Union/intersection vs. alternative/conjunction - defining posterior hypotheses in C2 systems
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Union/intersection vs. alternative/conjunction - defining posterior hypotheses in C2 systems Ksawery Krenc RS-SD R&D Marine Technology Centre Gdynia, Poland [email protected] Adam Kawalec The Institute of Radioelectronics WAT Military University of Technology Warsaw, Poland [email protected] Abstract – This paper discusses the problem of application of the logical operators while defining the posterior hypotheses, that is hypotheses which are not directly created upon the sensor data. In the authors’ opinion the application of the logical sentence operators is constrained to some specific cases, where the sets operators may be applied as well. On the other hand, the sets operators enable to provide much more adequate posterior hypotheses, which results in higher precision of the fusion final decision. In order to present that an analysis has been made and some examples, related to attribute information fusion in C2 systems have been delivered. Keywords: Classification, observation, soft-decision fusion, union, intersection, alternative, conjunction, evidence, DST, DSmT. 1 Introduction One of the most important requirements imposed on maritime Command & Control (C2) systems is to elaborate the so called Common Operational Picture (COP). In order to achieve that, the C2 systems must be equipped with specific information fusion techniques, which enable to integrate both precise information as well as uncertain, incomplete or even conflicting information. When the information is vague, sophisticated reasoning processes are performed to elaborate the final optimal decision [1], [2], [3]. In such a case it is very important to create hypotheses upon the gathered evidence as much adequate as possible. Some of them (primary hypotheses) result directly from the sensors’ resolution and may be regarded as the basis for constructing the frame of discernment. Others (posterior hypotheses) are created upon the primary hypotheses with usage of logical relations. The definition of the posterior hypotheses is very important and should be a subject of the serious considerations. Certainly, one can imagine the posterior hypotheses may be regarded as completely different classes. However, that implies two problems: The first problem is evaluation of these new hypotheses, based on observation data, which is necessary if these hypotheses are intended to be utilised effectively. The second problem is that the reasoning system, which performs the fusion of the gathered information, does not have a ‘notion’ of the meaning of these new hypotheses unless they are defined based on the hypotheses that already exist. Among the specialists there have been developed two contradict opinions related to definitions of the secondary hypotheses. The first view, found typically in the military literature [4], [6], [7], suggests that the posterior hypotheses should be created using the logical operations of conjunction and alternative. The second one, found mostly in the fusion and approximate reasoning science literature [1], [2], [3], [5] indicates the sets operations of intersection and union as much more adequate. In the next sections these two opinions are going to be discussed in details and illustrated with examples, typical for the marine C2 systems purposes with particular emphasis on merits and drawbacks of each of these views. 2 Process of observation It is suggested to the reader to consider the following example of the target threat classification, performed upon observation by the C2 reconnaissance means. The ground truth is that the target performs a friendly vessel, acting as hostile for the exercise purposes. Additionally, it is assumed that the sensors used for the classification enable to distinguish only between two classes: FRIEND (F) and HOSTILE (H). In terms of the NATO STANAGs [4], [6], [7] the described vessel is defined as FAKER (K). In order to find the formalism for the class of FAKER with respect to the logical operations, mentioned in the introduction, the following four expressions should be taken into account: H F K ∨ = (1) H F K ∧ = (2) H F K ∪ = (3) H F K ∩ = (4) Possible interpretations of these formalisms are going to be discussed in the following section. Whereas this section aims to scrutinise the process of observation, which may be performed by sensors as well as by the human being.
description
This paper discusses the problemof application of the logical operators while defining the posterior hypotheses, that is hypotheses which are not directly created upon the sensor data.
Transcript of Union/intersection vs. alternative/conjunction - defining posterior hypotheses in C2 systems
Union/intersection vs. alternative/conjunction - defining posterior hypotheses in C2 systems Ksawery Krenc RS-SD R&D Marine Technology Centre Gdynia, Poland [email protected] Adam Kawalec The Institute of Radioelectronics WAT Military University of Technology Warsaw, Poland [email protected] AbstractThispaperdiscussestheproblem of applicationofthelogicaloperatorswhiledefining the posteriorhypotheses,thatishypotheseswhichare not directly created upon the sensor data.Intheauthorsopiniontheapplicationofthelogical sentence operators is constrained to some specific cases, wherethesetsoperatorsmaybeappliedaswell. On the otherhand,thesetsoperatorsenabletoprovide much more adequate posterior hypotheses, which results in higher precision of the fusion final decision.Inordertopresentthatananalysishasbeenmade and someexamples,relatedtoattributeinformation fusion in C2 systems have been delivered.Keywords:Classification,observation,soft-decision fusion,union,intersection,alternative,conjunction, evidence, DST, DSmT. 1Introduction Oneofthemostimportantrequirementsimposed on maritimeCommand&Control(C2)systemsis to elaboratethesocalledCommonOperationalPicture (COP).Inordertoachievethat,theC2systemsmustbe equippedwithspecificinformationfusiontechniques, which enable to integrate both precise information as well as uncertain, incomplete or even conflicting information.Whentheinformationisvague,sophisticatedreasoning processesareperformedtoelaboratethefinaloptimal decision [1], [2], [3]. In such a case it is very important to createhypothesesuponthegatheredevidenceasmuch adequate as possible.Some of them (primary hypotheses) resultdirectlyfromthesensorsresolutionandmaybe regardedasthebasisforconstructingtheframe of discernment.Others(posteriorhypotheses)arecreated uponthe primaryhypotheseswithusageoflogical relations.Thedefinitionoftheposteriorhypothesesisvery importantandshouldbeasubjectoftheserious considerations.Certainly,onecanimaginetheposterior hypothesesmayberegardedascompletelydifferent classes.However,thatimpliestwoproblems:Thefirst problemisevaluationofthesenewhypotheses,based on observationdata,whichisnecessaryifthese hypothesesareintendedtobeutilisedeffectively. The secondproblemisthatthereasoningsystem,which performsthefusionof thegatheredinformation,doesnot haveanotionof the meaningofthesenewhypotheses unlesstheyaredefinedbasedonthehypothesesthat already exist.Amongthespecialiststherehavebeendevelopedtwo contradict opinions related todefinitions of the secondary hypotheses. The first view, found typically in themilitary literature[4],[6],[7],suggeststhattheposterior hypothesesshouldbecreatedusingthelogicaloperations ofconjunctionandalternative.Thesecondone,found mostlyinthefusionandapproximatereasoningscience literature[1],[2],[3],[5]indicatesthesetsoperations of intersection and union as much more adequate. Inthenextsectionsthesetwoopinionsaregoingtobe discussedindetailsandillustratedwithexamples,typical forthemarineC2systemspurposeswithparticular emphasis on merits and drawbacks of each of these views.2Process of observation Itissuggestedtothereadertoconsiderthefollowing example of the target threat classification, performed upon observation by the C2 reconnaissance means. Thegroundtruthisthatthetargetperformsafriendly vessel,actingashostilefortheexercisepurposes. Additionally,itisassumedthatthesensorsusedfor the classificationenableto distinguishonlybetweentwo classes: FRIEND (F) and HOSTILE (H). IntermsoftheNATOSTANAGs[4],[6],[7] the described vessel is defined as FAKER (K). InordertofindtheformalismfortheclassofFAKER with respecttothelogicaloperations,mentioned in the introduction,the followingfourexpressionsshould be taken into account: H F K =(1) H F K = (2) H F K =(3) H F K =(4) Possibleinterpretationsoftheseformalismsaregoing to bediscussedinthefollowingsection.Whereasthis sectionaimstoscrutinisetheprocessofobservation, whichmaybeperformedbysensorsaswellasby the human being. Inthetypicalreconnaissanceprocesstargetclassification is based upon distinctive features of the target. That means thetargetclassificationperformsasortof conclusion relatedtothesetoftheobservedtargetfeatures.This, apparently obvious fact, is the key argument for the thesis thatclassificationhypothesesshouldbecreatedwith usage of the set operators of union and intersection but not with alternative nor conjunction.Figure1showstheexampleofthemaritimeobservation processwithaparticularemphasisonrecognising the distinctive features of the target. Notice,thatsomeofthesefeatures(e.g.targethull number)maynotbeaccessiblefortherecognitiondue to the possibledifficultiesthatmayoccurduring the observation process. Figure 1 Observation of targets with emphasised specific features Figure1showsthatFAKERmayhavesomeproperties of FRIENDandsomeofHOSTILE.Nevertheless,itis extremely improbable (and almostimpossible in practice) for the target to have all the features1 of both classes. Therefore,intheauthorsopinionthemostaccurate formalism will be the equation (4). Figure 2 Venn's diagram of the observed target features 1 In such case all means all accessible for observation. Figure2showstheVennsdiagramoftheobserved situationwherethesubsetofFAKERcontains the commonfeaturesofFRIENDandHOSTILEtarget classes.Noticethepositionofthehullnumberattribute, whichafterscrutinymaybemovedeithertowards FRIEND or HOSTILE when the identification data occur. 3Interpretation of acquired information Consideringtheadequacyoftherestoftheformalisms regardingtothegroundtruthsituation,itissuggested to examine possible interpretations of these equations. Theformalismbasedonthelogicalsentenceoperators seemstobeverycategorical.Ifonewishestouseit to reflectanothersituation,wheretwoclosely-spaced targetsFRIENDandHOSTILEarebeingtracked, the statements (1) and (3) are equivalent2 in such a case.However,intheconsideredobservationexample, any attemptofdefiningFAKERclasswithusage of the logicalsentenceoperatorsleadsinevitably to the seriousdegradationofinformationrelated to the observedtarget.Thestatement(2)appliedtothis verycaseisincorrect,duetothefact,the observedtarget isneitherfullyfriendlynorhostile.Acceptingsuch a formalismmayhaveanegativeimpactduringthestage of processing of this information.Thekeyproblemisthepreciseinterpretation of the hypothesesdefinedwithusageoftheconjunction operation. Classical interpretation of (2) says that FAKER performsFRIENDandHOSTILEsimultaneously. According to the binary logic as FRIEND, it possesses all thepropertiesofthefriendlytargetandasHOSTILEall thepropertiesofthehostiletarget.That,ontheother hand,leadstotheconclusionthatFAKERmaybe performedas theunionofFRIENDandHOSTILE as well.Thisisverydangerousduetothefactitmaybe confusedwithtwoclosely-spacedtargets,asmentioned above. Thisveryproblemalsoemergeswhilecalculating the respectivebelieffunctionsforeachofthese hypotheses.Namely,incaseofdefinitionsbased on the conjunctionoperator(2),thebelieffunction referring to the hypothesis of FRIEND is determined only by the massofFRIEND.Whereasthebelieffunction referringtoFAKERissupportedbyFAKERitself and FRIENDhypothesissinceFAKERaggregatesall the features of FRIEND and HOSTILE classes. ) ( ) ( F m F Bel =(5) ) ( ) ( ) ( F m K m K Bel + = (6) Thisviewcontradictsthecommonsense,duetothefact thatthedegreeofbeliefofthehypothesesFAKERis successivelyincreasedwiththemassreferringto FRIEND. 2 The equivalence is defined here in terms of informational income. Forcomparison:incaseof definitionsbasedonthesets operations,thehypothesis(4)supportsthehypothesis of FRIEND, when calculating the belief function Bel(F). ) ( ) ( ) ( K m F m F Bel + =(7) ) ( ) ( K m K Bel =(8) ThatmeansthatpresumingthetargetisFAKER,itis possibletoincreasethedegreeofbeliefthatthetargetis friendly.Howevertheconverseisnottrue,sinceitis unjustifiedtoincreasethedegreeofbelief of the hypothesisFAKERwiththemassreferring to FRIEND, which meets the reality. Doesitmeanthatthelogicaloperatorsdonothaveany applications in creating the posterior hypotheses? Itisdifficulttoanswerthisquestionunequivocally. The logicaloperatorsdohavetheirapplication,when aggregatingthetargetdistinctivefeatures,inorder to evaluatethegatheredinformation,andtoclassify the target. Table1showsexampledefinitions3ofdifferentvessel types,socalledplatforms,intermsoftheiractivities and theequipmentonboard.Accordingtothistableeach typemaybedefinedasthesetofitsdistinctivefeatures using the logical operators. Example 1: Table 1 Example definitions of surface platforms TransporterAUX AIR D TRAN CommandAUX S&MCAL AIR C2 Cruiser S&MCAL LCAL SSC AIR E INF C2 Destroyer S&MCAL SSC AIR E ATTC REC Patrolcraft Escort GUN E SUP HydrofoilGUN E SupportSUP where: AUX auxiliary vessel; S&MCALequippedwithartilleryofsmall and medium calibre; LCAL equipped with artillery of large calibre; SSC destroys surface, subsurface and coastal targets; E escort vessel; INFinfluencestotacticalandoperationalsituation; AIR against the air targets; D performs landing operations; C2 command & control; SUP support; 3Inthemajorityofcasesthe descriptionenablesto identifytheparticularplatformunambiguously.Therefore itissuggestedtoacceptthatasdefinitionforthe illustrative purposes.GUNequippedwithartilleryofsmallcalibre or machine guns; TRAN transport of landing forces; Withreferencetotheexampleabove,thefollowing statementmaybeformulated:Thelogicaloperatorsmay havetheapplicationincreatingposteriorhypotheses if the primaryhypothesesrefertotheobservablefeatures of thetarget,andadditionally,theyarepossibletobe verifiedinthebinarymanner.Forinstance:aPatrolcraft Escortmaybedefinedwithrespecttoitsfeaturesas a vesselthatpossessesthreefeatures:performsanescort, performsasupportanditisequippedwithagun. Nevertheless,similarlyasincaseofFAKER,a certain dangerresidesinsuchadefinition,whichmaylead to the misclassification.Namely,thePatrolcraft Escort(PE)encompassesallthe(tactical)features of a hydrofoil(HF)andanysupport(SUP)vessel,as Table1shows.ThusonecoulddefinethePatrolcraft Escort as: SUP HF PE =(9) which would be commonly interpreted as an absurd object thatperformsthehydrofoilandthesupportvesselat the same time.On the other hand defining the Patrolcraft Escort in terms of sets algebra would result in: SUP HF PE = (10) whichwouldbeinterpretedproperlyasavesselthat encompassesthecommonfeaturesoftherespective: hydrofoil and support entities.Uptonowtherehasbeenpresentedaspreadrange of applicationofthesetsoperatorsandapotential applicationofthelogicaloperatorsundertheassumption the hypotheses do refer to the directly observable features ofthetarget.Whathappensiftheydonot?Isitpossible to use the logical operators then? Inmostofthecaseswhentheposteriorhypothesesare created for the purpose of the target classification, there is aneedtotakeintoaccountfactorswhicharenotdirectly subjectedtotheobservationprocess.Forexample, the mentionedthreatattributeclassificationmaybe performedupontheobservationonlytosomeextent. The valueof thisveryattributeissoimportantthat an additionalplausibilityanalysisisoftenperformed to assess,whetheritispossibletoidentifyFRIEND, HOSTILEorFAKERtarget,accordingtosomeexternal sourcesofinformatione.g.databases,intelligence, general knowledge, etc. Abandoningtheobservabilityassumption,in the authors opinion,itispossibletoutilisethelogicaloperators, however,underanotherassumption,related to the exclusivityoftheprimaryhypotheses.Namely, if the primaryhypothesesdonotcontradicteachother the logicaloperatorsmaybeusedtocreatetheposterior hypothesesinordertoemphasisethecompleteness of the particular primary hypotheses.Example 2: Table 2 Example of mine warfare platforms, based on [4] MHOMine Hunter Ocean MSOMine Sweeper Ocean MHSOMine Hunter/Sweeper Ocean Accordingto[4]MHSOstandsforavessel,whichis capabletoperformmine-huntingactivitiesaswellas mine-sweeping.However,itisneitherapureMHOnor MSO.Thebestfittingformalismwouldprobablybe(11) whichindicatesthat,tosomeextent,MHSOhas functionalities of MHS and MHO. MSO MHO MHSO = (11) Thelargerthedegree(ofMHOaswellasMSO)is, the closertoMSO MHO MHSOis,whichmaybe formalised as (12). MSO MHO MHSOfullMHS MHSfullMHO MHO = (12) Figure 3 MHSO - the completeness of MHO and MSO functionalities Although this example seems to be similar to the FAKER case, it isworth noticing that, on the contrary to FAKER, theconceptofmaximalcompletenessoftheparticular primaryhypothesesdoesnotcontradictthecommon sense. The idea of existence of the target which possesses allthe functionalitiesofthetypicalmine-hunterand all the functionalitiesofthetypicalmine-sweeper simultaneously is reasonable, however improbable. That is duetothefacttheprimaryhypothesesdonotreferto exclusive concept as it was in the FAKER case. 4Operators and soft-decision fusion Beforedecidingaboutapplicationoftheexactoperators forcreatingthe posteriorhypotheses,itisveryimportant to considertheirpotentialinfluenceontheperformance of informationfusionmodules.Particularly,theoperators mayimpacttheadequacyoftheelaborateddecisionsdue tothefacttheprocessingofinformationisbased on logical operations (e.g. combination, conditioning). Asitwasmentionedintheprevioussections,application of the logical operators leads to introduction of categorical hypotheses,whichdonotreflectthepartialaffiliation of theconsideredtargetstotheparticularclasses,defined bytheprimaryhypotheses.Suchaviewistypicalfor hard-decision fusion approach. However,whileresolvingconflictinginformationfusion problemstheusabilityofsoft-decisionfusion,where insteadofdecisionsdeclarations(evaluatedhypotheses) areconsidered[5],ismuchgreater.Suchapproach enablestoelaboratemuchmoreadequatedecisionsdue to thefacttheprocessingofinformationisnotinterfered byanycategoricalassumptions.Forthisreason, applicationof the setsoperators,whichenabletokeep the hypotheses flexibility, seems to be justified. Figure 4 and Figure 5 show the models of the target threat evaluation.Theprocessofevaluationofthedefined hypothesesisanotherveryextensiveproblemwhichhas beendiscussedin[3]and[8]indetails.Although the modelshavebeenalsopresentedinthispaperfor the readertobeawarethatthecompleteness of the particularprimaryhypothesesofFRIEND and HOSTILEisupto the evaluationinthenextstage of processing of information. Thus, in the authors opinion itperformsanotherargumentfortheapplicationofthe sets operators. Forbasicdescription:theactivity-orientedmodel, in the firstmeasurementstage,resolveswhether (accordingtoobservedtargetsactivity)thetargetseems tobemorelikeFRIENDorHOSTILE.Inthefollowing stagesthe degreesofbeliefforeachofthesetwo hypothesesaredefinedbytheobservationofthereal target. Figure 4 Activity-oriented model where: primary hypotheses:F friend, H hostile, Uunknown(specificclassrepresents the ignorance about the target)posterior hypotheses:AF assumed friend,U F AF =S suspect,U H S =J joker,U H F J =Fk faker,H F K Fk = = Thethreat-orientedmodelinthefirstmeasurementstage resolvestherealthreatofthetarget.Inthefollowing stages,thedegreeofbelief(whetherthetargetactas SUSPECTorHOSTILE)aredefinedaccordingtothe current targets activity. Figure 5 Threat-oriented model where: primary hypotheses:F friend, H hostile, Uunknown(specificclassrepresents the ignorance about the target)posterior hypotheses:AF assumed friend,U F AF =S suspect,U H Sreal =J joker,U H F Jsim =Fk faker, simH F K Fk = =Thedetaileddefinitions(basedonobservations)ofeach of thetargetthreatvalueshavebeenshowninTable3, where ) ( hypi denotesthedistancemetricforthe hypothesishypinthei-thmeasurementstepofthethree-step measurement observation [3]. Table 3 Target threat models comparison ThreatActivity-oriented model Threat-oriented model FRD ) () () (FUFIIIIII ) () () (FUFIIIIII HOS ) () () (UHHIIIIII ) () () (UHHIIIIII UNK ) () () ( ) (UUF HIIIIII I ) () () ( ) (UUF HIIIIII I FAK ) () () ( ) (FHH FIIIIII I ) () () (UHFIIIIII JOK ) () ( ) () (FU HFIIIII III ) () ( ) () (UU HFIIIII III SUS ) () ( ) () (UU HHIIIII III ) () ( ) () (UU HHIIIII III AFR ) ( ) () () (F UUFIII IIIIII ) ( ) () () (F UUFIII IIIIII Thesetwomodelsshowthatconsideringtheposterior hypothesesassubsets(compositehypotheses)intarget threatclassificationproblemisnecessary.Thatisdue to the fact the pieces of information related to the targets hostilityanduncertaintyaremeasuredandeffectively used forcalculationoftheresultingmassesforeach of the posterior hypotheses. Simplificationoftheposteriorhypothesestological sentencesimpliescuttingoffthedetailsanddisables to utilisethesepartialinformation,whichleadstoserious problems with evaluation of these posterior hypotheses. Essentially,discussingtheproblemofdeterminism/ indeterminismintermsofcreatingcategorical/flexible hypotheses for the purpose of attribute information fusion thereisaneedtodistinguishtwopossiblestagesofthis determinism/indeterminism.Thesoft-decisionfusion approachisindeterministicinitselfandthisaimstobe the firststageoftheindeterminism(seeFigure6). The indeterminismofthesoft-decisionapproachcomes directlyfromthedefinitionofthisapproach,wherenone ofhard-decisionismadebutdeclarations(thestatement of all possible and evaluated hypotheses). Figure 6 Determinism/indeterminism in soft-decision fusion Creatingtheposteriorhypothesesisanotherproblem which,dependingontheusedoperators,maybemore or lessdeterministic.Incaseofusagethesetsoperators the wholeprocessofinformationfusion,including the creationoftheposteriorhypotheses,staysfully indeterministic. In case of usage the logical operators one interferesthetypicallyindeterministicprocessing of informationwithnotfullyjustifieddeterministic assumptionsthatcomefromthecategoricaldefinitions of the posterior hypotheses.5Conclusion Theaimofthispaperwastodiscussthepossible applicationsofthelogicaloperatorsaswellasthesets operatorsincreatingtheposteriorhypothesesfor the purpose of attribute information fusion in C2 systems.Intheauthorsopiniontheapplicationofthesets operatorsiscommon,intuitiveandinmanycases necessary. While the application of the logical operators is merely plausible and constrained to several cases. Itissuggestedbytheauthorstochoosethelogical operatorsforaggregationofthetargetfeatures or if the primaryhypothesesarederiveddirectlyfrom the observationsandadditionallytheymaybeassessed in binary manner. Anotherpossibleapplicationofthelogicaloperatorsis if the primary hypotheses do not contradict each other and thecompletenessoftheparticularprimaryhypotheses, included in the posterior hypotheses are confirmed. However, theutility ofthe sets operators isincomparably greaterandcoversallthecasesoftheapplicationsof the logical operators.6Acknowledgement ThisworkwassupportedbytheNationalCentrefor Research and Development for the years 2009-2011 under Commissioned Research Project MNiSW-OR00007509. References [1]FlorentinSmarandache,JeanDezert,Advancesand ApplicationsofDSmTforInformationFusion,Vol1, American Research Press Rehoboth, 2004. [2]FlorentinSmarandache,JeanDezert,Advancesand ApplicationsofDSmTforInformationFusion,Vol2, American Research Press Rehoboth, 2006. [3]FlorentinSmarandache,JeanDezert,Advancesand ApplicationsofDSmTforInformationFusion,Vol3, American Research Press Rehoboth, 2009. [4]TheJointC3InformationExchangeDataModel, Edition 3.1b, 2007 [5]A.K. Hyder et al. (eds.): Multisensor Fusion,2002. [6]NATOStandardizationAgency,TacticalData Exchange Link 11/11B, STANAG No. 5511, Ed. 6.[7]NATOStandardizationAgency,TacticalData Exchange Link 16, STANAG No. 5516, Ed. 3. [8]K. Krenc, A. Kawalec: An evaluation of the attribute informationforthepurposeofDSmTfusioninC&C systems, Fusion2008, Cologne, ISBN 978-3-00-024883-2, 2008.
