Our paper was motivated by (Chaudhuri and Rosenfeld, 1996), a paper in which several metrics related to the Hausdorff metric are given for fuzzy sets defined on the same nonempty support set S. The first metric given in (Chaudhuri and Rosenfeld, 1996), denoted F 0 in our paper, requires all the fuzzy sets considered by F 0 to have the same maximum value. Chaudhuri and Rosenfeld (1996) then modi...

In this paper, we shall present strong laws of large numbers (SLLN’s) for independent (not necessary identically distributed) fuzzy set-valued random variables whose base space is a separable Banach space or an Euclidean space, in the sense of the extended Hausdorff metric d∞ H .We apply the method to the sequence of independent identically distributed fuzzy set-valued random variables to give ...

Recently, Phiangsungnoen et al. [J. Inequal. Appl. 2014:201 (2014)] studied fuzzy mappings in the framework of Hausdorff fuzzy metric spaces. Following this direction of research, we establish the existence of fixed fuzzy points of fuzzy mappings. An example is given to support the result proved herein; we also present a coincidence and common fuzzy point result. Finally, as an application of o...

This paper introduces the notion of multidimensional fuzzy finite tree automata (MFFTA) and investigates its closure properties from the area of automata and language theory. MFFTA are a superclass of fuzzy tree automata whose behavior is generalized to adapt to multidimensional fuzzy sets. An MFFTA recognizes a multidimensional fuzzy tree language which is a regular tree language so that for e...

The study adopted the method of Herrera-Viedma et al.,(2004): consistent fuzzy preference relations (Fuzzy PreRa) to apply the questionnaire which Zhilin Yang et al.(2005) developed. The result shows that the most important of the five-dimension is “Usability” and the most important of the nineteen items is “Relevant information to the customer”. Compared to the traditional AHP method, Fuzzy Pr...

*Correspondence: [email protected]; [email protected]; [email protected] 1Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, Thailand 2Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani, 1...

Given a compact and connected metric space (continuum) X, we study topological and dynamical properties of the hyperspace of normal fuzzy sets F1(X) equipped with the Hausdorff, endograph or sendograph metric. Among the many results we show that it is contractible, path connected, locally contractible, locally path connected, locally simply connected and locally connected. For the endograph met...

We consider a certain class of de Rham’s functional equations. We consider Hausdorff dimension of the measure whose distribution function is the solution. We give a necessary and sufficient condition for singularity. We also show that they have a relationship with stationary measures.

We characterize the convergence of fuzzy sets in the supremum metric given by the supremum of the Hausdorff distances of the α-cuts of the fuzzy sets. We do it by dividing this metric into its lower and upper quasipseudometric parts. This characterization is given in the more general context with no assumption on the fuzzy sets. Furthermore, motivated from the theory of Convex Analysis, we also...