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Averaging aggregation functions for preferences expressed as Pythagorean membership grades and fuzzy orthopairs

conference contribution
posted on 2014-09-04, 00:00 authored by Gleb BeliakovGleb Beliakov, Simon JamesSimon James
Rather than denoting fuzzy membership with a single value, orthopairs such as Atanassov's intuitionistic membership and non-membership pairs allow the incorporation of uncertainty, as well as positive and negative aspects when providing evaluations in fuzzy decision making problems. Such representations, along with interval-valued fuzzy values and the recently introduced Pythagorean membership grades, present particular challenges when it comes to defining orders and constructing aggregation functions that behave consistently when summarizing evaluations over multiple criteria or experts. In this paper we consider the aggregation of pairwise preferences denoted by membership and non-membership pairs. We look at how mappings from the space of Atanassov orthopairs to more general classes of fuzzy orthopairs can be used to help define averaging aggregation functions in these new settings. In particular, we focus on how the notion of 'averaging' should be treated in the case of Yager's Pythagorean membership grades and how to ensure that such functions produce outputs consistent with the case of ordinary fuzzy membership degrees.

History

Pagination

298-305

Location

Beijing; China

Start date

2014-07-06

End date

2014-07-11

ISSN

1098-7584

ISBN-13

9781479920723

Language

eng

Publication classification

E Conference publication, E1 Full written paper - refereed

Copyright notice

2014, Institute of Electrical and Electronics Engineers Inc.

Editor/Contributor(s)

[Unknown]

Title of proceedings

FUZZ-IEEE 2014 : Proceedings of the 2014 IEEE International Conference on Fuzzy Systems

Event

IEEE International Conference on Fuzzy Systems (2014 : Beijing, China)

Publisher

IEEE

Place of publication

Piscataway, N.J.