Distances and orderings in a family of intuitionistic fuzzy numbers.
Published 1 January 2003
Przemysław Grzegorzewski
Citations80
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
Two families of metrics in space of intuitionistic fuzzy numbers are considered and a method of ranking intuitionist fuzzy numbers based on these metrics is suggested and invesigated.
Abstract
Two families of metrics in space of intuitionistic fuzzy numbers are considered. A method of ranking intuitionistic fuzzy numbers based on these metrics is also suggested and invesigated.
Keywords
Computer ScienceDecision SciencesMathematics
Fuzzy Sets and SystemsIntuitionistic fuzzy sets
16,153 Citations1986Krassimir Atanassov
Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
Fuzzy Sets and SystemsDistances between intuitionistic fuzzy sets
1,587 Citations2000Eulalia Szmidt, Janusz Kacprzyk
It is shown that all three parameters describing intuitionistic fuzzy sets should be taken into account while calculating those distances between intuitionistically fuzzy sets.
Intuitionistic Fuzzy Sets: Theory and Applications
1,380 Citations1999Krassimir Atanassov
The basic definitions and properties of the Intuitionistic Fuzzy Sets (IFSs) are introduced in the book and readers will find discussions on some of the IFS extensions (for example, interval-values IFSs, temporal I FSs and others) and applications.
Fuzzy Sets and SystemsThe mean value of a fuzzy number
743 Citations1987Didier Dubois, Henri Prade
Some light is shed on the debate between probability and possibility theory, and the problem of how to carry measure-theoretic notions into the field of possibility theory.
Fuzzy Sets and SystemsThe expected value of a fuzzy number
500 Citations1992Stanisław Heilpern
The expected interval is defined as the expectedvalue of an interval random set generated by the fuzzy number and the expected value of this number isdefined as the centre of the expected interval.
Fuzzy Sets and SystemsMetrics and orders in space of fuzzy numbers
181 Citations1998Przemysław Grzegorzewski
A method of ranking fuzzy numbers based on these metrics is proposed and investigated, and not only fuzzy numbers but also the left-sided and right-sided fuzzy numbers are considered.