Aggregation Operators and Distance Measures for Probabilistic q-Rung Orthopair Hesitant Fuzzy Sets and Their Applications

A q-rung orthopair fuzzy set (q-ROFS) is an effective tool for describing uncertainty and fuzziness, and is the promotion of intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs). This paper extends q-rung orthopair fuzzy environment to probabilistic q-rung orthopair hesitant fuzzy environment, and proposes the concept of probabilistic q-rung orthopair hesitant fuzzy sets (P-q-ROHFSs). Some desired operational laws and properties of P-q-ROHFSs are studied. And we develop the some aggregation operators for probabilistic q-rung orthopair hesitant fuzzy information. Then the relationship among these operators is discussed by comparing the score function. In order to measure the uncertain information, this paper proposes the four distance measures between two P-q-ROHFSs. Especially, ranking and expansion of P-q-ROHFSs are discussed in detail. Furthermore, we apply them to pattern recognition and multi-attribute group decision making (MAGDM) under probabilistic q-rung orthopair hesitant fuzzy environment. Finally, examples are given to show the rationality and practicability of the proposed method.