Iranian journal of fuzzy systems
Volume:12 Issue: 3, Jun 2015

This paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space Takagi-Sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. Lyapunov Krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the lower and upper delay bounds. Finally, numerical examples are provided to substantiate the theoretical results.

Ranking fuzzy numbers plays a main role in many applied models in real world and in particular decision-making procedures. In many proposed methods by other researchers may exist some shortcoming. The most commonly used approaches for ranking fuzzy numbers is based on defuzzification method. Many ranking fuzzy numbers cannot discriminate between two symmetric fuzzy numbers with identical core. In 2009, Abbasbandy and Hajjari proposed an approach for ranking normal trapezoidal fuzzy numbers, which computed the magnitude of fuzzy numbers namely ``Mag" method. Then Hajjari extended it for non-normal trapezoidal fuzzy numbers and also for all generalized fuzzy numbers. However, these methods have the weakness that we mentioned above. Moreover, the result is not consistent with human intuition in this case. Therefore, we are going to present a new method to overcome the mentioned weakness. In order to overcome the shortcoming, a new magnitude approach for ranking trapezoidal fuzzy numbers based on minimum and maximum points and the value of fuzzy numbers is given. The new method is illustrated by some numerical examples and in particular, the results of ranking by the proposed method and some common and existing methods for ranking fuzzy numbers is compared to verify the advantages of presented method.

Recently, Phiangsungnoen et al. [J. Inequal. Appl. 2014:201 (2014)] studied fuzzy mappings in the framework of Hausdorff fuzzy metric spaces. Following this direction of research, we establish the existence of fixed fuzzy points of fuzzy mappings. An example is given to support the result proved herein; we also present a coincidence and common fuzzy point result. Finally, as an application of our results, we investigate the existence of solution for some recurrence relations associated to the analysis of quicksort algorithms.

The purpose of this paper is to generalize the concepts of statistical convergence of sequences of fuzzy numbers defined by a modulus function using difference operator $Delta$ and give some inclusion relations.

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$ fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respective categories of topological structures are topological over their ground categories. The theory also extends the notion of topological system of S.~Vickers (and its numerous many-valued modifications of J.~T.~Denniston, A.~Melton and S.~E.~Rodabaugh), and shows that the categories of catalg topological structures are isomorphic to coreflective subcategories of the categories of catalg topological systems. This extension initiates a new approach to soft topology, induced by the concept of soft set of D.~Molodtsov, and currently pursued by various researchers.

In this paper, we consider First-order fuzzy differential equations with initial value conditions. The convergence, consistency and stability of difference method for approximating the solution of fuzzy differential equations involving generalized H differentiability, are studied. Then the local truncation error is defined and sufficient conditions for convergence, consistency and stability of difference method are provided and fuzzy stiff differential equation and one example are presented to illustrate the accuracy and capability of our proposed concepts.

The purpose of the present work is to establish a one-to-one correspondence between the family of interval type-2 fuzzy reflexive/tolerance approximation spaces and the family of interval type-2 fuzzy closure spaces.

A new definition of boundedness of linear order-homomorphisms (LOH) in $L$-topological vector spaces is proposed. The new definition is compared with the previous one given by Fang [The continuity of fuzzy linear order-homomorphism, J. Fuzzy Math. 5 (4) (1997) 829$-$838]. In addition, the relationship between boundedness and continuity of LOHs is discussed. Finally, a new uniform boundedness principle in $L$-topological vector spaces is established in the sense of a new definition of uniform boundedness for a family of LOHs.

In this paper we classify fuzzy subgroups of the dihedral group $D_{pqrs}$ for distinct primes $p$, $q$, $r$ and $s$. This follows similar work we have done on distinct fuzzy subgroups of some dihedral groups. We present formulae for the number of (i) distinct maximal chains of subgroups, (ii) distinct fuzzy subgroups and (iii) non-isomorphic classes of fuzzy subgroups under our chosen equivalence and isomorphism. Some results presented here hold for any dihedral group of order $2n$ where $n$ is a product of any number of distinct primes.

In this paper, we study the notion of solvable $L$-subgroup of an $L$-group and provide its level subset characterization and this justifies the suitability of this extension. Throughout this work, we have used normality of an $L$-subgroup of an $L$-group in the sense of Wu rather than Liu.