Extended multi-polarity and multi-polar-valued fuzzy sets

In this paper we introduce extended multi-polarity and discuss its relation to classification problems. We show a connection between extended multi-polarity and multi-polarity; and we define extended multi-polar aggregation operators. We also generalize the notion of bipolar-valued fuzzy sets into multi-polar-valued fuzzy sets and show their link to extended multi-polarity. Further we show that the same link is present between reduced form of multi-polar (bipolar)-valued fuzzy sets and multi-polar aggregation (bipolar aggregation). Several examples are also given including extended multi-polar t-norms.