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This paper is concerned with delay-dependent exponential stability analysis and stabilization for continuous-time T-S fuzzy Markovian jump systems with mode-dependent time-varying delay. By constructing a novel Lyapunov-Krasovskii functional and utilizing some advanced techniques, less conservative conditions are presented to guarantee the closed-loop system is mean-square exponentially stable. Then, the stabilization conditions are derived and the fuzzy controller can be obtained by solving a set solutions of LMIs. The upper bound of time-delay that the system can be stabilized is given by using an optimal algorithm. Two examples are presented to illustrate the effectiveness and potential of our methods.

Process capability indices are considered as an important concept in statistical quality control. They have been widely used in the manufacturing industry to provide numerical measures on process performance. Moreover, some incapability indices have been introduced to account the process performance. In this paper, we focus on the one proposed by Chen ~cite{Che:Stat}. In today's modern world, accurate and flexible information is needed. So, we apply fuzzy logic to measure the process incapability. Buckley's approach is used to fuzzify this index and to make a decision on process incapability, we utilize fuzzy critical value. Numerical examples are presented to demonstrate the performance and effectiveness of the proposed index.

Fixed charge solid transportation problems are formulated as profit maximization problems under a budget constraint at each destination. Here item is purchased in different depots at different prices. Accordingly the item is transported to different destinations from different depots using different vehicles. Unitsare sold from different destinations to the customers at different selling prices. Here selling prices, purchasing costs, unit transportation costs, fixed charges, sources at origins, demands at destinations, conveyances capacities are assumed to be crisp or fuzzy. Budget constraints at destinations are imposed. Itis also assumed that transported units are integer multiple of packets. So the problem is formulated as constraint optimization integer programming problem in crisp and fuzzy environments. Asoptimization of fuzzy objective as well as consideration of fuzzy constraint is not well defined, different measures possibility/necessity/credibility of fuzzy event are used to transform the problem into equivalent crisp problem. The reduced crisp problem is solved following generalized reduced gradient(GRG) method using lingo software. A dominance based genetic algorithm (DBGA) and a particle swarm optimization (PSO) technique using swap sequence are also developed for this purpose and are used to solve the model. The models are illustrated with numerical examples. The results obtained using DBGA and PSO are compared with those obtained from GRG.Moreover, a statistical analysis is presented to compare the algorithms.

The correlation between the performance of attributes and the overallsatisfaction such as they are perceived by the customers is often used tocalculate the importance of attributes in the crisp case. Recently, the methodwas extended, based on the standard Zadeh extension principle, to the fuzzycase, taking into account the specificity of the human thinking. Thedifficulties of calculation are important and only approximations of theanalytic results can be obtained. In the present paper we give a simplifiedand exact method to compute the derived importance of the attributes in thecase of input data given by triangular fuzzy numbers. The effectivecalculation is based on the $T_{W}$-extension principle and it uses reasonablecomputer resources even if a large number of attributes and customers isconsidered. The proposed derived method is later on compared with othermethods of calculation of the fuzzy importance of attributes. The results ofa survey with respect to the quality of hotel services in Oradea (Romania)are subject to the application of the proposed method.

Hyers-Ulam-Rassias stability have been studied in the contexts of several areas of mathematics. The concept of fuzziness and its extensions have been introduced to almost all branches of mathematics in recent times.Here we define the cubic functional equation in 2-variables and establish that Hyers-Ulam-Rassias stability holds for such equations in intuitionistic fuzzy Banach spaces.

This paper proposes a new approach based on Bonferroni mean operator and possibility degree to solve fuzzy multi-attribute decision making (FMADM) problems in which the attribute value takes the form of interval type-2 fuzzy numbers. We introduce the concepts of interval possibility mean value and present a new method for calculating the possibility degree of two interval trapezoidal type-2 fuzzy sets (IT2 TrFSs). Then, we develop two aggregation techniques, which are called the interval type-2 trapezoidal fuzzy Bonferroni mean (IT2TFBM) operator and the interval type-2 trapezoidal fuzzy weighted Bonferroni mean (IT2TFWBM) operator. We study their properties and discuss their special cases. Based on the IT2TFWBM operator and the possibility degree, a new method of multi-attribute decision making with interval type-2 trapezoidal fuzzy information is proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.

As an special intuitionistic fuzzy set defined on the real number set, triangular intuitionistic fuzzy number (TIFN) is a fundamental tool for quantifying an ill-known quantity. In order to model the decision maker's overall preference with mandatory requirements, it is necessary to develop some Bonferroni harmonic mean operators for TIFNs which can be used to effectively intergrate the information of attribute values for multi-attribute group decision making (MAGDM) with TIFNs. The purpose of this paper is to develop some Bonferroni harmonic operators of TIFNs and apply to the MAGDM problems with TIFNs. The weighted possibility means of TIFN are firstly defined. Hereby, a new lexicographic approach is presented to rank TIFNs sufficiently considering the risk preference of decision maker. The sensitivity analysis on the risk preference parameter is made. Then, three kinds of triangular intuitionistic fuzzy Bonferroni harmonic aggregation operators are defined, including a triangular intuitionistic fuzzy triple weighted Bonferroni harmonic mean operator (TIFTWBHM) operator, a triangular intuitionistic fuzzy triple ordered weighted Bonferroni harmonic mean (TIFTOWBHM) operator and a triangular intuitionistic fuzzy triple hybrid Bonferroni harmonic mean (TIFTHBHM) operator. Some desirable properties for these operators are discussed in detail. By using the TIFTWBHM operator, we can obtain the individual overall attribute values of alternatives, which are further integrated into the collective ones by the TIFTHBHM operator. The ranking order of alternatives is generated according to the collective overall attribute values of alternatives. A real investment selection case study verifies the validity and applicability of the proposed method.

The production of a process is expected to meet customer demands, specifications or engineering tolerances. The ability of a process to meet these expectations is expresed as a single number using a process capability index. When the quality of the products relates to more than one characteristic, multivariate process capability indices are applied. As it is known, in some circumstances we are faced with imprecise data. So, fuzzy logic is engaged to deal with them. In this article, the specification limits and the target value of each characteristic and also, the data gathered from the process are assumed to be imprecise and a new fuzzy multivariate capability vector is introduced. As a whole, the present article provides a research of the application of fuzzy logic in multivariate capability vector.

The definition of $L$-fuzzy Q-convergence spaces is presented by Pang and Fang in 2011. However, Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces is not investigated. This paper focuses on Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces, and it is shown that the category $L$-$mathbf{QFCS}$ of $L$-fuzzy Q-convergence spaces is Cartesian-closed.

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