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A Two-interval Forced-choice Task for Multisensory Comparisons

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Dominance-based ranking functions for interval-valued intuitionistic fuzzy sets.

Liang-Hsuan Chen, Chien-Cheng Tu

IEEE Transactions on Cybernetics

|October 11, 2013

Summary

This study introduces new ranking functions for interval-valued intuitionistic fuzzy sets (IvIFSs) using a dominance concept. These functions enable a complete ranking of IvIFSs by considering dominance and relative comparisons.

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Area of Science:

Fuzzy Set Theory
Decision Making
Information Granulation

Background:

Ranking interval-valued intuitionistic fuzzy sets (IvIFSs) is challenging due to inherent interval membership and non-membership values.
Existing methods may not fully capture the complex relationships within IvIFSs.
A robust ranking mechanism is crucial for effective decision-making in uncertain environments.

Purpose of the Study:

To propose novel ranking functions for IvIFSs based on the dominance concept.
To develop functions that incorporate boundary values and relative comparisons among IvIFSs.
To enable a comprehensive and accurate ranking of IvIFSs for decision support.

Main Methods:

Development of dominance-based ranking functions for IvIFSs.
Incorporation of bivariate framework considering membership and non-membership intervals.
Inclusion of bipolar evaluations with a parameter for decision-maker flexibility.
Definition of dual couple relationships based on four proposed ranking functions.

Main Results:

The proposed ranking functions effectively consider the dominance and non-dominance degrees of IvIFSs.
Functions integrate boundary values and relative inter-set relationships.
Bipolar evaluations allow for personalized decision-making attitudes.
Demonstrated ability to achieve a full ranking for all IvIFSs.

Conclusions:

The proposed dominance-based ranking functions offer a distinct and applicable method for ranking IvIFSs.
These functions provide a more comprehensive evaluation by considering dominance and relative comparisons.
The approach enhances decision-making capabilities in scenarios involving uncertain and interval-valued information.