Probabilistic Q-Rung Orthopair Hesitant Fuzzy Set And Its Applications

Q-rung orthopair fuzzy sets and probabilistic q-rung orthopair hesitant fuzzy sets are generalizations of intuitionistic fuzzy sets,which are more accurate than intuitionistic fuzzy sets in describing the ideas of decision makers.In order to solve problems of multi-attribute decision making and pattern recognition,this paper studies the entropy measure based on q-iung orthopair fuzzy environment.The concept of probabilistic q-iung orthopair hesitant fuzzy set is proposed,and the aggregation operator and distance measure in this fuzzy environment are discussed in detail.The specific content of this paper is as follows:(1)The q-rung orthopair fuzzy entropy plane is constructed by geometric method,and the specific formula of q-iung orthopair fuzzy entropy is proposed,which satisfies the properties of fuzzy entropy.The influence of parameter ? on fuzzy entropy is discussed.On the basis of the above discussion,the generalized q-rung orthopair fuzzy entropy is proposed.Finally,the multi-attribute decision making problem under q-rung orthopair fuzzy environment is studied,and an example is given to illustrate its effectiveness.(2)The concept of probabilistic q-rung orthopair hesitant fuzzy set is proposed,and its operational laws are discussed in detail.Considering that the sum of probabilities in probabilistic q-rung orthopair hesitant fuzzy numbers may be less than 1,this paper proposes a probability normalization method for probabilistic q-rung orthopair hesitant fuzzy numbers.Several aggregation operators of probabilistic q-rung orthopair hesitant fuzzy numbers are given,and their relationships are analyzed in detail.Finally,a model of solving multi-attribute decision making problems based on aggregation operators is proposed,and the rationality of the model is verified by an example.(3)Considering that the cardinality of different probabilistic q-rung orthopair hesitant fuzzy numbers may be different,this paper proposes a method for ranking and expansion of probabilistic q-rung orthopair hesitant fuzzy numbers.On this basis,four distance measures between two probabilistic q-rung orthopair hesitant fuzzy sets are given.And this paper degenerates the above-mentioned distance measures to q-rung orthopair fuzzy environment,Pythagorean fuzzy environment and intuitionistic fuzzy environment,their rationality is fully verified.Finally,distance measures are applied to multi-attribute group decision making and pattern recognition.