Research on Steady States of Fuzzy Cognitive Map and its Application in Three-Rivers Ecosystem

Zhen Peng,Lifeng Wu,Zhenguo Chen

doi:10.3390/su8010040

Abstract

Fuzzy Cognitive Map (FCM) offers many advantages such intuitive knowledge representation and fast numerical reasoning ability, etc. It suits modeling and decision-making of dynamic systems. With the aims to effectively help to analyze and control system sustainable evolution, the paper defines the steady states of fixed point and limited cycle of a FCM modeling system. Accordingly, the rules of steady states of the FCM model and the factors influencing the steady states are presented and proved. The Three-Rivers represents a system including population, ecological environment, social development and their relationships. Based on the relationships, the Three-Rivers ecosystem is modeled by FCM and the Three-Rivers ecosystemsustainable evolutionis analyzed bythe rules of the steady states of FCM.

Highlights

At present, there is an urgent need for a kind of intelligent tool to model dynamic systems for analysis and control
Over the last several years, a variety of Fuzzy Cognitive Map (FCM) have been used for representing knowledge and artificial intelligence in engineering applications, for instance infault detection [3], geographical information systems [4], social system modeling [5], medical decision-making [6], individual behaviors simulation [7], environmental management [8], etc
The second part [12,13,14,15] is used for system evaluation by the FCM inference mechanism, which focuses on the use of interactions between different concepts

Summary

Introduction

There is an urgent need for a kind of intelligent tool to model dynamic systems for analysis and control. The third part [16,17,18] is the state transformation of FCM, where the transforming rule and the transforming process of steady state are focused on. A, r1e]p, otshietivceo.ncepts arepoIsfittihvee.FCM transforms to a limited cycle, the system will return to the initial state. If initial states of all nodes in the FCM are zero and T = 0, it must transform toa zero fixedInpfoeirnent.ce 2. If initial states of all nodes in the FCM are zero and T = 0, it must transform toa zero fifixedIpnofeirnetn.ce Inference. The number of state transformations is twice the number of nodes whose states change in the FCM arriving ata limited cycle. The proofs of Inference 1–Inference 9 are shown in Appendix

The Application in Three-Rivers Ecosystem

FCM Modeling Three-Rivers EcosystemBased on NHL

Situation4

Findings

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