Intuitionistic fuzzy type basic uncertain information

Recently, a new paradigm for uncertain information has been proposed that can effectively handle various types ofuncertainty in decision-making problems. This approach utilizes a certainty degree, which is represented by a realnumber indicating the level of certainty associated with input values. However, just like intuitionistic fuzzy informationcan handle more problems that cannot be well modeled by fuzzy information, the certainty degree in basic uncertaininformation can also be intuitionistic fuzzy granule, which allows it to handle more uncertainty involved decision makingsituations. In this paper, we introduce the concept of intuitionistic fuzzy type basic uncertain information and explainits parameters. We also define a weighted arithmetic mean for aggregating this type of information and discuss differentapproaches for allocating induced weights based on trust preferred preference from four perspectives: (i) preference forhigher certainty degrees; (ii) aversion to higher levels of uncertainty; (iii) preference for greater differences in certaintydegrees; and (iv) preference for intuitionistic fuzzy certainties. Additionally, we explore trichotomic rules-based decisionmaking using intuitionistic fuzzy type basic uncertain information. Finally, we present an objective-subjective evaluationnumerical example utilizing these methods.