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Interval Estimations of Solution Sets to Real-Valued Systems of Linear or Non-Linear Equations
TLDR
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
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Formal Solution to Systems of Interval Linear or Non-Linear Equations
TLDR
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
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Interpretability and Optimality
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 theExpand
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Modal Interval Analysis: New Tools for Numerical Information
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
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A New Point of View for Fuzzy Numbers and Their Defuzzification
TLDR
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
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Model Intervals
TLDR
This paper summarizes the most important results and features of Modal Interval Analysis. Expand
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Numerical Clouds-A Treatment for Indiscernibility
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 aExpand
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A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory
TLDR
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
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Quantified trapezoidal fuzzy numbers
TLDR
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
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