Asymmetry in Similarity Formation: Extension of Similarity Theory to Open Sets of Features

Abstract

Abstract The current work shows the extension of similarity theory to open sets of features. Increasing similarity between two objects while deleting distinctive features and adding common features results in different effects depending on the original similarity. When the similarity is greater than 0.5, deleting distinctive features is more effective. When the similarity value is less than 0.5, adding common features is more effective. When we compare an object with its ideal, common features are positive and distinctive features are negative, whereas when we compare an object with its anti-ideal, common features are negative and distinctive features are positive. Consequently, greater strength of negative or positive features in increasing similarity depends on both the value of original similarity and whether the object is compared with its ideal or to its anti-ideal. In this way the positive–negative asymmetry is revealed. Theoretical simulations and a brief empirical demonstration of how the model works have shown that for similarity exceeding 0.5 of a compared object to its ideal, deleting negative features had a stronger effect on the positive image of a particular object than adding positive features of the same value. The mechanism presented is universal and refers to estimation and comparison of all natural stimuli, which can be defined by means of open sets of features.