This paper is concerned with a branch of computational biology related to protein prediction and analysis of secondary structure of proteins. Although traditional methods use a simple amino acid composition to predict the secondary structure content, hydrophobicity has been recently found to improve the results in this and several related prediction tasks. To this end, we propose and analyze advantages of two new hydrophobicity index-based scales that incorporate information about long-range interactions along the protein sequence and contrast them with currently used raw hydrophobic index values. We also compare three leading hydrophobicity indices, i.e., Eisenberg's, Fauchere-Pliska's, and Cid's, using the proposed scales. The analysis is performed using fuzzy cognitive maps that quantify the strength of relation between the hydrophobicity scales/indices and the protein content values. A set of empirical tests that involve generation of fuzzy cognitive map models for a set of 200 low homology proteins have been performed. The results show that the secondary structure content along the protein sequence is characterized by about 2.5 times stronger relation with the two proposed hydrophobicity scales when compared with the currently used raw index values. The new scales exhibit stronger relation irrespective of the applied hydrobhobicity indices. Analysis of different scales shows superiority of the Eisenberg's hydrophobicity index, when used with the new scales. In contrast, the Fauchere-Pliska's index is found to perform better when compared with the two other indices when using raw hydrophobic index values that disregard the long-range interactions.