TY - JOUR
T1 - Fuzzy Distribution Sets
AU - Batyrshin, Ildar Z.
N1 - Publisher Copyright:
© 2022 Instituto Politecnico Nacional. All rights reserved.
PY - 2022
Y1 - 2022
N2 - We introduce a new type of fuzzy set called Fuzzy Distribution Set (FDS). Fuzzy distribution sets are fuzzy sets defined on a finite domain subject to a sum of membership values equal to 1. Such fuzzy sets can serve as models of subjective probability distributions and subjective weight distributions. Considering these distributions as fuzzy sets gives a possibility to extend on such distributions the operations of fuzzy sets and, more generally, the calculus of fuzzy restrictions developed during the last decades. Recently Yager introduced the concept of negation of probability distributions. In our works, we studied several classes of such negations. Here we consider an involutive negation of probability distributions as a complement of FDS. We introduce the operations of union and intersection of fuzzy distribution sets. These basic operations on FDS can serve as a basis for the application of fuzzy logic methods to subjective probability and weight distributions. These operations can be used for the development of reasoning models with subjective probability distributions and subjective weighting functions. Weight distributions can be used in multicriteria, multi-person, and multi-attribute decisionmaking models.
AB - We introduce a new type of fuzzy set called Fuzzy Distribution Set (FDS). Fuzzy distribution sets are fuzzy sets defined on a finite domain subject to a sum of membership values equal to 1. Such fuzzy sets can serve as models of subjective probability distributions and subjective weight distributions. Considering these distributions as fuzzy sets gives a possibility to extend on such distributions the operations of fuzzy sets and, more generally, the calculus of fuzzy restrictions developed during the last decades. Recently Yager introduced the concept of negation of probability distributions. In our works, we studied several classes of such negations. Here we consider an involutive negation of probability distributions as a complement of FDS. We introduce the operations of union and intersection of fuzzy distribution sets. These basic operations on FDS can serve as a basis for the application of fuzzy logic methods to subjective probability and weight distributions. These operations can be used for the development of reasoning models with subjective probability distributions and subjective weighting functions. Weight distributions can be used in multicriteria, multi-person, and multi-attribute decisionmaking models.
KW - Fuzzy set
KW - complement of distributions
KW - intersection of distributions
KW - probability distribution
KW - union of distributions
KW - weight distribution
UR - http://www.scopus.com/inward/record.url?scp=85139323141&partnerID=8YFLogxK
U2 - 10.13053/CYS-26-3-4360
DO - 10.13053/CYS-26-3-4360
M3 - Artículo
AN - SCOPUS:85139323141
SN - 1405-5546
VL - 26
SP - 1411
EP - 1416
JO - Computacion y Sistemas
JF - Computacion y Sistemas
IS - 3
ER -