TY - JOUR
T1 - Generating negations of probability distributions
AU - Batyrshin, Ildar
AU - Villa-Vargas, Luis Alfonso
AU - Ramírez-Salinas, Marco Antonio
AU - Salinas-Rosales, Moisés
AU - Kubysheva, Nailya
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2021/6
Y1 - 2021/6
N2 - Recently, the notation of a negation of a probability distribution was introduced. The need for such negation arises when a knowledge-based system can use the terms like NOT HIGH, where HIGH is represented by a probability distribution (pd). For example, HIGH PROFIT or HIGH PRICE can be considered. The application of this negation in Dempster–Shafer theory was considered in many works. Although several negations of probability distributions have been proposed, it was not clear how to construct other negations. In this paper, we consider negations of probability distributions as point-by-point transformations of pd using decreasing functions defined on [0,1] called negators. We propose the general method of generation of negators and corresponding negations of pd, and study their properties. We give a characterization of linear negators as a convex combination of Yager’s and uniform negators.
AB - Recently, the notation of a negation of a probability distribution was introduced. The need for such negation arises when a knowledge-based system can use the terms like NOT HIGH, where HIGH is represented by a probability distribution (pd). For example, HIGH PROFIT or HIGH PRICE can be considered. The application of this negation in Dempster–Shafer theory was considered in many works. Although several negations of probability distributions have been proposed, it was not clear how to construct other negations. In this paper, we consider negations of probability distributions as point-by-point transformations of pd using decreasing functions defined on [0,1] called negators. We propose the general method of generation of negators and corresponding negations of pd, and study their properties. We give a characterization of linear negators as a convex combination of Yager’s and uniform negators.
KW - Dempster–Shafer theory
KW - Negation
KW - Probability distribution
UR - http://www.scopus.com/inward/record.url?scp=85104729628&partnerID=8YFLogxK
U2 - 10.1007/s00500-021-05802-5
DO - 10.1007/s00500-021-05802-5
M3 - Artículo
AN - SCOPUS:85104729628
SN - 1432-7643
VL - 25
SP - 7929
EP - 7935
JO - Soft Computing
JF - Soft Computing
IS - 12
ER -