| Summary: | Research on SPA sets is an important part of the processing and decision of uncertain information in intelligent information processing, which is of great theoretical significance and practical application value in such methods as multi-attribute decision-making, fuzzy information processing, artificial intelligence and group decision. This paper uses SPA (set pair analysis) sets and the advanced correlate theory to create a more extensive Vague set theory from three aspects, i.e., identity (same), discrepancy (uncertain) and contradistinction (contradictory), with a view to dealing with uncertainties, randomness and fuzziness of information and the correlation laws of such properties. On this basis, we conduct research on operation, distance, similarity, ranking and decision of Vague sets as well as mutual transformation methods and relevant properties of Vague sets, Fuzzy sets and SPA sets.
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