Extended evidential cognitive maps and its applications

Evidential cognitive maps (ECMs) are uncertain graph structure for describing causal reasoning through the cognitive maps (CMs) and Dempster-Shafer (D-S) theory, and utilize the basic probability assignments (BPAs) and intervals to denote connections among concepts and the state of concepts, respectively. ECMs have been proved effective and convenient in modeling those systems with both subjective and objective uncertainty. However, ECMs may get unreasonable results in system modeling when facing the problem of combining knowledge. To overcome the drawbacks of ECMs, we present extended evidential cognitive maps (EECMs) based on evidential reasoning (ER) theory, distance measure and convex optimization for the development of ECMs. In contrast with ECMs, in the EECMs, the default connections are redefined, a scheme of combining knowledge is established through the ER theory, and a convex-optimization-based approach is proposed for determining the weights of different EECMs. Both theoretical analysis and numerical examples indicate that EECMs not only develop ECMs, but also can overcome the limitations suffered by ECMs and other high-order cognitive maps including fuzzy grey cognitive maps (FGCMs), interval-valued fuzzy cognitive maps (IVFCMs) and intuitionistic fuzzy cognitive maps (IFCMs).