Abstract: Evolution strategy (ES) is a well-known instance of evolutionary algorithms, and there have been many studies on ES. In this paper, the author proposes an extended ES for solving fuzzy-valued optimization problems. In the proposed ES, genotype values are not real numbers but fuzzy numbers. Evolutionary processes in the ES are extended so that it can handle genotype instances with fuzzy numbers. In this study, the proposed method is experimentally applied to the evolution of neural networks with fuzzy weights and biases. Results reveal that fuzzy neural networks evolved using the proposed ES with fuzzy genotype values can model hidden target fuzzy functions even though no training data are explicitly provided. Next, the proposed method is evaluated in terms of variations in specifying fuzzy numbers as genotype values. One of the mostly adopted fuzzy numbers is a symmetric triangular one that can be specified by its lower and upper bounds (LU) or its center and width (CW). Experimental results revealed that the LU model contributed better to the fuzzy ES than the CW model, which indicates that the LU model should be adopted in future applications of the proposed method.
Abstract: The author proposes an extension of genetic algorithm (GA) for solving fuzzy-valued optimization problems. In the proposed GA, values in the genotypes are not real numbers but fuzzy numbers. Evolutionary processes in GA are extended so that GA can handle genotype instances with fuzzy numbers. The proposed method is applied to evolving neural networks with fuzzy weights and biases. Experimental results showed that fuzzy neural networks evolved by the fuzzy GA could model hidden target fuzzy functions well despite the fact that no training data was explicitly provided.
Abstract: In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi, Gaussian quadratures for approximate of fuzzy integrals, Applied Mathematics and Computation 170 (2005) 874-885]. The obtained results are illustrated by solving some numerical examples.
Abstract: The join dependency provides the basis for obtaining
lossless join decomposition in a classical relational schema. The
existence of Join dependency shows that that the tables always
represent the correct data after being joined. Since the classical
relational databases cannot handle imprecise data, they were
extended to fuzzy relational databases so that uncertain, ambiguous,
imprecise and partially known information can also be stored in
databases in a formal way. However like classical databases, the
fuzzy relational databases also undergoes decomposition during
normalization, the issue of joining the decomposed fuzzy relations
remains intact. Our effort in the present paper is to emphasize on this
issue. In this paper we define fuzzy join dependency in the
framework of type-1 fuzzy relational databases & type-2 fuzzy
relational databases using the concept of fuzzy equality which is
defined using fuzzy functions. We use the fuzzy equi-join operator
for computing the fuzzy equality of two attribute values. We also
discuss the dependency preservation property on execution of this
fuzzy equi- join and derive the necessary condition for the fuzzy
functional dependencies to be preserved on joining the decomposed
fuzzy relations. We also derive the conditions for fuzzy join
dependency to exist in context of both type-1 and type-2 fuzzy
relational databases. We find that unlike the classical relational
databases even the existence of a trivial join dependency does not
ensure lossless join decomposition in type-2 fuzzy relational
databases. Finally we derive the conditions for the fuzzy equality to
be non zero and the qualification of an attribute for fuzzy key.