In this paper we study t-norms on the lattice of closed subintervals of the unit interval. Unlike for t-norms on a product lattice for which there exists a straightforward characterization of t-norms which are join-morphisms, respectively meet-morphisms, the situation is more complicated for t-norms in interval-valued fuzzy set theory. In previous papers several characterizations were given of ...

Classification algorithms based on different forms of support vector machines (SVMs) for dealing with interval-valued training data are proposed in the paper. L2-norm and L∞-norm SVMs are used for constructing the algorithms. The main idea allowing us to represent the complex optimization problems as a set of simple linear or quadratic programming problems is to approximate the Gaussian kernel ...

This paper proposes an extension of the ARAS method which, due to the use of intervalvalued fuzzy numbers, can be more appropriate for solving real-world problems. In order to overcome the complexity of real-world decision-making problems, the proposed extension also includes the use of linguistic variables and a group decision making approach. In order to highlight the proposed methodology an ...

In this paper, a new soft computing group decision method based on the concept of compromise ratio is introduced for determining decision makers (DMs)' weights through the group decision process under uncertainty. In this method, preferences and judgments of the DMs or experts are expressed by linguistic terms for rating the industrial alternatives among selected criteria as well as the relativ...

Multi-attribute decision-making (MADM) is usually used to aggregate fuzzy data successfully. Choosing the best option regarding not generally symmetric on grounds that it does provide complete information. Since Aczel-Alsina aggregation operators (AOs) have great impact due their parameter variableness, they been well applied in MADM under construction. Recently, AOs intuitionistic sets (IFSs),...

The purpose of this paper is propose a simple de…nition of an interval-valued probability measure and to examine some of the implications of this de…nition. This de…nition provides a method for characterizing certain types of imprecise probabilities. We develop some properties of this de…nition and propose a de…nition of integration with respect to it. We show that this de…nition is a generaliz...