BDD, BNN, and FPGA on Fuzzy Techniques for Rapid System Analysis

This paper looks at techniques to simplify data analysis of large multivariate military sensor systems. The approach is illustrated using representative raw data from a video-scene analyzer. First, develop fuzzy neural net relations using Matlab. This represents the best fidelity fit to the data and will be used as reference for comparison. The data is then converted to Boolean, and using Boolean Decision Diagrams (BDD) techniques, to find similar relations between input vectors and output parameter. It will be shown that such Boolean techniques offer dramatic improvement in system analysis time, and with minor loss of fidelity. To further this study, Boolean Neural Net techniques (BNN) were employed to bridge the Fuzzy Neural Network (FNN) to BDD representations of the data. Neural network approaches give an estimation method for the complexity of Boolean Decision Diagrams, and this can be used to predict the complexity of digital circuits. The neural network model can be used for complexity estimation over a set of BDDs derived from Boolean logic expressions. Experimental results show good correlation with theoretical results and give insights to the complexity. The BNN representations can be useful as a means to FPGA implementation of the system relationships and can be used in embedded processor based multi-variate situations

Fuzzy Maximum Satisfiability

In this paper, we extend the Maximum Satisfiability (MaxSAT) problem to {\L}ukasiewicz logic. The MaxSAT problem for a set of formulae {\Phi} is the problem of finding an assignment to the variables in {\Phi} that satisfies the maximum number of formulae. Three possible solutions (encodings) are proposed to the new problem: (1) Disjunctive Linear Relations (DLRs), (2) Mixed Integer Linear Programming (MILP) and (3) Weighted Constraint Satisfaction Problem (WCSP). Like its Boolean counterpart, the extended fuzzy MaxSAT will have numerous applications in optimization problems that involve vagueness.Comment: 10 page

Formalization of Human Categorization Process Using Interpolative Boolean Algebra

Since the ancient times, it has been assumed that categorization has the basic form of classical sets. This implies that the categorization process rests on the Boolean laws. In the second half of the twentieth century, the classical theory has been challenged in cognitive science. According to the prototype theory, objects belong to categories with intensities, while humans categorize objects by comparing them to prototypes of relevant categories. Such categorization process is governed by the principles of perceived world structure and cognitive economy. Approaching the prototype theory by using truth-functional fuzzy logic has been harshly criticized due to not satisfying the complementation laws. In this paper, the prototype theory is approached by using structure-functional fuzzy logic, the interpolative Boolean algebra. The proposed formalism is within the Boolean frame. Categories are represented as fuzzy sets of objects, while comparisons between objects and prototypes are formalized by using Boolean consistent fuzzy relations. Such relations are directly constructed from a Boolean consistent fuzzy partial order relation, which is treated by Boolean implication. The introduced formalism secures the principles of categorization showing that Boolean laws are fundamental in the categorization process. For illustration purposes, the artificial cognitive system which mimics human categorization activity is proposed