Fuzzy linear regression is an interesting tool for handling uncertain data samples as an alternative to a probabilistic approach. This paper sets forth uses a linear regression model for fuzzy variables; the model is optimized through convex methods. A fuzzy linear programming model has been designed to solve the problem with nonlinear fuzzy data by combining the fuzzy arithmetic theory with co...

The aim of this note is to point out and correct some errors in the definition of the four arithmetic operations for triangle intuitionistic fuzzy numbers introduced by Shu et al. [Shu MH, Cheng CH, Chang JR. Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly. Microelectron Reliab 2006;46:2139–48]. 2008 Elsevier Ltd. All rights reserved. Based on the conce...

In this paper we generate fuzzy relations and fuzzy operators using different kind of generators and we study the relationship between them. Firstly, we introduce a new fuzzy preorder induced by a fuzzy operator. We generalize this preorder to a fuzzy relation generated by two fuzzy operators and we analyze its properties. Secondly, we introduce and explore two ways of inducing a fuzzy operator...

Generally fuzzy sets are used to analyze the fuzzy system reliability. Here intuitionistic fuzzy set theory has been used for analyzing the fuzzy system reliability. To analyze the fuzzy system reliability, the reliability of each component of the system is considered as a triangular intuitionistic fuzzy number. At first triangular intuitionistic fuzzy number and their arithmetic operations are...

In the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to avoid this shortcoming, a new multiplicative operation of product type is introduced, the so-called cross-product of fuzzy numbers. Th...

Two different but related measurement problems are considered within the fuzzy set theory. The first problem is the membership measurement and the second is property ranking. These two measurement problems are combined and two axiomatizations of fuzzy set theory are obtained. In the first one, the indifference is transitive but in the second one this drawback is removed by utilizing interval or...

In practice, some special LR fuzzy numbers, like the triangular fuzzy number, the Gaussian fuzzy number and the Cauchy fuzzy number, are widely used in many areas to deal with various vague information. With regard to these special LR fuzzy numbers, called regular LR fuzzy numbers in this paper, an operational law is proposed for fuzzy arithmetic, providing a novel approach to analytically and ...

Fuzzy arithmetic, based on Zadeh’s extension principle, is presented as a tool to solve engineering problems with uncertain model parameters. Fuzzy numbers are introduced, and different concepts to practically implement the uncertainty of the parameters are discussed. As an example, a rather simple but typical problem of engineering mechanics is considered. It consists of determining the displa...

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 po...

Graph-based semi-supervised learning has recently emerged as a promising approach to data-sparse learning problems in natural language processing. They rely on graphs that jointly represent each data point. The problem of how to best formulate the graph representation remains an open research topic. In this paper, we introduce a type-2 fuzzy arithmetic to characterize the edge weights of a form...