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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 inreal world and in particular decision-making procedures. In manyproposed methods by other researchers may exist some shortcoming.The most commonly used approaches for ranking fuzzy numbers isbased on defuzzification method. Many ranking fuzzy numberscannot discriminate between two symmetric fuzzy numbers withidentical core. In 2009, Abbasbandy and Hajjari proposed anapproach for ranking normal trapezoidal fuzzy numbers, whichcomputed the magnitude of fuzzy numbers namely ``Mag" method.Then Hajjari extended it for non-normal trapezoidal fuzzy numbersand also for all generalized fuzzy numbers. However, thesemethods have the weakness that we mentioned above. Moreover, theresult is not consistent with human intuition in this case.Therefore, we are going to present a new method to overcome thementioned weakness. In order to overcome the shortcoming, a newmagnitude approach for ranking trapezoidal fuzzy numbers based onminimum and maximum points and the value of fuzzy numbers isgiven. The new method is illustrated by some numerical examplesand in particular, the results of ranking by the proposed methodand some common and existing methods for ranking fuzzy numbers iscompared 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 somerecurrence relations associated to the analysis of quicksort algorithms.

The purpose of this paper is to generalize the concepts of statisticalconvergence of sequences of fuzzy numbers defined by a modulus functionusing 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 iscompared with the previous one given by Fang [The continuity offuzzy linear order-homomorphism, J. Fuzzy Math. 5 (4) (1997)829$-$838]. In addition, the relationship between boundedness andcontinuity of LOHs is discussed. Finally, a new uniform boundednessprinciple in $L$-topological vector spaces is established in thesense of a new definition of uniform boundedness for a family ofLOHs.

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.

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