Paper Info
Title
RL-numbers: An alternative to fuzzy numbers for the representation of imprecise quantities.
Abstract
In this paper we define imprecise quantities on the basis of a new representation of imprecision introduced by the authors called RI-representation (for restriction-level representation). We call the corresponding RL-representation of imprecise quantities RL-numbers. We first define RL-natural numbers on the basis of the notion of cardinality. The usual arithmetic operations of addition, product and division are extended and RL-integers, RL-rationals and RL-real numbers are defined so that solution is provided to any kind of equation involving those operations, as with precise numbers. We show that the algebraic properties of precise numbers with respect to the ordinary arithmetic operators are preserved. In addition, and remarkably, we show that the imprecision of the quantities being operated can be increased, preserved or diminished. Ranking of RL-numbers is introduced by means of the notion of RL-ranking as an extensive RL-representation defined on the set {<, =, >}. in our view, fuzzy numbers correspond to the definition of imprecise intervals corresponding to linguistic concepts like approximately x. We discuss about the relationship between RL-numbers and fuzzy numbers, and how they complement each other. Specifically, we propose to use RL-numbers in order to represent imprecise quantities obtained by measuring properties, and fuzzy numbers (equivalently, RL-intervals) to define concepts and to provide a linguistic approximation of RL-numbers.
Year
DOI
Venue
2008
10.1109/FUZZY.2008.4630653
FUZZ-IEEE
Keywords
Field
DocType
approximation theory,computational linguistics,fuzzy set theory,fuzzy numbers,imprecise quantities representation,linguistic approximation,ordinary arithmetic operators,restriction-level ranking,restriction-level representation
Discrete mathematics,Ranking,Computational linguistics,Cardinality,Approximation theory,Fuzzy set,Artificial intelligence,Fuzzy control system,Algebraic properties,Fuzzy number,Machine learning,Mathematics
Conference
ISSN
Citations 
PageRank 
1098-7584
10
0.74
References 
Authors
3
3
Name
Order
Citations
PageRank
Daniel Sánchez196760.29
Miguel Delgado21452121.94
María Amparo Vila Miranda3118293.57