| The inclusion degree is a powerful tool to measure the degree of inclusion between the two sets in the uncertainty reasoning theory.Its theory has been widely used in various fields of artificial intelligence.The interval-valued hesitant fuzzy inclusion degree is an extension of the fuzzy inclusion degree.The purpose of this paper is to give some construction method for the interval-valued hesitant fuzzy inclusion degree.Based on the inclusion degree is a,real number between[0,1],the definition of the hybrid monotonic inclusion degree for interval-valued hesitant fuzzy sets is introduced.then we give some order relationships of interval-valued hesitant fuzzy sets in extended and unextended environment,and some hybrid monotonic inclusion degree for interval-valued hesitant fuzzy sets have be constructed based on the order relationships and be proved in detail.In addition,we discuss the relationship between the hybrid monotonic inclusion degree for interval-valued hesitant fuzzy sets and similarity degree.distance and fuzzy entropy.Based on the feature of inclusion degree and the practicality of interval number ex-pression.the definition of interval inclusion degree for interval-valued hesitant fuzzy sets is presented.which allows the value of the inclusion degree is given in the form of an interval contained in[0.1],and we construct the specific interval inclusion degree by the method of aggregating interval fuzzy implication.Then we define several weak interval inclusion degrees for interval-valued hesitant fuzzy sets and proves its rationality. |
