Fuzzy Cognitive Maps Based on D-Number Theory

Abstract

In real life, there will be a lot of uncertainty problems, one of which is due to the vagueness of the concept of things, that is, it is difficult to determine whether an object conforms to this concept. This situation widely exists in some states, phenomena, parameters and interrelationships between things. For such uncertain events with heavy subjective influencing factors and incomplete data, it is suitable to use fuzzy methods to deal with them. In present our work, we firstly introduce the notion of D-number cognitive maps (DCMs), which are intelligent framework models based on D-number theory and cognitive maps. Compared with Evidential Cognitive Maps (ECMs) and Fuzzy Cognitive Maps (FCMs), DCMs can fuse multiple sources of information with uncertainty and construct a cognitive map model with incomplete and conflicting information. To better solve the problem of knowledge combination, D-number fuzzy cognitive maps (DFCMs) are also constructed based on D-number theory and fuzzy cognitive maps. In many practical applications, the establishment of fuzzy cognitive maps is usually completed by using a simple arithmetic average method for multiple experts to obtain comprehensive fuzzy cognitive maps. This simple processing method may lead to the loss of some important information so that the synthesized results do not reflect reality. To overcome this challenge, we synthesize the knowledge of multiple experts by using D-number theory and the characteristics of the representation of expert knowledge in FCMs. It is based on expert knowledge, and the synthesized reliability distribution function is used as the basis of final weight synthesis.