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Conjunctive and Disjunctive Combination of Belief Functions Induced by Non Distinct Bodies

Conjunctive and Disjunctive Combination of Belief Functions Induced by Non Distinct Bodies of Evidence1

Thierry Den?ux

UMR CNRS6599Heudiasyc

Universit′e de Technologie de Compi`e gne

BP20529-F-60205Compi`e gne cedex-France

Thierry.Denoeux@hds.utc.fr

May30,2007

1This paper is an extended version of[6].

Abstract

Dempster’s rule plays a central role in the theory of belief functions.However,it assumes the combined bodies of evidence to be distinct,an assumption which is not always veri?ed in practice.In this paper,a new operator,the cautious rule of com-bination,is introduced.This operator is commutative,associative and idempotent. This latter property makes it suitable to combine belief functions induced by reliable, but possibly overlapping bodies of evidence.A dual operator,the bold disjunctive rule,is also introduced.This operator is also commutative,associative and idempo-tent,and can be used to combine belief functions issues from possibly overlapping and unreliable sources.Finally,the cautious and bold rules are shown to be particular members of in?nite families of conjunctive and disjunctive combination rules based on triangular norms and conorms.

Keywords:Evidence theory,Dempster-Shafer theory,Transferable Belief Model, Distinct Evidence,Idempotence,Information fusion.

1Introduction

Dempster’s rule of combination[3,29]is known to play a pivotal role in the theory of belief functions,together with its unnormalized version introduced by Smets in the Transferable Belief Model(TBM)[31],hereafter referred to as the TBM conjunctive rule.Justi?cations for the origins and uniqueness of these rules have been provided by several authors[9,31,23,22].However,although they appear well founded theo-retically,the need for greater?exibility through a larger choice of combination rules has been recognized by many researchers involved in real-world applications.Two limitations of Dempster’s rule and its unnormalized version seem to be their lack of robustness with respect to con?icting evidence(a criticism which mainly applies to Dempster’s rule),and the requirement that the items of evidence combined be distinct.

The issue of con?ict management has been addressed by several authors,who proposed alternative rules which,unfortunately,are generally not associative(see, e.g.,[41,12,26],and reviews in[28]and[38]).The disjunctive rule of combination [10,32](hereafter referred to as the TBM disjunctive rule)is both associative and more robust than Dempster’s rule in the presence of con?icting evidence,and its use is appropriate when the con?ict is due to poor reliability of some of the sources.It may also be argued that problems with Dempster’s rule(and,to a lesser extent,with the TBM conjunctive rule)are often due to incorrect or incomplete modelisation of the problem at hand,and that these rules often yield reasonable results when they are properly applied[18].In[38],an expert system approach is advocated in case of large con?ict,to determine its origin and revise the underlying hypotheses accordingly.

The other,and perhaps more fundamental,limitation of Dempster’s rule lies in the assumption that the items of evidence combined be distinct or,in other words, that the information sources be independent.As remarked by Dempster[3],the real-world meaning of this notion is di?cult to describe.The general idea is that,in the combination process,no elementary item of evidence should be counted twice.Thus, non overlapping random samples from a population are clearly distinct items of evi-dence,whereas“opinions of di?erent people based on overlapping experiences could not be regarded as independent sources”[3].When the nature of the interaction be-tween items of evidence can be described mathematically,then it is possible to extend Dempster’s rule or the TBM conjunctive rule so as to include this knowledge(see,e.g., [9,30]).However,it is often the case that,although two items of evidence(such as, e.g.,opinions expressed by two experts sharing some experiences,or observations of correlated random quantities)can clearly not be regarded as distinct,the interaction between them is ill known and,in many cases,almost impossible to describe.

In such a common situation,it would be very helpful to have a combination rule that would not rely on the distinctness assumption.An early attempt to provide such a rule is reported in[27],but it was limited to the combination of simple belief functions(i.e.,belief functions having at most two focal sets,including the frame of discernment).This method was extended to separable belief functions(i.e.,belief functions that can be decomposed as the conjunctive sum of simple belief functions) in[16].However,not all belief functions are separable,and the justi?cation for this approach was unclear.

A natural requirement for a rule allowing the combination of overlapping bodies of evidence is idempotence.The arithmetic mean does possess this property,but it is not

associative,another requirement often regarded as essential.Following an approach initiated by Dubois and Prade in[9],Cattaneo[1]studied a family of rules gener-alizing the TBM conjunctive rule,based on the de?nition of a joint belief function on a product space,whose marginals are the belief functions to be combined.Inside this family,he proposed a rule minimizing the con?ict,which happens to be idempo-tent.However,he showed that,within this particular family of rules,associativity is incompatible both with idempotency,and with con?ict minimization.

In contrast,associative and idempotent operators exist in possibility theory,based on the minimum triangular norm and its dual,the maximum triangular conorm. Dubois and Yager[15]showed that agregation operators for possibility distributions (or,equivalently,fuzzy set connectives)can be deduced from assumptions on multi-valued mappings underlying the possibility distributions viewed as consonant belief functions.This approach,however,has not made it possible to extend possibilistic agregation operators to arbitrary belief functions while maintaining such properties as associativity and idempotency.New operators satisfying these properties are pro-posed in this paper,following a completely di?erent approach based on some ideas suggested to the author by the late Philippe Smets[36].

The rest of this paper is organized as follows.The underlying fundamental con-cepts,including the canonical decomposition and the relative information content of belief functions,are?rst recalled in Section2.The cautious conjunctive rule and its dual,the bold disjunctive rule are then introduced in Sections3and4,respectively. The cautious and bold rules are shown in Section5to be particular members of in?nite families of conjunctive and disjunctive combination rules based on triangular norms and conorms.Finally,the e?ciency of the cautious rule to combine information from dependent features in a classi?er fusion problem is demonstrated experimentally in Section6,and Section7concludes the paper.

2Fundamental Concepts

In this section,the main building blocks of new combination rules de?ned later are introduced.The basic concepts and terminology related to belief functions are?rst summarized in Section2.1.Section2.2then focuses on the canonical conjunctive decomposition of non dogmatic belief functions,which allows their representation in the form of conjunctive weight functions taking values in(0,+∞).This section is essential,as the cautious conjunctive rule introduced in this paper will be expressed as a function of conjunctive weights.Finally,Section2.3recalls known de?nitions and results related to the ordering of belief functions according to their information content;a new partial ordering relation based on conjunctive weights is also intro-duced.This ordering relation will play an important role in the derivation of the new combination rules.

2.1Basic De?nitions and Notations

In this paper,the TBM[39,34]is accepted as a model of uncertainty.An agent’s state of belief expressed on a?nite frame of discernmentΩ={ω1,...,ωK}is represented by a basic belief assignment(BBA)m,de?ned as a mapping from2Ωto[0,1]verifying

A?Ωm(A)=1.Subsets A ofΩsuch that m(A)>0are called focal sets of m.A

BBA m is said to be

?normal if?is not a focal set(this condition is not imposed in the TBM);

?subnormal is?is a focal set;

?dogmatic ifΩis not a focal set;

?vacuous ifΩis the only focal set;

?simple if it has at most two focal sets and,if it has two,Ωis one of those;

?categorical if it has only one focal set;

?Bayesian if its focal sets are singletons.

A subnormal BBA m can be transformed into a normal BBA m?by the normalization operation de?ned as follows:

m?(A)=

k·m(A)if A=?,

0otherwise,

(1)

for all A?Ω,with k=(1?m(?))?1.

A simple BBA(SBBA)m such that m(A)=1?w for some A=Ωand m(Ω)=w can be noted A w(the advantage of this notation will become apparent later).The vacuous BBA can thus be noted A1for any A?Ω,and a categorical BBA can be noted A0for some A=Ω.A BBA m can equivalently be represented by its associated belief,implicability,plausibility and commonality functions de?ned,respectively,as:

bel(A)=

? =B?A

m(B),(2)

b(A)=

B?A

m(B)=bel(A)+m(?),(3)

pl(A)=

B∩A=?

m(B),(4)

and

q(A)=

B?A

m(B),(5) for all A?Ω.BBA m can be recovered from any of these functions.For instance:

m(A)=

B?A

(?1)|B|?|A|q(B),?A?Ω,(6)

and

m(A)=

B?A

(?1)|A|?|B|b(B),?A?Ω,(7) where|A|denotes the cardinality of A.

The negation(or complement)m of a BBA m is de?ned as the BBA verifying m(A)=m(A)for all A?Ω,where A denotes the complement of A[10].It may easily be shown that the implicability function b associated to m and the commonality function q associated to m are linked by the following relation:

b(A)=q(A),?A?Ω.(8)

A BBA m is said to be consonant if its focal sets are nested.This is known to be equivalent to the following condition[29]:

pl(A∪B)=pl(A)∨pl(B),?A,B?Ω,

where∨denote the maximum operator.The above equation de?nes a possibility measure[42].Consequently,a consonant BBA uniquely de?nes a possibility measure. The corresponding possibility distribution is then given by

π(ω)=pl({ω})=q({ω}),?ω∈Ω.

Given a BBA m and a coe?cientα∈[0,1],the discounting of m with discount rateαyields the new BBAαm de?ned by:

αm=(1?α)m+αmΩ,

where mΩdenotes the vacuous BBA[29,page252].The discounting operation is used to model a situation where a source S provides a BBA m,and the reliability of S is measured by1?α.If S is fully reliable(1?α=1),then m is left unchanged.If S is not reliable at all,m is transformed into the vacuous BBA.In intermediate situations, m is replaced by a convex combination of m and the vacuous BBA.

The TBM conjunctive rule and Dempster’s rule are noted∩ and⊕,respectively. They are de?ned as follows.Let m1and m2be two BBAs,and let m1∩ 2and m1⊕2 be the result of their combination by∩ and⊕.We have:

m1∩ 2(A)=

B∩C=A

m1(B)m2(C),?A?Ω,(9) and,assuming that m1∩ 2(?)=1:

m1⊕2(A)=

0if A=?,

m1∩ 2(A)

1?m1∩ 2(?)otherwise.

(10)

Dempster’s rule is just equivalent to the TBM conjunctive rule followed by normaliza-tion using(1).Both rules are commutative,associative,and admit a unique neutral element:the vacuous BBA.They both assume the combined items of evidence to be distinct.Let A w1and A w2be two SBBAs with the same focal element A=Ω.The result of their∩ -combination is the SBBA A w1w2.The⊕operator yields the same result as long as A=?.The TBM conjunctive rule has a simple expression in terms of commonality functions:with obvious notations,we have:

q1∩ 2=q1·q2.(11)

In the TBM,conditioning by B?Ωis equivalent to conjunctive combination with a categorical BBA m B focused on B.The result is noted m[B],with m[B]=m∩ m B. This conditional BBA quanti?es our belief onΩ,in a context where B holds.

Let us now assume that m1∩ 2has been obtained by combining two BBAs m1and m2,and then we learn that m2is in fact not supported by evidence and should be “removed”from m1∩ 2.This“decombination”operation was introduced in[33].It is well de?ned if m2is non dogmatic.Denoting∩ this operator,we can write:

m1∩ 2∩ m2=m1.

Decombination can easily be computed for any two BBAs m1and m2using the cor-responding commonality functions as:

q1∩ 2(A)=q1(A)

q2(A)

,?A?Ω.(12)

Note that q2(A)>0for all A as long as m2is non dogmatic.One should also be aware that the quotient of two commonality functions is not always a commonality function.Consequently,m1∩ m2is not necessarily a BBA.

A disjunctive rule of combination∪ also exists[10,32]:it is de?ned as

m1∪ 2(A)=

B∪C=A

m1(B)m2(C),?A?Ω.(13)

This rule,called the TBM disjunctive rule,is also commutative and associative.It has a simple expression in terms of implicability functions,which is the counterpart of(11):

b1∪ 2=b1·b2.(14) As for the TBM conjunctive rule,an inverse operation may also be de?ned for the

TBM disjunctive rule:

b1∪ 2(A)=b1(A)

b2(A)

,?A?Ω.(15)

This operation is well-de?ned as long as m2is subnormal(in which case we have b2(A)>0for all A).However,it does not necessarily produce a belief function.Its interpretation is similar to that of∩ :it removes,or“decombines”’,evidence which has been combined disjunctively with prior knowledge.

The dual nature of∩ and∪ becomes apparent when one notices that these two operators are linked by De Morgan’s laws[10]:

m1∪ m2=m1∩ m2,(16)

m1∩ m2=m1∪ m2,(17) for all m1and m2.

As remarked by Smets[32],the TBM conjunctive rule is based on the assumption that the belief functions to be combined are induced by reliable sources of information, whereas the TBM disjunctive rule only assume that at least one source of information is reliable,but we do not know which one.Both rules assume the sources of information to be independent(i.e.,they are assumed to provide distinct,non overlapping pieces of evidence).

In the TBM,combination rules belong to the credal level where evidence aggre-gation takes place,whereas decisions are made at the pignistic level[39],where each BBA m is mapped to a pignistic probability function Betp m de?ned by

Betp m(ω)=

{A:ω∈A}m?(A)

|A|,?ω∈Ω,(18)

where m?denotes the normalized version of m.

2.2Canonical Conjunctive Decomposition of a Belief Function Shafer[29,Chapter4]de?ned a separable BBA as the result of the⊕combination of SBBAs.For every separable BBA in the sense of Shafer,one has:

? =A?Ω

A w(A),(19)

with w(A)∈[0,1]for all A?Ω,A=?.This representation is unique if m is non dogmatic.Shafer named this representation the canonical decomposition of m.

The concept of separability can be extended to subnormal BBAs in two ways:?We will say that a BBA m is u-separable(where“u”stands for“unnormalized”) if we have

m=∩ A?ΩA w(A),(20) with w(A)∈[0,1]for all A?Ω;

?We will say that a BBA m is n-separable(where“n”stands for“normalized”) if we have

m?=

? =A?Ω

A w(A),(21)

where w(A)∈[0,1]for all A?Ω,A=?,and m?is the normalized form of m. Again,the decompositions(20)and(21)are unique as long as m is non dogmatic. Clearly,(20)implies(21),but the converse is not true,as will be shown below.Con-sequently,u-separability is a stronger notion than n-separability.

2.2.1Extension to non dogmatic BBAs

The canonical decomposition of a separable BBA was extended to any non dogmatic BBA by Smets[33].The key to such a generalization is the notion of generalized simple BBA(GSBBA),de?ned as a functionμfrom2Ωto R verifying

μ(A)=1?w,(22)

μ(Ω)=w,(23)

μ(B)=0?B∈2Ω\{A,Ω},(24) for some A=Ωand some w∈[0,+∞).Any GSBBAμcan thus be noted A w for some A=Ωand w∈[0,+∞).When w≤1,μis a SBBA.When w>1,μis not a BBA,since it is no longer a mapping from2Ωto[0,1].Such a function can be

referred to as an inverse simple BBA (ISBBA),using a terminology similar to that used in [33].The TBM conjunctive rule can be trivially extended to combine SBBAs

and ISBBAs alike.In particular,the relationship A w 1∩

A w 2=A w 1w 2still holds for w 1,w 2∈[0,+∞).

In [33],Smets proposed an interpretation of an ISBBA as representing a state of belief in which one has some reasons not to believe in A .By combining A w for some w >1with the SBBA A 1/w using the TBM conjunctive rule,one obtains the vacuous bba A 1.Hence,the ISBBA A w corresponds to a situation where the agent has a “debt of belief”in A ,and some evidence has to be accumulated before it starts to believe in A .

Using the concept of GSBBA,and extending Shafer’s approach,Smets showed that any non dogmatic BBA can be uniquely represented as the conjunctive combination of GSBBAs:

m =∩

A ?ΩA w (A ),(25)with w (A )∈(0,+∞)for all A ?Ω.Equation (25)is clearly an extension of (19).It de?nes the canonical conjunctive decomposition of m (we will see in Section 4.1that a canonical disjunctive decomposition also exists).The weights w (A )for every A ?Ωcan be obtained from the commonalities using the following formula:w (A )=

B ?A q (B )(?1)|B |?|A |+1,(26)=????????????? B ?A,|B | ∈2N q (B ) B ?A,|B |∈2N q (B )

if |A |∈2N B ?A,|B |∈2N q (B ) B ?A,|B | ∈2N q (B )otherwise,

(27)where 2N denotes the set of even natural numbers.Eq.(26)can be equivalently written ln w (A )=?

B ?A

(?1)|B |?|A |ln q (B ),?A ?Ω.(28)One notices the similarity with (6).Hence,any procedure for transforming q to m (such as the Fast M¨o bius Transform [21]or matrix multiplication [35])can be used to compute ln w from ?ln q .

The function w :2Ω\{Ω}→(0,+∞)(hereafter referred to as the conjunctive weight function)is thus yet another equivalent representation of any non dogmatic BBA (together with bel ,pl ,q ,etc.).This concept of conjunctive weight function can be extended to a dogmatic BBA m by discounting it with some discount rate and letting tend towards 0[33].However,this extension requires some mathematical subtleties.Furthermore,it may be argued that most (if not all)states of belief,being based on imperfect and not entirely conclusive evidence,should be represented by non dogmatic belief functions,even if the mass m (Ω)is very small.For instance,consider a coin tossing experiment.It is natural to de?ne a BBA on Ω={Heads,T ails }as m ({Heads })=0.5and m ({T ails })=0.5.However,this assumes the coin to be perfectly balanced,a condition never exactly veri?ed in practice.So,a more appropriate BBA may be m ({Heads })=0.5(1? ),m ({T ails })=0.5(1? )and m (Ω)= for some small >0.

Example 1Let Ω={a,b,c }be a frame of discernment,and m the BBA shown in Table 1.The weights can be computed from the commonalities using (26)as follows:

w (?)=

q ({a })q ({b })q ({c })q ({a,b,c })q (?)q ({a,b })q ({a,c })q ({b,c })=0.5×1×0.7×0.21×0.5×0.2×0.7=1w ({a })=

q ({a,b })q ({a,c })q ({a })q ({a,b,c })=0.5×0.20.5×0.2=1w ({b })=

q ({a,b })q ({b,c })q ({b })q ({a,b,c })=0.5×0.71×0.2=7/4w ({a,b })=

q ({a,b,c })q ({a,b })=0.20.5=2/5w ({c })=

q ({a,c })q ({b,c })q ({c })q ({a,b,c })=0.2×0.20.7×0.2=1

w ({a,c })=

q ({a,b,c })q ({a,c })=0.20.1=1w ({b,c })=q ({a,b,c })q ({b,c })=0.20.7=2/7.We can see that m can be represented as the conjunctive combination of two SBBAs {a,b }2/5and {b,c }2/7,and an ISBBA {b }7/4.

Table 1:A BBA with its commonality and weight functions.

A m (A )q (A )w (A )?011{a }00.51{b }017/4{a,b }0.30.52/5{c }00.71{a,c }00.21{b,c }

0.50.72/7

Ω0.20.22.2.2Special cases

In the following two propositions,we provide analytical formulas for the conjunctive weight functions associated to two important classes of BBAs.

Proposition 1Let A 1,...,A n be n subsets of Ωsuch that A i ∩A j =?for all i,j ∈{1,...,n },and let m be a BBA on Ωwith focal sets A 1,...,A n ,and Ω.We assume that m (Ω)+ n k =1m (A k )≤1,so that ?may also be a focal set.The conjunctive weight function associated to m is:w (A )=?????m (A k )m (A k )+m (Ω),A =A k ,m (Ω) n k =1 1+m (A k )m (Ω) ,A =?,1,otherwise.

Proof:We have:

q(A)=?

m(A k)+m(Ω),A?A k,

1,A=?,

m(Ω),otherwise.

Consequently,m may be expressed as a function of q as follows:

m(A k)=q(A k)?q(Ω),k=1,...,n,(29)

m(Ω)=q(Ω)(30)

m(?)=q(?)?q(Ω)?

k=1

(q(A k)?q(Ω))(31)

m(A)=0,?A/∈{A1,...,A n,Ω,?}.(32) As explained above,ln w may be obtained from?ln q using any procedure that transforms q to m.Consequently,we may,in the above equations,replace m by ln w and q by?ln q(except in(30),because w(Ω)is not de?ned).We obtain from(29):

ln w(A k)=?ln q(A k)+ln q(Ω)=ln q(Ω) q(A k)

which implies

w(A k)=

m(A k)

m(A k)+m(Ω)

,k=1,...,n.

Now,from(31)we get

ln w(?)=?ln q(?)+ln q(Ω)+

k=1

(ln q(A k)?ln q(Ω)),

=ln

q(Ω)1?n

k=1

q(A k)

=ln

m(Ω)1?n

k=1

(m(Ω)+m(A k))

which implies

w(?)=m(Ω)

k=1

m(A k)

m(Ω)

Finally,(32)implies that w(A)=1,for all A/∈{A1,...,A n,Ω,?}.

The BBAs studied in Proposition1may be termed“quasi-Bayesian”,as they can be obtained by discounting Bayesian BBAs de?ned on a coarsening ofΩ.This class of BBAs is closed under the TBM conjunctive rule.Quasi-Bayesian BBAs are de?ned by a small number of masses,and are frequently encountered in applications.

Another important case concerns consonant BBAs,whose focal sets are nested. The following proposition provides formulas to compute the weight function associated to a consonant BBA.

Proposition 2Let m be a consonant BBA,with associated possibility distribution π(ωk )=q ({ωk }),k =1,...,K .We note πk =π(ωk )and we assume that the elements of Ωhave been arranged in decreasing order of plausibility,i.e.,we have

1≥π1≥π2≥...≥πK >0.

Let A k ={ω1,...,ωk },k =1,...,K .The focal sets of m are in {A 1,...,A K ,?}(m is subnormal if π1<1,and it is non dogmatic since we have assumed πK >0).The conjunctive weight function associated to m is:

w (A )=???π1A =?,πk +1πk ,A =A k ,1≤k

Proof .As shown in [8],m can be computed from π1,...,πK as:

m (A )=???????1?π1,A =?,πk ?πk +1,A =A k ,1≤k

Since πk =q ({ωk }),we may deduce that ln w (A )=???ln π1,A =?,?ln πk +ln πk +1,A =A k ,1≤k

from which the desired expression of w can be easily derived.

2.2.3Normalization and combination It may be remarked that normalizing a subnormal BBA m using (1)amounts to combining it with the ISBBA ?k :

m ?=m ∩

?k .Consequently,the weight function w ?associated to m ?is identical to w ,except for

the weight assigned to ?.If m =∩

A ?ΩA w (A ),we have m ?=?k ∩ ?w (?)∩ ∩ ? =A ?ΩA w (A ) =?

k ·w (?)∩ ∩ ? =A ?ΩA w (A ) ,=∩ A ?ΩA w ?(A )

with w ?(?)=k ·w (?)and w ?(A )=w (A )for all A ∈2Ω\{?,Ω}.We can write,equivalently:m ?=

? =A ?Ω

A w (A ).(33)As a direct consequence of the above remark,it is easy to formulate criteria for u-separability and n-separability:

?A BBA m is u-separable i?w (A )≤1,for all A ?Ω;

?A BBA m is n-separable i?w (A )≤1,for all A ?Ω,A =?.

For instance,quasi-Bayesian BBAs studied in Proposition 1are n-separable,but they are not u-separable in general (we may have w (?)>1).In contrast,consonant BBAs are u-separable,since they satisfy the condition w (A )≤1for all A ?Ω.

The w representation appears particularly interesting when it comes to combining BBAs using the TBM conjunctive rule or Dempster’s rule.Indeed,let m 1and m 2be two BBAs with weight functions w 1and w 2.We have:

m 1∩ m 2= ∩ A ?ΩA w 1(A ) ∩ ∩ A ?ΩA w 2(A ) (34)

=∩ A ?ΩA w 1(A )w 2(A ).(35)

We can thus write,with obvious notations:

w 1∩ 2=w 1·w 2,

which is reminiscent of (11).The inverse TBM conjunctive rule ∩

also has a simple expression in the w -space,similar to (33):we have w 1∩ 2=w 1/w 2.Hence,

m 1∩

m 2= ∩ A ?ΩA w 1(A ) ∩ ∩ A ?ΩA w 2(A ) (36)=∩ A ?ΩA w 1(A )/w 2(A ).(37)

Finally,using (33),it is easy to see that

m 1⊕m 2=

? =A ?ΩA w 1(A )w 2(A ).(38)

2.2.4Latent belief structure

Let m be a non dogmatic belief function,and w its associated conjunctive weight function.For each weight w (A )let us de?ne the following two quantities:

w c (A )=1∧w (A ),

(39)and

w d (A )=1∧1w (A ),(40)

where ∧denotes the minimum operator.It is clear that we have

w (A )=w c (A )w d (A )

.(41)Consequently,we can write

m =∩ A ?ΩA w c (A )/w d (A )(42)=

∩ A ?ΩA w c (A ) ∩ ∩ A ?ΩA w d (A ) (43)=m c ∩ m d .(44)

Any non dogmatic BBA m can thus be decomposed into two u-separable BBAs m c and m d called,respectively,its con?dence and di?dence components.The pair(m c,m d) forms what Smets called a latent belief structure(LBS)[33].He proposed to interpret m c as representing positive evidence,i.e.,good reasons to believe in various propo-sitions A?Ω,and m d as representing negative evidence,i.e.,good reasons not to believe in the same propositions.The BBA m is obtained by removing the negative evidence m d from the positive evidence m c.Note that we have the following property with respect to the TBM conjunctive rule:if(m c1,m d1)and(m c2,m d2)are two LBSs associated to non dogmatic BBAs m1and m2,respectively,then(m c1∩ m c2,m d1∩ m d2) is a LBS associated to m1∩ m2.

2.3Informational Comparison of Belief Functions

In the TBM,the Least commitment Principle(LCP)plays a role similar to the prin-ciple of maximum entropy in Bayesian Probability Theory.As explained in[32],the LCP indicates that,given two belief functions compatible with a set of constraints, the most appropriate is the least informative.To make this principle operational,it is necessary to de?ne ways of comparing belief functions according to their information content.Three such partial orderings,generalizing set inclusion,were proposed in the 1980’s by Yager[40]and Dubois and Prade[10];they are de?ned as follows:?pl-ordering:m1 pl m2i?pl1(A)≤pl2(A),for all A?Ω;

?q-ordering:m1 q m2i?q1(A)≤q2(A),for all A?Ω;

?s-ordering:m1 s m2i?there exists a square matrix S with general term S(A,B),A,B∈2Ωverifying

S(A,B)=1,?A?Ω,

B?Ω

S(A,B)>0?A?B,A,B?Ω,

such that

S(A,B)m2(B),?A?Ω.(45)

m1(A)=

B?Ω

The term S(A,B)may be seen as the proportion of the mass m2(B)which is transferred(“?ows down”)to A.Matrix S is named a specialization matrix [23,35],and m1is said to be a specialization of m2.

As shown in[10],these three de?nitions are not equivalent:m1 s m2implies m1 pl m2and m1 q m2,but the converse is not true.Additionally,pl-ordering and q-ordering are not comparable.However,in the set of consonant BBAs,these three partial orders are equivalent.The interpretation of these ordering relations is discussed in[10]from a set-theoretical perspective,and in[13]from the point of view of the TBM.Whenever we have m1 x m2,with x∈{pl,q,s},we will say that m1is x-more committed than m2.

Another concept which leads to an alternative de?nition of informational order-ing is that of Dempsterian specialization[23].m1is said to be a Dempsterian spe-cialization of m2,which we note m1 d m2,i?there exists a BBA m such that

m 1=m ∩

m 2.As shown in [23],this is a stronger condition than specialization,i.e.,we have m 1 d m 2?m 1 s m 2,but the converse is false.If m 1=m ∩

m 2,then there is a specialization matrix S m de?ned as a function of m ,called a Dempsterian specialization matrix,allowing to compute m 1from m 2using relation (45).

Finally,we can think of one more de?nition of informational ordering based on the weight function recalled in Section 2.2:given two non dogmatic BBAs m 1and m 2,we can say that m 1is w -more committed than m 2,which we note m 1 w m 2,i?w 1(A )≤w 2(A ),for all A ?Ω.Because of (35),this is equivalent to the existence

of a u-separable BBA m ,with weight function w =w 1/w 2,such that m 1=m ∩

m 2.Consequently,w -ordering is strictly stronger than d -ordering.The meaning of d and w is clear:if m 1 d m 2or m 1 w m 2,it means that m 1is the result of the combination of m 2with some BBA m ;consequently,m 1has a higher information content than m 2.In the case of w ,the requirement that m be u-separable may seem arti?cial.However,it may be argued that most belief functions encountered in practice result from the pooling of simple evidence,and are therefore u-separable.As shown in Section 2.2.2,this is also the case for consonant belief funtions,a class of belief functions often encountered in applications because of its simplicity.Furthermore,we will see that w -ordering happens to be a simpler and more convenient notion,for some purposes,than other orderings.A slightly weaker notion based on n-separability will be de?ned later in Section 3.3.We defer the introduction of this additional notion for clarity of presentation.

In summary,we thus have,for any two non dogmatic BBAs m 1and m 2:m 1 w m 2?m 1 d m 2?m 1 s m 2? m 1 pl m 2m 1 q m 2,

(46)where all implications are strict.

The vacuous BBA m Ω(with weight function w Ω(A )=1,for all A ?Ω)is the unique greatest element for partial orderings x with x ∈{pl,q,s,d },i.e.,we have

m x m Ω,?m,?x ∈{pl,q,s,d }.

In contrast,m Ωis only a maximal element for w ,i.e.,we have the following weaker property

m Ω w m ?m =m Ω.

The BBAs that are w -less speci?c than m Ωare the u-separable ones.Non u-separable BBAs are not comparable with m Ωaccording to relation w .

As emphasized by Dubois and Prade in [10],relations x with x ∈{pl,q,s }generalize set inclusion:if m A and m B are two categorical BBAs such that m A (A )=1and m B (B )=1,then m A x m B ,with x ∈{pl,q,s },if and only if A ?B .The same is true for relation d .For relation w ,this property does not hold,since categorical BBAs,being dogmatic,cannot be compared according to w .However,we can still have a similar property if we consider a categorical BBA as the limit of a sequence of non dogmatic BBAs.More precisely,let ( n ),n =1,2,...,∞be a real sequence such that n ∈[0,1]for all n ,and lim n →∞ n =0.For any A ?Ω,let m n A the BBA with following weight function:w n A (C )= n if C ?A 1otherwise,

for all C?Ω.It is clear that m n A(A)≥1? n.Consequently,we have lim n→∞m n A(A)= 1and lim n→∞m n A(C)=0,for all C=A.This means that the categorical BBA m A may seen as the limit of the sequence(m n A),this sequence being uniquely de?ned, given( n).Using this representation,we can state the following proposition. Proposition3Let A and B be two subsets ofΩ,m A and m B the categorical BBAs focused on A and B,and(m n A)and(m n B)their representations as sequences of BBAs as de?ned above.Then,we have

A?B?m n A w m n B,?n≥1.

Proof:Assume that A?B.Let C be an arbitrary subset ofΩ:

?if C?B,then C?A,and we have w n A(C)=w n B(C)= n;

?if C?B,then w n B(C)=1≥w n A(C).

Conversely,assume that w n A(C)≤w n B(C)for all C?Ω.Then w n A(B)≤w n B(B)= n. Consequently,w n A(B)= n,and A?B.

Equipped with these de?nitions of the relative information content of belief func-tions,it is possible to give an operational meaning of the LCP.Let M be a set of BBA compatible with a set of constraints.The LCP dictates to choose a greatest element in M,if one such element exists,according to one of the partial ordering x,for some x∈{pl,q,s,d,w}.These partial orderings seem equally well justi?ed and reasonable and,in the absence of any decisive argument to discard any of them,considerations of simplicity,existence of a solution and tractability of calculations can be invoked to choose a particular ordering for a given problem.For instance,q-ordering is adopted in[13]to derive the expression of the q-least committed BBA with given pignistic probability function.In the following section,the same principle is used to derive a rule of combination,using partial ordering w.

3The Cautious Conjunctive Rule

3.1Derivation from the LCP

Just as relations x may be seen as generalizing set inclusion,it is possible to conceive conjunctive combination rules generalizing set intersection,by reasoning as follows. Assume that we have two sources of information,one of which indicates that the true value of the variable of interestωlies in A?Ω,while the other one indicates that it lies in B?Ω,with A=B.If we consider both sources as reliable,then we can deduce thatωlies in some set C such that C?A,and C?B.The largest of these subsets is the intersection A∩B of A and B.

Let us now assume that the two sources provide BBAs m1and m2,and the sources are both considered to be reliable.The agent’s state of belief,after receiving these two pieces of information,should then be represented by a BBA m12more informative than m1,and more informative than m2.Let us denote by S x(m)the set of BBAs m such that m x m,for some x∈{pl,q,s,d,w}.We thus have m12∈S x(m1) and m12∈S x(m2)or,equivalently,m12∈S x(m1)∩S x(m2).According to the LCP,

one should select the x-least committed element in S x(m1)∩S x(m2).This de?nes

a conjunctive combination rule,provided that an x-least committed element(i.e.,a greatest element with respect with partial order x)exists and is unique.

In[13],this approach was used to justify the minimum rule for combining possibil-ity distributions,from the point of view of the TBM.Let m1and m2be two consonant BBAs,and let q1and q2be their respective commonality functions.Then,the con-sonant BBA m12with commonality function q12(A)=q1(A)∧q2(A)for all A?Ωis claimed in[13]to be the s-least committed element in the set S s(m1)∩S s(m2).This approach,however,cannot be blindly transposed to non consonant BBAs,since the minimum of two commonality functions is not,in general,a commonality function.

However,applying this approach with the w ordering does yield an interesting solution,as shown by the following lemma and proposition.

Lemma1Let m by a non dogmatic BBA with conjunctive weight function w,and let w be a mapping from2Ω\Ωto(0,+∞)such that w (A)≤w(A)for all A?Ω.Then

w is the conjunctive weight function of some BBA m .

Proof:We have

w (A)=w(A)·w (A)

w(A)

,?A?Ω.

Since w (A)/w(A)≤1for all A?Ω,w /w is the weigth function of a u-separable BBA.Consequently,w is the weigth function of a BBA m obtained by combining m with a u-separable BBA using the TBM conjunctive rule. Proposition4Let m1and m2be two non dogmatic BBAs.The w-least committed element in S w(m1)∩S w(m2)exists and is unique.It is de?ned by the following weight function:

w1∧ 2(A)=w1(A)∧w2(A),?A?Ω.(47) Proof:For i=1and i=2,we have m∈S w(m i)i?w(A)≤w i(A)for all A?Ω. Hence,m∈S w(m1)∩S w(m2)i?w(A)≤w1(A)∧w2(A)for all A?Ω.Let us consider function w1∧ 2de?ned by w1∧ 2(A)=w1(A)∧w2(A),for all A?Ω.This is the conjunctive weight function of a valid BBA,as a consequence of Lemma1. Consequently,it corresponds to the unique w-least committed element in S w(m1)∩S w(m2).

Equation(47)de?nes a new rule which can be formally de?ned as follows. Definition1(Cautious conjunctive rule)Let m1and m2be two non dogmatic BBAs.Their combination using the cautious conjunctive rule(or cautious rule for short)is noted m1∧ 2=m1∧ m2.It is de?ned as the BBA with the following weight

function:

w1∧ 2(A)=w1(A)∧w2(A),?A?Ω.

We thus have

m1∧ m2=∩ A?ΩA w1(A)∧w2(A).(48) Note that this rule happens to generalize a method proposed by Kennes[20]for combining u-separable BBAs induced by non distinct items of evidence,based on an application of category theory to evidential https://www.wendangku.net/doc/636788445.html,ing the canonical decompo-sition of non dogmatic belief functions and the concept of w-ordering,the new rule

described in this paper proves to be well justi?ed for combining the wider class of non dogmatic belief functions.

As another remark,it must also be emphasized that the cautious rule provides a BBA m1∧ m2which is the w-least committed in the set S w(m1)∩S w(m2)of BBAs that are w-more committed than both m1and m2.When either m1or m2is not u-separable,then m1∩ m2does not belong to that set(because,e.g.,w1(A)w2(A)> w1(A)whenever w2(A)>1).Consequently,we do not have m1∩ m2 w m1∧ m2in general,except when both m1and m2are separable.

In practice,the cautious combination of two non dogmatic BBAs m1and m2can thus be computed as follows:

?Compute the commonality functions q1and q2using(5);

?Compute the weight functions w1and w2using(26);

?Compute m1∧ 2=m1∧ m2as the∩ combination of GSBBAs A w1(A)∧w2(A),for all A?Ωsuch that w1∧w2(A)=1.

Example2Table2shows the weight functions of two BBAs m1and m2onΩ= {a,b,c},a well as the combined weight function w1∧ 2and BBA m1∧ m2.In this case,m1∧ 2is obtained as the TBM conjunctive combination of three SBBAs:{b}0.7, {a,b}2/5and{b,c}2/7.By combining the?rst two we get a mass0.3on{b},3/5×0.7= 0.42on{a,b}and2/5×0.7=0.28onΩ.Combination with{b,c}2/7then yields

m1∧ 2({b})=0.3×(2/7+5/7)+0.42×5/7=0.6,

m1∧ 2({a,b})=0.42×2/7=0.12,

m1∧ 2({b,c})=0.28×5/7=0.2,

m1∧ 2(Ω)=0.28×2/7=0.08.

The result of the combination of m1and m2using the TBM conjunctive rule directly from(9)is shown in the last column of Table2for comparison.

Table2:Combination of two BBAs using the cautious rule.

A m1(A)w1(A)m2(A)w2(A)w1∧ 2(A)m1∧ 2(A)m1∩ 2(A)

?0101100

{a}0101100

{b}07/40.30.70.70.60.42

{a,b}0.32/5012/50.120.09

{c}0101100

{a,c}0101100

{b,c}0.52/70.43/72/70.20.43

Ω0.20.30.080.06

3.2Properties

Proposition5The cautious conjunctive rule has the following properties:

Commutativity:for all m1and m2,m1∧ m2=m2∧ m1;

Associativity:for all m1,m2and m3,m1∧ (m2∧ m3)=(m1∧ m2)∧ m3; Idempotence:for all m,m∧ m=m;

Distributivity of∩ with respect to∧ :for all m1,m2and m3,

m1∩ (m2∧ m3)=(m1∩ m2)∧ (m1∩ m3).

Proof:Commutativity,associativity and idempotence result directly from correspond-

ing properties of the minimum operator.Distributivity of∩ with respect to∧ is a

consequence of distribution of the product with respect to the minimum:

w1(w2∧w3)=(w1w2)∧(w1w3),?w1,w2,w3.

The last property(distributivity)is actually quite important,as it explains why

the cautious rule can be considered to be more relevant than the TBM conjunctive

rule∩ when combining non distinct items of evidence:if two sources provide BBAs

m1∩ m2and m1∩ m3having some evidence m1in common,the shared evidence is not counted twice.

The following proposition is linked to the notion of LBS introduced in Section

2.2.4.It will be useful to explain some additional properties of the cautious rule. Proposition6Let m1and m2be two non dogmatic BBAs with conjunctive weight functions w1and w2.Let(m c1,m d1)and(m c2,m d2)denote the LBSs associated to m1 and m2,respectively,and let(w c1,w d1)and(w c2,w d2)denote the corresponding weights. Then the LBS(m c1

,m d1∧ 2)associated to m1∧ m2is de?ned by

∧ 2

m c1∧ 2=∩ A?ΩA w c1∧w c2,

m d1∧ 2=∩ A?ΩA w d1∨w d2,

where∨denotes the maximum operation.

Proof:For any A?Ω,we have

w c1∧ 2(A)=1∧w1∧ 2(A)

=1∧w1(A)∧w2(A)

=(1∧w1(A))∧(1∧w2(A))

=w c1(A)∧w c2(A),

and

w d1∧ 2(A)=1∧

w1∧ 2(A)

=1∧

w1(A)∧w2(A)

=1∧

w1(A)

∨1

w2(A)

1∧

w1(A)

∨

1∧

w2(A)

=w d1(A)∨w d2(A).

We thus see that,using the cautious rule,the con?dence parts are combined con-junctively,whereas the di?dence parts are combined disjunctively by taking the maxi-mum of the two weight functions w d1and w d2.Note that such a disjunctive combination is well de?ned only for u-separable BBAs(see Section4for further discussion on this issue and the de?nition of a disjunctive counterpart of the cautious rule).Combining the di?dence components disjunctively does seem to make sense,as shown by the following informal argument.According to Smets[33],m d(A)should be interpreted as the strength of evidence that one should not believe A.If I receive two pieces of evidence,one of which tells me not to believe A while the other tells me not to believe B,then I am inclined not to believe A∪B,hence the disjunctive nature of the combi-nation.Consequently,there seems to be some form of duality between the con?dence and di?dence components of a LBS,which translates into di?erent mechanisms for combining each of the two components.

As is well known,the vacuous BBA is the neutral element for the TBM con-junctive rule,whereas it is an absorbing element for the TBM disjunctive rule.As a consequence of the dual conjunctive/disjunctive nature of the cautious rule,cau-tious combination of a BBA m with the vacuous BBA has the e?ect of absorbing the di?dence component,while leaving the con?dence component unchanged.This is formalized in the following proposition.

Proposition7For any non dogmatic BBA m with corresponding LBS(m c,m d):

m∧ mΩ=m c.

Proof.This is a direct consequence of Proposition6.Let w c and w d denote,respec-tively,the weight functions of m c and m d.The weights associated to the con?dence component of m∧ mΩare w c(A)∧1=w c(A)for all A?Ω,whereas those associated to the di?dence component are w d(A)∨1=1for all A?Ω.

The following proposition follows directly from the previous one.

Proposition8For any non dogmatic BBA m,mΩ∧ m=m i?m is u-separable. Proof.m is u-seperable i?it is equal to its con?dence component,i.e.m=m c,hence the result.

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古代汉语练习题词类活用

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C．见灵辄饿，问其病，曰：“不食三日矣。”食之，舍其半 D．仓廪实而知礼节，衣食足而知荣辱四、指出并具体说明下列文句中的词类活用现象： 1．秦数败赵军，赵军固壁不战。（秦与赵兵相距长平） 2．赵王不听，遂将之。（秦与赵兵相距长平） 3．身所奉饭饮而进食者以十数，所友者以百数。（秦与赵兵相距长平） 4．括军败，数十万之众遂降秦，秦悉阬之。（秦与赵兵相距长平） 5．信数与萧何语，何奇之。（韩信拜将） 6．王必欲长王汉中，无所事信。（韩信拜将） 7．吾亦欲东耳，安能郁郁久居此乎？（韩信拜将） 8．何闻信亡，不及以闻，自追之。（韩信拜将） 9．今大王举而东，三秦可传檄而定也。（韩信拜将） 10．遇有以梦得事白上者，梦得于是改刺连州。（柳子厚墓志铭） 11．自子厚之斥，遵从而家焉，逮其死不去。（柳子厚墓志铭） 12．以如司农治事堂，栖之梁木上。（段太尉逸事状） 13．踔厉风发，率常屈其座人。（柳子厚墓志铭） 14．晞一营大噪，尽甲。（段太尉逸事状） 15．即自取水洗去血，裂裳衣疮，手注善药。（段太尉逸事状） 16．黄罔之地多竹，大者如椽。竹工破之，刳去其节，用代陶瓦。（黄冈竹楼记）17．晋灵公不君。厚敛以彫墙。（晋灵公不君） 18．既而与为公介，倒戟以御公徒而免之。（晋灵公不君） 19．盛服将朝，尚早，坐而假寐。（晋灵公不君） 20．晋侯饮赵盾酒，伏甲将攻之。（晋灵公不君）五、说明下列文句中的词类活用现象，并将全文译为现代汉语：

精神分裂症的发病原因是什么

精神分裂症的发病原因是什么精神分裂症是一种精神病，对于我们的影响是很大的，如果不幸患上就要及时做好治疗，不然后果会很严重，无法进行正常的工作和生活，是一件很尴尬的事情。因此为了避免患上这样的疾病，我们就要做好预防，今天我们就请广州协佳的专家张可斌来介绍一下精神分裂症的发病原因。精神分裂症是严重影响人们身体健康的一种疾病，这种疾病会让我们整体看起来不正常，会出现胡言乱语的情况，甚至还会出现幻想幻听，可见精神分裂症这种病的危害程度。 (1)精神刺激：人的心理与社会因素密切相关，个人与社会环境不相适应，就产生了精神刺激，精神刺激导致大脑功能紊乱，出现精神障碍。不管是令人愉快的良性刺激，还是使人痛苦的恶性刺激，超过一定的限度都会对人的心理造成影响。 (2)遗传因素：精神病中如精神分裂症、情感性精神障碍，家族中精神病的患病率明显高于一般普通人群，而且血缘关系愈近，发病机会愈高。此外，精神发育迟滞、癫痫性精神障碍的遗传性在发病因素中也占相当的比重。这也是精神病的病因之一。 (3)自身：在同样的环境中，承受同样的精神刺激，那些心理素质差、对精神刺激耐受力低的人易发病。通常情况下，性格内向、心胸狭窄、过分自尊的人，不与人交往、孤僻懒散的人受挫折后容易出现精神异常。 (4)躯体因素：感染、中毒、颅脑外伤、肿瘤、内分泌、代谢及营养障碍等均可导致精神障碍，。但应注意，精神障碍伴有的躯体因素，并不完全与精神症状直接相关，有些是由躯体因素直接引起的，有些则是以躯体因素只作为一种诱因而存在。孕期感染。如果在怀孕期间，孕妇感染了某种病毒，病毒也传染给了胎儿的话，那么，胎儿出生长大后患上精神分裂症的可能性是极其的大。所以怀孕中的女性朋友要注意卫生，尽量不要接触病毒源。上述就是关于精神分裂症的发病原因，想必大家都已经知道了吧。患上精神分裂症之后，大家也不必过于伤心，现在我国的医疗水平是足以让大家快速恢复过来的，所以说一定要保持良好的情绪。

基于单片机的自动存包系统设计

基于单片机的自动存包系统设计摘要近年来，随着生活水平的提高，人们对于社会消费品的质量和数量的要求也在逐渐增加。为了更好的为广大顾客服务，在一些商场、影院、超市等公共场合通常设置有自动存包柜，本次便是针对这一现象进行设计。本文详细介绍了国内自动存包控制系统的发展现状，发展中所面临的问题。并详细介绍了本系统采用的AT89S52单片机做控制器，可以同时管理四个存包柜。柜门锁是由继电器控制，当顾客需要存包的时候，可以自行到存包柜前按“开门”键，需要顾客向光学指纹识别系统输入个指纹，然后通过继电器进行开门（用亮灯表示），顾客即可存包，并需将柜门关上。当顾客需要取包时，要将只要将之前输入的指纹放置于指纹识别器前方，指纹识别器采集到指纹信息输出相应的高低电平信号传给单片机，系统比较密码一致后，发出开箱信号至继电器将柜门打开，顾客即可将包取出。它具有功能实用、操作简便、安全可靠、抗干扰性强等特点。关键词：自动存包柜,单片机,指纹识别器

李少鹏：基于单片机的自动存包系统设计 Based on single chip microcomputer automatic package design Abstract In recent years, with the improvement of living standards, people for social consumer goo ds quality and quantity requirements are to increase gradually. In order to better service for the g eneral customers, in some stores, movie theaters, supermarkets public Settings are to be put auto matically usually bag ark, it is functional practical, simple operation, safe and reliable, anti-jamm ing strong sexual characteristics. Domestic deposit automatic control system are introduced in detail in this paper the development of the status quo, problems faced in the development of. And introduces in detail the system adopts single chip microcomputer controller, can simultaneously manage multiple pack ark. Cupboard door lock controlled by relay, when customers need to save package, will be allowed to save package before the ark according to the "open" button, need customer to the system input fingerprint, and then through the relay to open the door (with lighting), customers can save package, and the cupboard door must be closed. When customers need to pick up package, as long as before the input fingerprint should be placed on the fingerprint recognizer, fingerprint recognizer collecting to the fingerprint information and output the corresponding high and low level signal to the microcontroller, the system is password consistent, signal out of the box to the relay Key words: Automatic Storage Bag, Microcontroller, Fingerprint recognizer。

初中所学文言文中的五类常见词类活用现象

古代汉语中的词类活用现象五种类型：名词用作动词动词、形容词、名词的使动用法形容词、名词的意动用法名词用作状语动词用作状语（一）名词用如动词古代汉语名词可以用如动词的现象相当普遍。如：从左右，皆肘．之。（左传成公二年）晋灵公不君．。（左传宣公二年）孟尝君怪其疾也，衣冠．．而见之。（战国策·齐策四）马童面．值，指王翳曰：“此项王也。”（史记·项羽本纪）夫子式．而听之。（礼记·檀弓下）曹子手．剑而从之。（公羊传庄公十三年）假舟楫者，非能水．也，而绝江河。（荀子·劝学）左右欲刃．相如。（史记·廉颇蔺相如列传）秦师遂东．。（左传僖公三十二年）汉败楚，楚以故不能过荥阳而西．。（史记·项羽本纪）以上所举的例子可以分为两类：前八个例子是普通名词用如动词，后两个例子是方位名词用如动词。名词用作动词是由上下文决定的。我们鉴别某一个名词是不是用如动词，须要从整个意思来考虑，同时还要注意它在句中的地位，以及它前后有哪些词类的词和它相结合，跟他构成什么样的句法关系。一般情况有如下四种：

①代词前面的名词用如动词（肘之、面之），因为代词不受名词修饰； ②副词尤其是否定副词后面的名词用如动词（“遂东”、“不君”）； ③能愿动词后面的名词也用如动词（“能水”、“欲刃”）； ④句中所确定的宾语前面的名词用如动词（“脯鄂侯”“手剑”）（二）动词、形容词、名词的使动用法一、动词的使动用法。定义：主语所代表的人物并不施行这个动词所表示的动作，而是使宾语所代表的人或事物施行这个动作。例如：《左传隐公元年》：“庄公寤生，惊姜氏。”这不是说庄公本人吃惊，而是说庄公使姜氏吃惊。在古代汉语里，不及物动词常常有使动用法。不及物动词本来不带宾语，当它带有宾语时，则一定作为使动用法在使用。如：焉用亡．郑以陪邻？《左传僖公三十年》晋人归．楚公子榖臣与连尹襄老之尸于楚，以求知罃。（左传成公三年）大车无輗，小车无杌，其何以行．之哉？《论语·为政》小子鸣．鼓而攻之可也。《论语·先进》求也退，故进．之；由也兼人，故退．之。《论语·先进》故远人不服，则修文德以来．之。《论语·季氏》有时候不及物动词的后面虽然不带宾语，但是从上下文的意思看，仍是使动用法。例如《论语·季氏》：“远人不服而不能来也”这个“来”字是使远人来的意思。古代汉语及物动词用如使动的情况比较少见。及物动词本来带有宾语，在形式上和使动用法没有什么区别，区别只在意义上。使动的宾语不是动作的接受者，而是主语所代表的人物使它具有这种动作。例如《孟子·梁惠王上》“朝秦楚”，不食齐宣王朝见秦楚之君，相反的，是齐宣王是秦楚之君朝见自己。下面各句中的及物动词是使动用法：问其病，曰：“不食三日矣。”食．之。《左传·宣公二年》

精神分裂症的病因是什么

精神分裂症的病因是什么精神分裂症是一种精神方面的疾病，青壮年发生的概率高，一般在16～40岁间，没有正常器官的疾病出现，为一种功能性精神病。精神分裂症大部分的患者是由于在日常的生活和工作当中受到的压力过大，而患者没有一个良好的疏导的方式所导致。患者在出现该情况不仅影响本人的正常社会生活，且对家庭和社会也造成很严重的影响。精神分裂症常见的致病因素： 1、环境因素：工作环境比如经济水平低低收入人群、无职业的人群中，精神分裂症的患病率明显高于经济水平高的职业人群的患病率。还有实际的生活环境生活中的不如意不开心也会诱发该病。 2、心理因素：生活工作中的不开心不满意，导致情绪上的失控，心里长期受到压抑没有办法和没有正确的途径去发泄，如恋爱失败，婚姻破裂，学习、工作中不愉快都会成为本病的原因。 3、遗传因素：家族中长辈或者亲属中曾经有过这样的病人，后代会出现精神分裂症的机会比正常人要高。 4、精神影响：人的心里与社会要各个方面都有着不可缺少的联系，对社会环境不适应，自己无法融入到社会中去，自己与社会环境不相

适应，精神和心情就会受到一定的影响，大脑控制着人的精神世界，有可能促发精神分裂症。 5、身体方面：细菌感染、出现中毒情况、大脑外伤、肿瘤、身体的代谢及营养不良等均可能导致使精神分裂症，身体受到外界环境的影响受到一定程度的伤害，心里受到打击，无法承受伤害造成的痛苦，可能会出现精神的问题。对于精神分裂症一定要配合治疗，接受全面正确的治疗，最好的疗法就是中医疗法加心理疗法。早发现并及时治疗并且科学合理的治疗，不要相信迷信，要去正规的医院接受合理的治疗，接受正确的治疗按照医生的要求对症下药，配合医生和家人，给病人创造一个良好的治疗环境，对于该病的康复和痊愈会起到意想不到的效果。

自动存包柜的设计与仿真

自动存包柜的设计与仿真摘要本课题是基于单片机的自动存包柜设计。自动存包柜是新一代的存包柜，具有功能实用、操作简单、管理方便、安全可靠等特点，能够更好的服务于不同市场的广大群众，使用者可以根据简明清晰的操作说明自行完成存包取包工作。本系统由MCS-51单片机构成核心控制系统，整个系统由主控部分、键盘显示控制部分、执行部分三部分组成，通过随机密码的产生和核对完成自动存包取包过程。本设计中各元器件便于安装且操作简单，能基本实现存包取包功能。关键词：自动存包柜；单片机；随机密码

Design and Simulation of Automatic Lockers ABSTRACT This topic is microcontroller-based automatic lockers.Automatic lockers is a new generation of lockers, with a practical, simple operation, easy management, safe and reliable, able to better serve the broad masses of the different markets, users are based on a clear and concise instructions to complete the deposit bags to take the package. The system consists of MCS-51 microcontroller core control system, the entire system from the main section, the keyboard display control part of the implementation of some of the three-part composition, random password generation and check completed automatically save the package to take the package process. Various components of this design is easy to install and easy to operate, can basically save the package to take package function. Key words :Automatic lockers; microcontroller; random password

卫生部办公厅关于印发《脐带血造血干细胞治疗技术管理规范(试行)

卫生部办公厅关于印发《脐带血造血干细胞治疗技术管理规范(试行)》的通知【法规类别】采供血机构和血液管理【发文字号】卫办医政发[2009]189号【失效依据】国家卫生计生委办公厅关于印发造血干细胞移植技术管理规范(2017年版)等15个“限制临床应用”医疗技术管理规范和质量控制指标的通知【发布部门】卫生部(已撤销) 【发布日期】2009.11.13 【实施日期】2009.11.13 【时效性】失效【效力级别】部门规范性文件卫生部办公厅关于印发《脐带血造血干细胞治疗技术管理规范（试行）》的通知（卫办医政发〔2009〕189号）各省、自治区、直辖市卫生厅局，新疆生产建设兵团卫生局：为贯彻落实《医疗技术临床应用管理办法》，做好脐带血造血干细胞治疗技术审核和临床应用管理，保障医疗质量和医疗安全，我部组织制定了《脐带血造血干细胞治疗技术管理规范（试行）》。现印发给你们，请遵照执行。二〇〇九年十一月十三日

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