João Paulo Carvalho

Truly qualitative modelling of qualitative dynamic systems is a delicate issue in a sense that even when one uses a "qualitative modelling tool" one often end up adopting quantitative model approaches in disguise. In this paper, we use rule based fuzzy cognitive maps to obtain and simulate a qualitative model of an economic system.

A wide range of applications can be identified for time series prediction, including energy systems planning, currency forecasting, or traffic prediction. Specifically, stock exchange operations can greatly benefit from efficient forecast techniques. Therefore, a number of different prediction approaches have been proposed such as linear models, feedforward neural network models, recurrent neural networks or fuzzy neural models. In this paper one presents a prediction model based on fuzzy rules that relate past data values with the next unknown value to be estimated. A fuzzy Boolean neural network has been used for this purpose, which has been applied to the Nasdaq index prediction. The results turned to be encouraging, namely on the percentage of correct up/down trend prediction.

This paper focuses on the rule based fuzzy cognitive maps (RB-FCM) potential to model the dynamics of qualitative real-world systems that include feedback links. It presents a general overview of RB-FCM and proposes a set of possible concepts and relations. It also provides guidelines to introduce time as an important qualitative entity of cognitive maps

Fuzzy Boolean Networks are Boolean networks with nature like characteristics, such as organization of neurons on cards or areas. random individual connections, structured meshes of links between cards. They also share with natural systems some interesting properties: relative noise immunity, capability of approximate reasoning and learning from sets of experiments. An interesting problem related with these nets is the number of different rules that they are able to capture front experiments, that is, their rule capacity. This work establishes a lower bound for this number, proving that it depends on the number of inputs per consequent neurons.

Time is essential in the study of system dynamics. When representing and analyzing the dynamics of complex quantitative systems, the problem of expressing the "effect" of time flow is naturally solved since the mathematical equations that describe the relations between the entities of the system are a function of time. However, if we are dealing with real world qualitative systems that are impossible or difficult to model using mathematical equations, then the use of natural language becomes the best tool to represent the system and expressing time influence becomes a real issue that has not been addressed before. This paper introduces a coherent procedure to implicitly represent time in rule based fuzzy cognitive maps which are a previously introduced methodology and tool to represent and simulate the dynamics of qualitative systems

In this paper one studies the learning behaviour of an entire rule base in fuzzy Boolean networks. It is analyzed the influence of a set of factors such as number of inputs per neuron, granularity of antecedent spaces and number of teaching experiments on learning effectiveness without cross influence between rules and on interpolation capabilities of the network. Both one dimensional problems and two dimensional problems are tested and results interpreted using theoretical results also presented.

Single input Fuzzy TPE systems, as proposed by Sudkamp and Hammel, allow a more efficient computational inference of a single input fuzzy rule base. This paper shows that it is possible to generalize single input Fuzzy TPE systems to 2-input systems, therefore extending its range of possible applications. The paper presents the details and proof of the extension validity, and shows benchmark results comparing the 2-input Fuzzy TPE with classical inference systems.

This paper shows how Rule Based Fuzzy Cognitive Maps can be useful to model qualitative socio-economic systems, by discussing and presenting a macroeconomic model that, although developed eight years ago and based on simple qualitative rules, described and predicted the current economic crisis when the policy behavior of the banking system regarding tax-rates was assumed similar to the one that

Fuzzy Cognitive Maps (FCM) have been around for more than twenty years, but the way how they have been used and the interpretation of their results are nowadays far from their original intended goal. This paper focus on discussing the structure, the semantics and the possible use of FCM as tools to model and simulate complex social, economic and political systems, while clarifying some issues that have been recurrent in published FCM papers.