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A Numerical Investigation of the Performance of Distance and Similarity Measures in Linguistic Approximation Under Different Linguistic Scales
Tomáš Talášek and Jan Stoklasa

The paper investigates the behavior of linguistic approximation under two distance measures of fuzzy numbers and two similarity measures of fuzzy numbers in the context of different linguistic scales. An analytic framework for the comparison of different distance/similarity measures in the linguistic approximation based on the minimization of distance (maximization of similarity) is introduced and numerical investigation of four chosen measures is performed. The focus of this paper is narrowed to symmetrical triangular fuzzy numbers as approximated objects and several different linguistic scales are considered. The presented results provide evidence of the existence of differences in the performance of the selected measures. Preference of more uncertain approximations, reduction of uncertainty and the emergence of ambiguity regions are among the identified effects of some of the measures. Conclusions concerning the suitability of specific distance/similarity measures in different contexts are drawn and possible drawbacks of their use are identified and discussed.

Keywords: Linguistic approximation, fuzzy number, distance, similarity, Bhattacharyya distance, dissemblance index, best-fit, linguistic scale.

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