For completeness of the explanation, a few basic concepts are introduced as follows.Definition 1 ��Let �� be a set of mutually exclusive and collectively exhaustive, indicted by��=E1,E2,��,Ei,��,EN.(1)The set �� is called frame of discernment. The power set of �� is indicated by 2��, where2��=?,E1,��,EN,E1,E2,��,E1,E2,��,Ei,��,��.(2)If new A 2��, A is called a proposition.Definition 2 ��For a frame of discernment ��, a mass function is a mapping m from 2�� to [0,1], formally defined bym:2����[0,1],(3)which satisfies the following ��A��2��m(A)=1.(4)In the Dempster-Shafer theory, a mass??condition:m(?)=0, function is also called a basic probability assignment (BPA). If m(A) > 0, A is called a focal element, the union of all focal elements is called the core of the mass function.

Definition 3 ��For a proposition A��, the belief function Bel : 2�� �� [0,1] is defined asBel(A)=��B?Am(B).(5)The plausibility function Pl : 2�� �� [0,1] is defined asPl(A)=1?Bel(A?)=��B��A��?m(B),(6)where A-=��-A. Obviously, Pl(A) �� Bel(A); these functions Bel and Pl are the lower limit function and upper limit function of proposition A, respectively.Consider two pieces of evidence indicated by two BPAs m1 and m2 on the frame of discernment ��; the Dempster’s rule of combination is used to combine them. This rule assumes that these BPAs are independent.Definition 4 ��The Dempster’s rule of combination, also called orthogonal sum, denoted by m = m1?m2, is defined as follows:m(A)={11?K��B��C=Am1(B)m2(C),A��?;0,A=?,(7)withK=��B��C=?m1(B)m2(C).

(8)Note that the Dempster’s rule of combination is only applicable to such two BPAs which satisfy the condition K < 1.3. Proposed MethodIn this section, a new transmembrane protein topology prediction method is proposed based on evidential reasoning. For the sake of convenience, it is briefly written down as TOPPER (Topology prediction of transmembrane protein based on evidential reasoning). The proposed prediction method TOPPER is on the basis of the combination of multiple individual prediction algorithms. In order to obtain the combination predictor, the process is presented step by step as follows.3.1. The Selection of Basic PredictorBecause the proposed topology prediction method is the combination of multiple individual prediction methods, the basic predictors should be constructed first. Here, five individual prediction algorithms, OCTOPUS [3], PRO-TMHMM and PRODIV-TMHMM [38], SCAMPI-msa, and SCAMPI-seq [13], have been selected to construct these basic predictors. In pattern recognition, the Carfilzomib prediction performance of each predictor is expressed by confusion matrix.