The arithmetic of continuous Z-numbers

In order to deal with imprecision and partial reliability of real-world information, Prof. Zadeh suggested the concept of a Z-number Z=(A, B), as an ordered pair of continuous fuzzy numbers A and B. The first describes a linguistic value, and the second one is the associated reliability. Unfortunate...

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Bibliographic Details
Published in:Information sciences Vol. 373; pp. 441 - 460
Main Authors: Aliev, R.A., Huseynov, O.H., Zeinalova, L.M.
Format: Journal Article
Language:English
Published: Elsevier Inc 10.12.2016
Subjects:
A continuous fuzzy number
A probability measure
A random variable
Algebra
Arithmetic
Arithmetic operations
BASIC (programming language)
Convolution
Division
Fuzzy systems
Linguistics
Nonlinearity
Optimization
Z-number
A continuous fuzzy number
Convolution
Arithmetic operations
A random variable
A probability measure
Z-number
ISSN:0020-0255, 1872-6291
Online Access:Get full text
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Summary:In order to deal with imprecision and partial reliability of real-world information, Prof. Zadeh suggested the concept of a Z-number Z=(A, B), as an ordered pair of continuous fuzzy numbers A and B. The first describes a linguistic value, and the second one is the associated reliability. Unfortunately, up to day there is no works devoted to arithmetic of continuous Z-numbers in existence. An original formulation of operations over continuous Z-numbers proposed by Zadeh includes complex non-linear variational problems. We propose an alternative approach which has a better computational complexity and accuracy tradeoff. The proposed approach is based on linear programming and other simple optimization problems. We developed basic arithmetic operations such as addition, subtraction, multiplication and division, and some algebraic operations as maximum, minimum, square and square root of continuous Z-numbers. Vast compendium of examples shows validity of the suggested approach.
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ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2016.08.078