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Measurement results contain different kinds of uncertainty. Besides systematic errors andrandom errors individual measurement results are also subject to another type of uncertainty,so-called emph{fuzziness}. It turns out that special fuzzy subsets of the set of real numbers $RR$are useful to model fuzziness of measurement results. These fuzzy subsets $x^*$ are called emph{fuzzy numbers}. The membership functions of fuzzy numbers have to be determined. In the paper firsta characterization of membership function is given, and after that methods to obtainspecial membership functions of fuzzy numbers, so-called emph{characterizing functions} describingmeasurement results are treated.

The main condition of the differently implicational inferencealgorithm is reconsidered from a contrary direction, which motivatesa new fuzzy inference strategy, called the double fuzzyimplications-based restriction inference algorithm. New restrictioninference principle is proposed, which improves the principle of thefull implication restriction inference algorithm. Furthermore,focusing on the new algorithm, we analyze the basic property of itssolution, and then obtain its optimal solutions aiming at theproblems of fuzzy modus ponens (FMP) as well as fuzzy modus tollens(FMT). Lastly, comparing with the full implication restrictioninference algorithm, the new algorithm can make the inferencecloser, and generate more, better specific inference algorithms.

Trapezoidal intuitionistic fuzzy numbers (TrIFNs) express abundant and flexible information in a suitable manner and are very useful to depict the decision information in the procedure of decision making. In this paper, some new aggregation operators, such as, trapezoidal intuitionistic fuzzy weighted power harmonic mean (TrIFWPHM) operator, trapezoidal intuitionistic fuzzy ordered weighted power harmonic mean (TrIFOWPHM) operator, trapezoidal intuitionistic fuzzy induced ordered weighted power harmonic mean (TrIFIOWPHM) operator and trapezoidal intuitionistic fuzzy hybrid power harmonic mean (TrIFhPHM) operator are introduced to aggregate the decision information. The desirable properties of these operators are presented in detail. A prominent characteristic of these operators is that, the aggregated value by using these operators is also a TrIFN. It is observed that the proposed TrIFWPHM operator is the generalization of trapezoidal intuitionistic fuzzy weighted harmonic mean (TrIFWHM) operator, trapezoidal intuitionistic fuzzy weighted arithmetic mean (TrIFWAM) operator, trapezoidal intuitionistic fuzzy weighted geometric mean (TrIFWGM) operator and trapezoidal intuitionistic fuzzy weighted quadratic mean (TrIFWQM) operator, {it i.e.,} we can easily reduce the TrIFWPHM operator to TrIFWHM, TrIFWGM, TrIFWAM and TrIFWQM operators, depending upon the decision situation. Further, we develop an approach to multi-attribute group decision making (MAGDM) problem on the basis of the proposed aggregation operators. Finally, the effectiveness and applicability of our proposed MAGDM model, as well as comparison analysis with other approaches are illustrated with a practical example.

In the present paper, we investigate a connection between two fuzzy inner product one of which arises from Felbin's fuzzy norm and the other is based on Bag and Samanta's fuzzy norm. Also we show that, considering a fuzzy inner product space, how one can construct another kind of fuzzy inner product on this space.

In this paper, we give some new coupled common fixed point theorems for probabilistic $varphi$-contractions in Menger probabilistic metric spaces. As applications of the main results, we obtain some coupled common fixed point theorems in usual metric spaces and fuzzy metric spaces. The main results of this paper improvethe corresponding results given by some authors. Finally, we give one example to illustrate the main results of this paper.

In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.

With the unit interval [0,1] as the truth value table, Chen and Wupresented the concept of possibility computation over dcpos.Indeed, every possibility computation can be considered as a[0,1]-valued Scott open set on a dcpo. The aim of this paper is tostudy Chen-Wu's duality on quantale-valued setting. For clarity,with a commutative unital quantale $L$ as the truth value table, weintroduce a concept of fuzzy possibility computations over fuzzydcpos and then establish an equivalence between their denotationalsemantics and their logical semantics.

The purpose of this paper is to present some coincidence point and common fixed point theorems for multivalued contraction maps in complete fuzzy metric spaces endowed with a partial order. As an application, we give an existence theorem of solution for general classes of integral inclusions by the coincidence point theorem.

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