Bipolar fuzzy Dombi aggregation operators and its application in multiple-attribute decision-making process

The operations of t-norm and t-conorm introduced by Dombi was known as Dombi operations can have a lead of good flexibility with the general parameter. The Dombi operations have so far not yet been applied for bipolar fuzzy sets. Motivated from Dombi operations, we have proposed bipolar fuzzy Dombi weighted averaging operator, bipolar fuzzy Dombi order weighted averaging operator, bipolar fuzzy Dombi hybrid weighted averaging operator, bipolar fuzzy Dombi weighted geometric operator , bipolar fuzzy Dombi order weighted geometric operator and bipolar fuzzy Dombi hybrid weighted geometric operator as these operators have good advantage of flexibility in operational behavior. Many properties of these operators are investigated. Then, we developed a model for multiple attribute decision-making problem for bipolar fuzzy Dombi aggregation operators under the bipolar fuzzy environment. Finally, a practical example for selection of investment alternatives is given to demonstrate for the utility and application of the proposed work.