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Intuitionistic and interval-valued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. (English) Zbl 1183.91038
Fuzzy Optim. Decis. Mak. 8, No. 2, 123-139 (2009); erratum ibid. 11, No. 3, 351-352 (2012).
Summary: E. Szmidt and J. Kacprzyk [in: Artificial intelligence and soft computing – ICAISC 2004. 7th international conference, Zakopane, Poland, June 7–11, 2004. Proceedings. Berlin: Springer. Lecture Notes in Computer Science 3070. Lecture Notes in Artificial Intelligence, 388–393 (2004; Zbl 1058.68667)] introduced a similarity measure, which takes into account not only a pure distance between intuitionistic fuzzy sets but also examines if the compared values are more similar or more dissimilar to each other. By analyzing this similarity measure, we find it somewhat inconvenient in some cases, and thus we develop a new similarity measure between intuitionistic fuzzy sets. Then we apply the developed similarity measure for consensus analysis in group decision making based on intuitionistic fuzzy preference relations, and finally further extend it to the interval-valued intuitionistic fuzzy set theory.

MSC:
91B06 Decision theory
91B10 Group preferences
62C86 Statistical decision theory and fuzziness
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