Fuzzy relational equations play an important role in fuzzy set theory and fuzzy logic systems, from both of the theoretical and practical viewpoints. The notion of fuzzy relational equations is associated with the concept of "composition of binary relations." In this survey paper, fuzzy relational equations are studied in a general lattice-theoretic framework and classified into two basic categories according to the duality between the involved composite operations. Necessary and sufficient conditions for the solvability of fuzzy relational equations are discussed and solution sets are characterized by means of a root or crown system under some specific assumptions.

A survey on fuzzy relational equations, part I: classification and solvability

Human gait modeling consists of studying the biomechanics of this human movement. Its importance lies in the fact that its analysis can help in the diagnosis of walking and movement disorders or rehabilitation programs, among other medical situations. Fuzzy finite state machines can be used to model the temporal evolution of this type of phenomenon. Nevertheless, the definition of details of the model in each particular case is a complex task for experts. In this paper, we present an automatic method to learn the model parameters that are based on the hybridization of fuzzy finite state machines and genetic algorithms leading to genetic fuzzy finite state machines. This new genetic fuzzy system automatically learns the fuzzy rules and membership functions of the fuzzy finite state machine, while an expert defines the possible states and allowed transitions. Our final goal is to obtain a specific model for each person's gait in such a way that it can generalize well with different gaits of the same person. The obtained model must become an accurate and human friendly linguistic description of this phenomenon, with the capability to identify the relevant phases of the process. A complete experimentation is developed to test the performance of the new proposal when dealing with datasets of 20 different people, comprising a detailed analysis of results, which shows the advantages of our proposal in comparison with some other classical and computational intelligence techniques.

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K. Peeva

Papers

Fuzzy automata and languages: theory and applications