TY - JOUR
T1 - Negations of Probability Distributions
T2 - A Survey
AU - Batyrshin, Ildar Z.
AU - Kubysheva, Nailya I.
AU - Bayrasheva, Venera R.
AU - Kosheleva, Olga
AU - Kreinovich, Vladik
N1 - Publisher Copyright:
© 2021 Instituto Politecnico Nacional. All rights reserved.
PY - 2021
Y1 - 2021
N2 - In recent years many papers have been devoted to the analysis and applications of negations of finite probability distributions (PD), first considered by Ronald Yager. This paper gives a brief overview of some formal results on the definition and properties of negations of PD. Negations of PD are generated by negators of probability values transforming element-byelement PD into a negation of PD. Negators are nonincreasing functions of probability values. There are two types of negators: PD-independent and PD-dependent negators. Yager's negator is fundamental in the characterization of linear PD-independent negators as a convex combination of Yager's negator and uniform negator. Involutivity of negations is important in logic, and such involutive negator is considered in the paper. We propose a new simple definition of the class of linear negators generalizing Yager's negator. Different examples illustrate properties of negations of PD. Finally, we consider some open problems in the analysis of negations of probability distributions.
AB - In recent years many papers have been devoted to the analysis and applications of negations of finite probability distributions (PD), first considered by Ronald Yager. This paper gives a brief overview of some formal results on the definition and properties of negations of PD. Negations of PD are generated by negators of probability values transforming element-byelement PD into a negation of PD. Negators are nonincreasing functions of probability values. There are two types of negators: PD-independent and PD-dependent negators. Yager's negator is fundamental in the characterization of linear PD-independent negators as a convex combination of Yager's negator and uniform negator. Involutivity of negations is important in logic, and such involutive negator is considered in the paper. We propose a new simple definition of the class of linear negators generalizing Yager's negator. Different examples illustrate properties of negations of PD. Finally, we consider some open problems in the analysis of negations of probability distributions.
KW - Involutive negation
KW - Linear negator
KW - Negation
KW - Probability distribution
UR - http://www.scopus.com/inward/record.url?scp=85122163456&partnerID=8YFLogxK
U2 - 10.13053/CyS-25-4-4094
DO - 10.13053/CyS-25-4-4094
M3 - Artículo
AN - SCOPUS:85122163456
SN - 1405-5546
VL - 25
SP - 775
EP - 781
JO - Computacion y Sistemas
JF - Computacion y Sistemas
IS - 4
ER -