Modularity equation plays an important role in the eld of information fusion, which helps to select aggregation functions and reduce the failure rate in the process of aggregation. Based on this, we focus on the study of Modularity equation between overlap (grouping) functions and semi-t-operators. We give the solutions of this equation between overlap (grouping) functions and semi-t-operators with continuous pseudo-t-norm or continuous pseudo-t-conorm in the corresponding cases.

Abstract. In this paper, we have introduced and studied the notion of a fuzzy independent pair and obtain some properties of fuzzy α-modular pairs and independent pairs.

In literature, for the four common classes of uninorms, the Modularity equation has been solved except for the kind of ones having continuous underlying functions. This paper is devoted to solving the Modularity equation involving two uninorms with continuous underlying functions.We discuss this Modularity equation in detail by dividing the main section into two parts. The structure characterization of the two uninorms is almost completely obtained and it is found that they are equal in the unit square except in a subdomain.

In the cognitive sciences, two distinct theories have been proposed about the structure of the human mind, both of which are evolutionary but also different. One of them is the theory of evolutionary psychology and its related claim to the massive Modularity hypothesis, which considers the mind as a set of modules. Another is the simple heuristic and its related claim to the existence of an adaptive toolbox in cognitive methods that assigns mind guidance to the existence of a set of heuristics. Both theories seek to explain cultural diversity by applying these modules/ heuristics. Although proponents of each do not routinely mention the existence of another theory, both theories, both the massive Modularity hypothesis and the existing idea of heuristics in the mind, seek to provide explanations not only from an evolutionary perspective but also in comparative psychology (Which compares the behavior of non-human species) are also acceptable. They also want to explain how cognitive processes are processed in our minds. However, at first, there are reasons to think that these theories offer explanations of human cognition that are incompatible with each other or undermine each other. What is challenged in this article is how a human being, who has always been influenced by a variety of heuristics, cognitive biases, and irrationality in reasoning, judgment, and decision-making during the process of evolution, can have a massive modular cognitive structure in its mind. And be organized to have a logical function