This is a second paper devoted to present the Modal Interval Analysis as a framework where the search of formal solutions for a set of simultaneous interval linear or non-linear equations is started on, together with the interval estimations for sets of solutions of real-valued systems in which coefficients and right-hand sides belong to certain intervals.Expand

This is the first of two papers which present the Modal Interval Analysis as a framework where the search and interpretation of formal solutions for a set of simultaneous interval linear or non-linear equations is started on, together with the interval estimations for sets of solutions of real-valued systems in which coefficients and right-hand sides belong to certain intervals.Expand

The Semantic Theorems show that \({f}^{{\ast}}(\boldsymbol{X})\) and \({f}^{{\ast}{\ast}}(\boldsymbol{X})\) are optimal from a semantic point of view, and clarify which ⊆ -sense of rounding is the… Expand

This book presents an innovative new approach to interval analysis. Modal Interval Analysis (MIA) is an attempt to go beyond the limitations of classic intervals in terms of their structural,… Expand

In this paper we develop a new graphical representation of fuzzy numbers, which we then employ to propose a geometrical approach to their defuzzification.Expand

The need to process numerical information has led to the development of interval analysis and fuzzy numbers in an effort to reflect reality more accurately. Exact numbers are rare and we propose a… Expand

We propose a generalization of trapezoidal fuzzy numbers based on modal interval theory and we study some of the related properties and structures, proving that the inclusion relation provides a lattice structure on this set.Expand

The aim of this work is to construct quantified trapezoidal fuzzy numbers, by using modal intervals and accepting the possibility that the α-cuts of a trapezoid fuzzy number may also be improper intervals.Expand