconformity and manage fuzziness and uncertainty of expert knowledge. These facts demonstrate the usefulness and advantages of the proposed methods in complex real-world applications.