Iranian journal of fuzzy systems
Volume:10 Issue: 3, Jun 2013

The main purpose of this paper is to achieve improvement in the speed of Fuzzy Joint Points (FJP) algorithm. Since FJP approach is a basis for fuzzy neighborhood based clustering algorithms such as Noise-Robust FJP (NRFJP) and Fuzzy Neighborhood DBSCAN (FN-DBSCAN), improving FJP algorithm would an important achievement in terms of these FJP-based meth- ods. Although FJP has many advantages such as robustness, auto detection of the optimal number of clusters by using cluster validity, independency from scale, etc., it is a little bit slow. In order to eliminate this disadvantage, by im- proving the FJP algorithm, we propose a novel Modi ed FJP algorithm, which theoretically runs approximately n= log2 n times faster and which is less com- plex than the FJP algorithm. We evaluated the performance of the Modi ed FJP algorithm both analytically and experimentally.

In this article we found the solution of fuzzy linear controlled system with fuzzy initial conditions by using -cuts and presentation of numbers in a more compact form by moving to the eld of complex numbers. Next, a fuzzy optimal control problem for a fuzzy system is considered to optimize the expected value of a fuzzy objective function. Based on Pontryagin Maximum Principle, a constructive equation for the problem is presented. In the last section, three examples are used to show that the method in e ective to solve fuzzy and fuzzy optimal linear controlled systems.

In this paper, we introduce and study the concepts of $mathcal{I}_2$-convergence, $mathcal{I}_2^{*}$-convergence for double sequences of fuzzy real numbers, where $mathcal{I}_2$ denotes the ideal of subsets of $mathbb N times mathbb N$. Also, we study some properties and relations of them.

n this paper we study the Hyers-Ulam-Rassias stability of Cauchy equation in Felbin''s type fuzzy normed linear spaces. As a result we give an example of a fuzzy normed linear space such that the fuzzy version of the stability problem remains true, while it fails to be correct in classical analysis. This shows how the category of fuzzy normed linear spaces differs from the classical normed linear spaces in general.

The paper continues the study of the authors on relationships between emph{topological systems} of S.~Vickers and emph{attachments} of C.~Guido. We extend topological systems to emph{algebraically-topological systems}. A particular instance of the latter, called emph{attachment system}, incorporates the notion of attachment, thus, making it categorically redundant in mathematics. We show that attachment systems are equipped with an internal topology, which is similar to the topology induced by locales. In particular, we provide an attachment system analogue of the well-known categorical equivalence between sober topological spaces and spatial locales.

We present some model theoretic results for {L}ukasiewicz predicate logic by using the methods of continuous model theory developed by Chang and Keisler. We prove compactness theorem with respect to the class of all structures taking values in the {L}ukasiewicz $texttt{BL}$-algebra. We also prove some appropriate preservation theorems concerning universal and inductive theories. Finally, Skolemization and Morleyization in this framework are discussed and some natural examples of fuzzy theories are presented.

In this paper, we investigate the properties of some recently pro- posed fuzzy distance measures. We find out some shortcomings for these dis- tances and then the obtained results are illustrated by solving several examples and compared with the other fuzzy distances.

In this paper, our purpose is twofold. Firstly, the tensor and residuum operations on $L-$nested systems are introduced under the condition of complete residuated lattice. Then we show that $L-$nested systems form a complete residuated lattice, which is precisely the classical isomorphic object of complete residuated power set lattice. Thus the new representation theorem of $L-$subsets on complete residuated lattice is obtained. Secondly, we introduce the concepts of $L-$family and the system of $L-$subsets, then with the tool of the system of $L-$subsets, we obtain the representation theorem of intersection-preserving $L-$families on complete residuated lattice.

In this paper, we study the existence of extremal solutions for impulsive delay fuzzy integrodifferential equations in $n$-dimensional fuzzy vector space, by using monotone method. We show that obtained result is an extension of the result of Rodr''{i}guez-L''{o}pez cite{rod2} to impulsive delay fuzzy integrodifferential equations in $n$-dimensional fuzzy vector space.

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore, the Fundamental Homomorphism Theorem is established. Finally, it is proved that the class of all fuzzy convex lattice-ordered subgroups of a lattice-ordered group $G$ forms a complete Heyting sublattice of the lattice of fuzzy subgroups of $G$.