The Methods Of Constructing The Generalized Compromise Operator

In many decision-making problems of the real-life, we need to have an overallevaluation of them. But it is usually involves many kinds of variables and the modelsof the information aggregations. In the fuzzy set theory, the firstly used as a model ofthe information aggregation is triangular norms and t-conorms, but we find that thesemethods have no compensatory function, and this seemed as a serious limitation. Inorder to compensate this, that is how to choose the aggregation operators as amathematical model to achieve our compromise behavior. We put forward averagingoperator, uninorm operators, nullnorms,-operators, exponential compensatoryoperators, and convex-linear compensatory operators. In order to put all thecompensatory operators into the complete space of the possibility function spaceframe theory, professor Xudong Luo put forward general aggregation operator, andindicates that the operators have general application in the knowledge reasoning,case-based reasoning, and neural network by examples. Unfortunately, ProfessorXudong Luo has does not deeply research the operators from the mathematicallyaspect. In fact, uninorm operator--the special general aggregation operator, wehaven’t completely characterized its structure, so the research on the structure of theoperator will be very difficult. So this paper researches in other aspect, and it lists fourmethods of the construction of the general compromise operator, and it also indicatesthat the results are not correct if one of the prerequisites does not hold. Meanwhile, wecorrect a mistake in [36]. Specifically as follows:The first method is the pseudo inverse construction method; this method is withthe help of a known compromise operator and a monotone mapping to construct anew compromise operator;The second method is the ordinal sum method, the idea of this method is dividesthe region of the[0, τ]nand the[τ,1]nmany times, and instead of many differentcompromise operators and the min function in each piece of the region, and then pastea bigger general aggregation operators;The third method is semigroup method, here we use three exchange orderedsemigroups and three monotone mappings to construct a new general aggregationoperators, and then we can construct general aggregation operators by otheroperations besides addition operator;The fourth method is to mix the three methods to be a kind of effectivemethod—mix method. By introducing these methods, we can construct compromise operator in variousway. Not only that, this paper also gives the condition of theC_τ^（0）,C_τ^（p）,C_τ^（o-p）,C_τ^（p-o）,C_τ^（o-n）,C_τ^（p-n）,C_τ^（n-o）,C_τ^（n-p）, diversify the operator types.