Iranian journal of fuzzy systems
Volume:12 Issue: 2, Apr 2015

In this paper, we introduce a Takagi-Sugeno (TS) fuzzy model which is derived from a typical Multi-Layer Perceptron Neural Network (MLP NN). At first, it is shown that the considered MLP NN can be interpreted as a variety of TS fuzzy model. It is discussed that the utilized Membership Function (MF) in such TS fuzzy model, despite its flexible structure, has some major restrictions. After modifying the MF, we introduce a TS fuzzy model whose MFs are tunable near and far from focal points, separately. To identify such TS fuzzy model, an incremental learning algorithm, based on an efficient space partitioning technique, is proposed. Through an illustrative example, the methodology of the learning algorithm is explained. Next, through two case studies: approximation of a nonlinear function for a sun sensor and identification of a pH neutralization process, the superiority of the introduced TS fuzzy model in comparison to some other TS fuzzy models and MLP NN is shown.

In this paper the fuzzy structural reliability index was determined through modeling epistemic uncertainty arising from ambiguity in statistical parameters of random variables. The First Order Reliability Method (FORM) has been used and a robust genetic algorithm in the alpha level optimization method has been proposed for the determination of the fuzzy reliability index. The sensitivity level of fuzzy response due to the introduced epistemic uncertainty was also measured using the modified criterion of Shannon entropy. By introducing bounds of uncertainty, the fuzzy response obtained from the proposed method presented more realistic estimation of the structure reliability compared to classic methods. This uncertainty interval is of special importance in concrete structures since the quality of production and implementation of concrete varies in different cross sections in reality. The proposed method is implementable in reliability problems in which most of random variables are fuzzy sets and in problems containing non-linear limit state functions and provides a precise acceptable response. The capabilities of the proposed method were demonstrated using different examples. The results indicated the accuracy of the proposed method and showed that classical methods like FORM cover only special case of the proposed method.

In this paper we continue development of formal theory of a special class of fuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of the MTL-logic in which the basic connective is implication, the basic connective in EQ-logics is equivalence. Therefore, a new algebra of truth values called EQ-algebra was developed. This is a lower semilattice with top element endowed with two binary operations of fuzzy equality and multiplication. EQ-algebra generalizes residuated lattices, namely, every residuated lattice is an EQ-algebra but not vice-versa. In this paper, we introduce additional connective $logdelta$ in EQ-logics (analogous to Baaz delta connective in MTL-algebra based fuzzy logics) and demonstrate that the resulting logic has again reasonable properties including completeness. Introducing $Delta$ in EQ-logic makes it possible to prove also generalized deduction theorem which otherwise does not hold in EQ-logics weaker than MTL-logic.

The purpose of the present work is to introduce the concept of bifuzzy core of a fuzzy automaton, which induces a bifuzzy topology on the state-set of this fuzzy automaton. This is shown that this bifuzzy topology can be used to characterize the concepts such as bifuzzy family of submachines, bifuzzy separable family and bifuzzy retrievable family of a fuzzy automaton.

In this paper the fixed point theorem of Schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy Volterra integral equations. Then using some conditions the uniqueness of the solution is investigated.

In this paper, existence theorems for the fuzzy Volterra-Fredholm integral equations of mixed type (FVFIEMT) involving fuzzy number valued mappings have been investigated. Then, by using Banach's contraction principle, sufficient conditions for the existence of a unique solution of FVFIEMT are given. Finally, illustrative examples are presented to validate the obtained results.

In this paper, we introduce and study fuzzy variational-like inclusion, fuzzy resolvent equation and $H(cdot,cdot)$-$phi$-$eta$-accretive operator in real uniformly smooth Banach spaces. It is established that fuzzy variational-like inclusion is equivalent to a fixed point problem as well as to a fuzzy resolvent equation. This equivalence is used to define an iterative algorithm for solving fuzzy resolvent equation. Some examples are given.

In this paper a first step in classifying the fuzzy normal subgroups of a finite group is made. Explicit formulas for the number of distinct fuzzy normal subgroups are obtained in the particular cases of symmetric groups and dihedral groups.

In this paper, we use parametric form of fuzzy number, then an iterative approach for obtaining approximate solution for a class of nonlinear fuzzy Fredholm integro-differential equation of the second kind is proposed. This paper presents a method based on Newton-Cotes methods with positive coefficient. Then we obtain approximate solution of the nonlinear fuzzy integro-differential equations by an iterative approach.

In this paper, we extend the construction of a fuzzy subgroup generated by a fuzzy subset to $L$-setting. This construction is illustrated by an example. We also prove that for an $L$-subset of a group, the subgroup generated by its level subset is the level subset of the subgroup generated by that $L$-subset provided the given $L$-subset possesses sup-property.

In the present paper, we give a new approach to Caristi's fixed point theorem on non-Archimedean fuzzy metric spaces. For this we define an ordinary metric $d$ using the non-Archimedean fuzzy metric $M$ on a nonempty set $X$ and we establish some relationship between $(X,d)$ and $(X,M,ast)$%. Hence, we prove our result by considering the original Caristi's fixed point theorem.