Comparison theorems for summability methods of sequences of fuzzy numbers

In this study we compare Ces\`{a}ro and Euler weighted mean methods of summability of sequences of fuzzy numbers with Abel and Borel power series methods of summability of sequences of fuzzy numbers. Also some results dealing with series of fuzzy numbers are obtained.Comment: publication information is added, typos correcte

Algorithm of arithmetical operations with fuzzy numerical data

In this article the theoretical generalization for representation of arithmetic operations with fuzzy numbers is considered. Fuzzy numbers are generalized by means of fuzzy measures. On the basis of this generalization the new algorithm of fuzzy arithmetic which uses a principle of entropy maximum is created. As example, the summation of two fuzzy numbers is considered. The algorithm is realized in the software "Fuzzy for Microsoft Excel".fuzzy measure (Sugeno), fuzzy integral (Sugeno), fuzzy numbers; arithmetical operations; principle of entropy maximum

Solving P - Norm Intuitionistic Fuzzy Programming Problem

In this paper, notion of p - norm generalized trapezoidal intuitionistic fuzzy numbers is introduced. A new ranking method is introduced for p - norm generalized trapezoidal intuitionistic fuzzy numbers. Also we consider linear programming problem in intuitionistic fuzzy environment. In this problem, all the coefficients and variables are represented by p - norm generalized trapezoidal intuitionistic fuzzy numbers. To overcome the limitations of the existing methods, a new method is proposed to compute the intuitionistic fuzzy optimal solution for intuitionistic fuzzy linear programming problem. An illustrative numerical example is solved to demonstrate the efficiency of the proposed approach.Comment: some erro

Approximation of fuzzy numbers by convolution method

In this paper we consider how to use the convolution method to construct approximations, which consist of fuzzy numbers sequences with good properties, for a general fuzzy number. It shows that this convolution method can generate differentiable approximations in finite steps for fuzzy numbers which have finite non-differentiable points. In the previous work, this convolution method only can be used to construct differentiable approximations for continuous fuzzy numbers whose possible non-differentiable points are the two endpoints of 1-cut. The constructing of smoothers is a key step in the construction process of approximations. It further points out that, if appropriately choose the smoothers, then one can use the convolution method to provide approximations which are differentiable, Lipschitz and preserve the core at the same time.Comment: Submitted to Fuzzy Sets and System at Sep 18 201

A short survey of normative properties of possibility distributions

In 2001 Carlsson and Full´er [1] introduced the possibilistic mean value, variance and covariance of fuzzy numbers. In 2003 Full´er and Majlender [4] introduced the notations of crisp weighted possibilistic mean value, variance and covariance of fuzzy numbers, which are consistent with the extension principle. In 2003 Carlsson, Full´er and Majlender [2] proved the possibilisticCauc hy-Schwartz inequality. Drawing heavily on [1, 2, 3, 4, 5] we will summarize some normative properties of possibility distributions

A generalization of Hukuhara difference for interval and fuzzy arithmetic

We propose a generalization of the Hukuhara difference. First, the case of compact convex sets is examined; then, the results are applied to generalize the Hukuhara difference of fuzzy numbers, using their compact and convex level-cuts. Finally, a similar approach is seggested to attempt a generalization of division for real intervals and fuzzy numbers.Fuzzy Arithmetic, Interval Arithmetic, Hukuhara difference, Fuzzy Numbers.