Decomposition theorems and extension principles for hesitant fuzzy sets

• We prove a decomposition theorem for hesitant fuzzy sets, which states that every typical hesitant fuzzy set on a set can be represented by a well-structured family of fuzzy sets on that set. This decomposition is expressed by the novel concept of hesitant fuzzy set associated with a family of hesitant fuzzy sets, in terms of newly defined families of their cuts. Our result supposes the first representation theorem of hesitant fuzzy sets in the literature. Other related representation results are proven. We also define two novel extension principles that extend crisp functions to functions that map hesitant fuzzy sets into hesitant fuzzy sets.

Ämnesord

NATURVETENSKAP  -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences -- Computer Sciences (hsv//eng)

Nyckelord

Hesitant fuzzy set

Cut set

Decomposition theorem

Representation theorem

Extension principle

Skövde Artificial Intelligence Lab (SAIL)

Skövde Artificial Intelligence Lab (SAIL)

INF301 Data Science

INF301 Data Science

Publikations- och innehållstyp

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