Towards an Extension of the 2-tuple Linguistic Model to Deal With Unbalanced Linguistic Term sets

TL;DR

This paper extends the 2-tuple linguistic model to better handle unbalanced linguistic term sets by simplifying input requirements and improving partition fidelity, with implementations in jFuzzyLogic and FCL.

Contribution

It introduces a modified fuzzy partition approach for unbalanced linguistic sets and extends existing 2-tuple models with new aggregation algorithms.

Findings

Enhanced partition algorithm for unbalanced sets

Implementation of the extension in jFuzzyLogic and FCL

Comparison of aggregation methods in 2-tuple models

Abstract

In the domain of Computing with words (CW), fuzzy linguistic approaches are known to be relevant in many decision-making problems. Indeed, they allow us to model the human reasoning in replacing words, assessments, preferences, choices, wishes... by ad hoc variables, such as fuzzy sets or more sophisticated variables. This paper focuses on a particular model: Herrera & Martinez' 2-tuple linguistic model and their approach to deal with unbalanced linguistic term sets. It is interesting since the computations are accomplished without loss of information while the results of the decision-making processes always refer to the initial linguistic term set. They propose a fuzzy partition which distributes data on the axis by using linguistic hierarchies to manage the non-uniformity. However, the required input (especially the density around the terms) taken by their fuzzy partition algorithm may be considered as too much demanding in a real-world application, since density is not always easy to determine. Moreover, in some limit cases (especially when two terms are very closed semantically to each other), the partition doesn't comply with the data themselves, it isn't close to the reality. Therefore we propose to modify the required input, in order to offer a simpler and more faithful partition. We have added an extension to the package jFuzzyLogic and to the corresponding script language FCL. This extension supports both 2-tuple models: Herrera & Martinez' and ours. In addition to the partition algorithm, we present two aggregation algorithms: the arithmetic means and the addition. We also discuss these kinds of 2-tuple models.