Calculus of fuzzy numbers

Walenty Ostasiewicz. "Calculus of fuzzy numbers." Mathematica Applicanda 7.15 (1979): null. <http://eudml.org/doc/292863>.

@article{WalentyOstasiewicz1979,
abstract = {From the introduction: "In this article we attempt to use concepts of fuzzy set theory to formalize such ideas as `about 30', `approximately 5', few, many, etc. These ideas describe some numbers, but are not precise; hence, we call them imprecise, or fuzzy numbers. Despite their fuzzy character, one can perform various arithmetical and logical operations: X earns more than Y (even though both of them earn very little), Z earns as much as X and Y earn between them (a sum of two numbers), etc. The purpose of this paper is to define operations on these numbers so that they would reflect our intuitive ideas and would in some sense generalize corresponding operations performed on the `ordinary' real numbers. Attainment of the first objective is difficult because of its subjective character and the lack of formal criteria. For this reason, a large part of this article is devoted to the justification of this or that type of formalism.''},
author = {Walenty Ostasiewicz},
journal = {Mathematica Applicanda},
keywords = {Fuzzy sets and logic, Fuzzy set theory},
language = {eng},
number = {15},
pages = {null},
title = {Calculus of fuzzy numbers},
url = {http://eudml.org/doc/292863},
volume = {7},
year = {1979},
}

TY - JOUR
AU - Walenty Ostasiewicz
TI - Calculus of fuzzy numbers
JO - Mathematica Applicanda
PY - 1979
VL - 7
IS - 15
SP - null
AB - From the introduction: "In this article we attempt to use concepts of fuzzy set theory to formalize such ideas as `about 30', `approximately 5', few, many, etc. These ideas describe some numbers, but are not precise; hence, we call them imprecise, or fuzzy numbers. Despite their fuzzy character, one can perform various arithmetical and logical operations: X earns more than Y (even though both of them earn very little), Z earns as much as X and Y earn between them (a sum of two numbers), etc. The purpose of this paper is to define operations on these numbers so that they would reflect our intuitive ideas and would in some sense generalize corresponding operations performed on the `ordinary' real numbers. Attainment of the first objective is difficult because of its subjective character and the lack of formal criteria. For this reason, a large part of this article is devoted to the justification of this or that type of formalism.''
LA - eng
KW - Fuzzy sets and logic, Fuzzy set theory
UR - http://eudml.org/doc/292863
ER -