On similarity preservation in fuzzy relation systems with hedges

^1. Based on ‘Similarity Preservation in Fuzzy Relation Systems’, by P. Osicka, which appeared in the Proceedings of the 4th International IEEE Conference on Intelligent Systems IS'08, pp.15-29–15-34.

Abstract

We present results on how formulas of fuzzy logic preserve similarity. The basic questions are as follows: does an input–output mapping, which is defined by logical formulas and which maps fuzzy sets to fuzzy sets, preserve similarity? To what extent? More generally, can we estimate similarity degrees of the output fuzzy sets in terms of similarity degrees of the input fuzzy sets? In the present paper, we extend previously published results. Our extension consists of taking truth-stressing hedges, i.e. truth functions of connective ‘very true’, into account. We present the similarity estimation results and provide an example of application of our results.

Keywords:

• similarity
• fuzzy set
• fuzzy logic
• truth-stressing hedge

Acknowledgement

This work was supported by institutional support, research plan MSM 6198959214.

Notes

^1. Based on ‘Similarity Preservation in Fuzzy Relation Systems’, by P. Osicka, which appeared in the Proceedings of the 4th International IEEE Conference on Intelligent Systems IS'08, pp.15-29–15-34.