The Structure And Distributivity For 2-Uninorms Of A Special Type

The aggregation operator is a mathematical model for information fusion,its function is to obtain a single output after fusing multiple input information.In practical application,the structure and selection of aggregation operator is a complicated and significant work.Since the aggregation operator determines the pros and cons of the fusion effect,selecting a reasonable aggregation operator is essential for information fusion.As a very important aggregation operator,2-uninorms have been widely used in many fields,such as pattern discrimination,neural network,data fusion and so on.In reference[43],the author gives the approximate structure of the 2-uninorms,but the characterization of one of the two types of regions is still not given.Therefore,this paper starts from the structure of 2-uninorms studied in reference[43],and further characterizes the structure of 2-uninorms in reference[43] under the condition that the underlying uniform of 2-uninorms is a special type.In our research,we give a more specific structure of a certain type of 2-uninorms.In addition,the research of distributivity has a very wide application in fuzzy logic and image processing,2-uninorms and semi-toperators are two special classes of aggregation operators and have been deemed to be useful in several areas,such as desicion making,approximate reasoning,etc.So the study of distributivity between these two operators will be very interesting.Therefore,this paper focuses on the study of the 2-uninorms,mainly discusses the characterization of the internal structure of the 2-uninorms and its distributivity.The work of this paper is divided into two parts: the first part studies the distributivity for 2-uninorms over semi-t-operators;the second part studies the structure of specific type of 2-uninorms.