The problem of sparse fuzzy rule bases is introduced. Because of the high computational complexity of the original compositional rule of inference (CRI) method, it is strongly suggested that the number of rules in a final fuzzy knowledge base is drastically reduced. Various methods of analogical reasoning available in the literature are reviewed. The mapping style interpretation of fuzzy rules ...

The concept of upper and lower semicontinuity of fuzzy mappings introduced by Bao and Wu [Y.E. Bao, C.X. Wu, Convexity and semicontinuity of fuzzy mappings, Comput. Math. Appl., 51 (2006) 1809–1816] is redefined by using the concept of parameterized triples of fuzzy numbers. On the basis of the linear ordering of fuzzy numbers proposed by Goetschel and Voxman [R. Goetschel, W. Voxman, Elementar...

Rule Based Fuzzy Cognitive Maps (RBFCM) are proposed as an evolution of Fuzzy Causal Maps (FCM) that allow a more complete representation of cognition, since relations other than monotonic causality are made possible. Their structure is based on traditional fuzzy systems with feedback. The main problem to solve while trying to implement a RBFCM is the causal relation itself, since traditional f...

In this paper, the relationships between semicontinuity and preinvexity of fuzzy mappings are investigated. The concepts of intermediate-point preinvex fuzzy mappings and weakly preinvex fuzzy mappings are first introduced, and the authors establish a characterization for a weakly preinvex fuzzy mapping in terms of its epigraph. In this context, a characterization of a preinvex fuzzy mapping in...

This paper focuses on the simulation of behavior for autonomous entities in virtual environments. The behavior of these entities must determine their responses not only to external stimuli, but also with regard to internal states. We propose to describe such behavior using fuzzy cognitive maps (FCM), whereby these internal states might be explicitly represented. This article presents the use of...

In this paper, we introduce a decomposition theory for fuzzy cognitive maps (FCMs). First, we partition the set of vertices of an FCM into blocks according to an equivalence relation, and by regarding these blocks as vertices we construct a quotient FCM. Second, each block induces a natural sectional FCM of the original FCM, which inherits the topological structure as well as the inference from...

In this paper we propose an extension to the Fuzzy Cognitive Maps (FCMs) that aims at aggregating a number of reasoning tasks into a one parallel run. The described approach consists in replacing real-valued activation levels of concepts (and further influence weights) by random variables. Such extension, followed by the implemented software tool, allows for determining ranges reached by concep...

In the last years, the increasing urbanization has constrained to face the dramatic growth of the urban waste production and the consequent socio-economical and environmental impact. The relevance of finding an optimal waste management further increases when it involves hazardous materials, since they represent a vulnerable infrastructure sector for homeland defense. Although there is a general...

A recently proposed swarm intelligence technique for Fuzzy Cognitive Map learning is described. The technique employs the Particle Swarm Optimization algorithm to minimize a proper objective function, whose global minimizers correspond to suboptimal weight matrices of the Fuzzy Cognitive Map. New instances of an industrial test problem are studied, justifying the usefulness of the technique as ...

A fuzzy cognitive map is a graphical means of representing arbitrarily complex models of interrelations between concepts. The purpose of this paper is to describe a fuzzy cognitive map based on the random neural network model called the random fuzzy cognitive map, and to illustrate its application in the modeling of process. This model is based on the probability of activation of the neurons/co...