Yudong Qi,Zhixue Wang,Qingchao Dong,and Hongyue He

1.Departmentof Weapon Science and Technology,Naval Aeronauticaland Astronautical University,Yantai264001,China;

2.Institute of Command Information System,PLAUniversity of Science and Technology,Nanjing 210007,China

Modeling and verifying SoS performance requirements of C4ISR systems

Yudong Qi1,Zhixue Wang2,*,Qingchao Dong1,and Hongyue He2

1.Departmentof Weapon Science and Technology,Naval Aeronauticaland Astronautical University,Yantai264001,China;

2.Institute of Command Information System,PLAUniversity of Science and Technology,Nanjing 210007,China

System-of-systems(SoS)engineering involves a complex process of refining high-level SoS requirements into more detailed systems requirements and assessing the extent to which the performances ofto-be systems may possibly satisfy SoS capability objectives.The key issue is how to modelsuch requirements to automate the process of analysis and assessment.This paper suggests a meta-model that defines both functional and nonfunctionalfeatures of SoS requirements for command and control, communication,computer,intelligence,surveillance reconnaissance(C4ISR)systems.A domain-specific modeling language is defined by extending unified modeling language(UML)constructed of class and association with fuzzy theory in order to model the fuzzy concepts of performance requirements.An efficiency evaluation function is introduced,based on B′ezier curves, to predict the effectiveness ofsystems.An algorithm is presented to transform domain models in fuzzy UML into a requirements ontology in description logic(DL)so that requirements verification can be automated with a popular DL reasoner such as Pellet.

performance requirements,efficiency evaluation function,description logic(DL),rationality.

1.Introduction

The system-of-systems(SoS)paradigm has emerged as an increasingly popular choice for being an economic and strategic approach for enhancing existing systems capabilities and generating additional capabilities,with widespread applications in the military,academia,industry and elsewhere[1].The development of SoS,such as the command and control,communication,computer,intelligence,surveillance and reconnaissance(C4ISR)system,should be aimed toward many satisfactory solutions based on capability requirements to accommodate more possibilities and unpredictable operating environments, as opposed to optimizing the performance of any individualsystem oran optimalsolution to a specific situation[2].

Architecture-based capability engineering,the popular SoS engineering for defense acquisition and C4ISR system development,is intended to cope with complexity and uncertainty early in the SoS design process,and to conceptualize the capabilities expected to be achieved by the entire SoS with the continuous evolution of its systems architecture[3].To support the capability engineering,the US Department of Defense issued a new version of standard architecture framework(DoDAF 2.0)[4] thatsuggested a meta-modelfor architecturaldescriptions (DM2)in a consistentand interoperable fashion.ButDM2 is stillundergoing a major evolution,and its semantic ambiguity may probably limit the full benefit of architecture analysis[5,6].Furthermore,using the principles of modeldriven architecture(MDA),current executable architecture modeling has been concerned with the construction of executable models through the model transformation from architectural descriptions[6,7].Most of such work is still a manual process involving multiple model transformations with weak model consistency checking due to semiformal semantics in static modeling languages.This means that more significant efforts may be required to preserve traceability and consistency between static and executable models[8].In addition,architecturaldata in iterative architecture refinements are needed to better support the SoS evolution and accommodate its changing requirements and context.

In software engineering,functionalrequirements can be modeled with unified modeling language(UML)[9],while there are few methods available for modeling performance requirements.To determine whetherthe system modelsatisfies the SoS performance requirements,engineers usually have to translate the conceptualmodelin UML or systems modeling language(SysML)into an executable model, such as Petrinet[10]or xUML[11],to facilitate verification and validation(V&V).In other words,it is necessary to incorporate static concepts of high-level SoS require-ments into dynamic concepts ofsystem execution.Itseems infeasible,forthe requirements analysis in the preliminary phase of a large-scale program may notlook forward into system design details.Besides,SoS performance requirements are usually stated with fuzzy concepts,for example,“we need a radar that detects a wider range of targets and provides pictures with higherprecision”,which makes them even harder to modeland verify.

Microsoft argued the capability-oriented thinking as a robust enterprise architecture strategy for the successful service-oriented architecture(SOA)solution,for“it can abstract the stable from the volatile,encapsulate the volatile within services and manage change through the information system requirements evolution”[12].And,an enterprise service model(ESM)was proposed to map services in an IT solution to capabilities in a capability model [13].

National Aeronautics and Space Administration (NASA)used model-based languages(such as SequenceL [14])and risk analysis methodologies to raise software development to the level of hardware development,hoping to achieve a fusion of systems and software engineering by replacing conventional software development techniques with capability engineering thatfocuses on a system’s full setof functionalities[15].

Dai and Cooper proposed the formal design analysis framework(FDAF)for software architecture modeling to bridge the gap between enterprise and early software models(requirements and architecture)[16].They used a UML business modeling extension[17]to model the business goals and standard UML use cases to analyze the software requirements.

Tsai and Liu argued that a formal requirements specification language plays an important role in software development.They report the experiences gained from the FRORL project and state the value of research in knowledge-based software engineering in verification, validation,requirementsanalysis,debugging,and transformation[18].

Kang et al.found that the enterprise model cannot express the semantics enough and defined the fact-based ontologies through which the relationships can be defined and reasoned semantically[19].

The above approaches inspire our research,and some achievements are absorbed into our research.But the nonfunctionalrequirements features,such as performance requirements,are not addressed.The suggested modeling language(like SequenceL)and frameworks(like FDAF) are allfocusing on functionalanalysis.However,the capability requirements analysis addresses both functions and performances of an SoS.The efficiency should be considered as an inseparable factor of SoS requirements in capability engineering.

There are various V&V approaches and techniques. Reference[20]classified them into three categories:nonformal,semi-formal,or formal.The non-formal V&V techniques are essentially based on human expertise and do notrequire such a high levelofformalization ofthe model. Butthe V&V process is hardly automated with such techniques.The semi-formal techniques are usually based on modelexecution.They remain a popular approach and are even regarded as sufficient and relevantin a large number of projects[21].However,they do not exclude erroneous results because of the non-exhaustiveness of the scenarios taken into consideration[22].The formal techniques are strongly related to formal methods[23].They usually require a high level of formalization of the modeling language with an adequate mathematical semantic based on interpretation rules and deduction rules thatmake itpossible to reason about the specifications in order to discover potentialerrors,mistakes or inconsistencies.

Ponsard et al.presented an integrated toolbox(named FAUST formal toolbox)implementing the formal techniques by a round trip mapping of KAOS[24]requirements level notations to the languages of formal V&V tools to ensure at an early stage that the right system is being builtand thatthe requirements modelis right[25].

Chapurlat et al.suggested that enterprise modeling be made in three processes:conceptualization,modeling and verification.In the conceptualization process,the domain expert captures the domain knowledge in the properties reference repository,defining a formalontology forthe selected domain.In the modeling process,the user models the enterprise using unified enterprise modelling language (UEML)[26]and specifies the properties corresponding to the needs that he or she wants to verify,using the domain ontology.In the verification process,the user would then prove some chosen properties on the modelby the use of formal mechanisms allowing him to increase his own knowledge and improve the model’s quality and relevance [27].

Floch et al.presented a model-driven development approach that combines UML modeling and ontology techniques for specifying and validating software component properties and a middleware platform that supports componentdiscovery,compatibility checking and deployment [28].

However,the above approaches and techniques do not address uncertain domain modeling and specification,and as a resultcannotbe used to reason on fuzzy knowledge.In ourapproach,we use a fuzzy extended UML(fuzzy UML) to cope with fuzzy concepts forthe complex objects so thatboth the function and non-function features of SoS requirements can be modeled.We provide an algorithm to convert the fuzzy UML models into the ontologies described in f-SHIN to enable modelverification through the logic inference mechanism.

In the paper,we provide a three-layer analysis framework to capture the domain knowledge for V&V process,extend the UML constructs of class and association with fuzzy theory in order to specify both functional and non-functionalfeatures of SoS requirements,introduce the fuzzy description logic(f-DL)[29]to formalize the UML model,and offer an algorithm to convert domain models in the fuzzy UML into a requirements ontology in f-DL so that requirements verification can be automated with a popular DL reasonersuch as Pellet.

The rest of the paper is organized as follows.Section 2 presents a method of SoS performance requirements modeling by introducing a three-layer modeling framework, extending UML for modeling fuzzy concepts and improving UML domain applicability.Section 3 discusses how to design an efficiency evaluation function(EEF)that facilitates the evaluation of SoS performances.Section 4 focuses on DL-based rationality analysis by introducing f-SHIN(a fuzzy extended DL),constructing the algorithm thattransforms the domain model into requirements ontology in f-DL and specifying rationality constraint rules in semantic web rule language(SWRL)for model verification.Section 5 provides a case study to demonstrate the proposed method,and Section 6 brings conclusions.

2.Performance requirements modeling

2.1 Three-layer requirements framework

Reference[30]proposed a three-layer requirements analysis framework.It allows requirement engineers to capture domain knowledge from high-level abstract concepts down to domain-specific concepts,and thereby build requirementsmodels with richersemantics thatdescribe both the architecturalconstraints and the domain user needs.

Based on the framework,we suggest an SoS performance requirements analysis framework for the C4ISR system.Itcan be used to capture SoS performance requirements by modeling the concepts of architecture,domain and application on three differentabstraction levels.

The meta concepts on the top level,shown in Fig.1, correspond to the UML M2 layer.They are built from the DM2/DoDAF2.0 that includes those of“Capability”,“Activity”,“Performer”,etc.A number of new concepts, such as“Task goal”,“Efficiency”,“Simple capability”and“Complex capability”,are added to facilitate performance requirementsanalysis.Those meta-concepts provide architecturalterms and modeling constraints fordomain models and application models.

The domain concepts on the medium level correspond to the UML M1 layer.They are instances of the metaconcepts,and are built by modeling individualsystem domains of an SoS.They make up of the domain knowledge for SoS requirements analysis and application development.

Fig.1 Meta-modelof SoS performance requirements

The application concepts are modeled on the bottom level that correspond to the UML M0 layer.They are instances of the domain concepts,and are built by modeling application orthe snapshots of run-time individualsystems.The SoS performance requirements analysis cannot be led until application models are built because the application concepts will be the evidence for validating SoS performance requirements.

2.2 UML extension with fuzzy constructs

The performance requirements are usually stated in terms of operation effectiveness of capabilities or systems.Thestatements may be full of uncertain and vague concepts that cannot be modeled with an ordinary UML tool[31]. For example,“Early detection”(in Fig.2)describes a requirement that an air target should be detected as early as the mission requires.The concept“Early detection”is by nature a qualitative description,and it is hard to set a certain value bound for quantitative description thatvaries from mission to mission.

Fig.2 Domain model of SoS performance requirements of city air defense application

Ma et al.[32,33]presented a fuzzy extension of UML (fuzzy UML)to cope with the fuzzy concepts of complex objects in a database.The core conceptof the extension is fuzzy class thatdefines a setoffuzzy objects with a similar structure and behaviors.There are three kinds offuzziness: (i)a class is fuzzy,because whether the objects belong to the class is uncertain,and the class is specified with an additionalattribute(μ)within the domain of0 and 1 to represent the objects membership degree;(ii)the domain of an attribute may be fuzzy and thus the class becomes fuzzy; (iii)a class is fuzzy,because itis specialized as a subclass of a fuzzy class or generalized as a superclass of a fuzzy class.

We introduce the theory to model the performance requirements.A fuzzy concept is modeled as a fuzzy class, with a membership attributeμ:X→[0,1].A fuzzy class is figured as a dashed box in the UML class diagram.To determine the objects membership degreesμ,we introduce the EEF which is discussed in Section 3.

2.3 UML improvementwith domain concepts

As a general-purposed modeling tool,UML is of poor domain applicability and needs domain ontology to qualify the domain modeling semantics[34].The meta-modelof SoS performance requirements shown in Fig.1 provides a DoDAF-compliant ontology to improve domain applicability of UML.The extension constructs can be used to model both certain and uncertain features of capability requirements.All we need to do is to define new stereotypes,such as“Capability”and“Efficiency”thatextend the constructs of class and association of UML/MOF (meta-objectfacility)[35]to provide architecturalsemantics.The defined UML profile specifies a domain-specific modeling language with which engineers can build domain models of SoS performance requirements for a specific C4ISR program.

Fig.2 provides a partialmodelon the domain of city air defense application.This model shows several core con-cepts centered on the“Air warning”and“Targetinterception”tasks.The requirements statements are given in Section 5.To commit the mission“City air defense”,the capability“Detection”is required and described by an efficiency requirement that the target should be detected as early as possible,where the concept“Early detect”an uncertain and vague concept,and is therefore modeled as a fuzzy class,and so as the other two concepts“Effectively intercept”and“Accurately identify”.Each of the fuzzy classes has the stereotype“Efficiency”thatcomes from the meta-model of SoS performance requirements,and each encapsulates a domain specific semantic of the C4ISRperformance requirements.

The performance requirements analysis focuses on the evaluation of the fuzzy membership attributeμ.For example,whether the required efficiency“Early detect”is satisfied or not,is determined by the evaluation result of the attributeμthat describes how early the target is detected. Section 3 discusses on how to build the EEF forthe SoS to facilitate performance evaluation.

3.EEF

3.1 Efficiency calculation based on B′ezier curves

Definition 1EEF is a function forcalculating the fuzzy membership attribute of a fuzzy conceptto predictthe degree of how wella capability willbe applied in an activity to achieve the mission goal with a desired effect.The domain ofan EEF is defined between 0 and 1.

Theoretically,itis hard to constructa generalEEF forall domains.When engineers construct an EEF,they should take into consideration the following factors:(i)the variations in missions or tasks because the performance may be varied from mission to mission where a capability is operated;(ii)the variations in operational environments because the performance is sensitive to differentoperational environments.For example,a car can run up to 120 km/h on a highway,butitruns no more than 40 km/h in a desert. Moreover,the EEF should be constructed satisfying the following constraints.

(i)Accurate

Wherever an EEF is constructed from a set of experimentaldata thatare given by domain experts according to their prior knowledge,the data mustbe relevantto the domain,and the results calculated by the EEF should notcontradictthe domain knowledge.

(ii)Flexible

More than one possible EEFs should be given for a capability so as to cope with mission change.

(iii)Easy to use

The EEF must be built to facilitate algorithm design in such a way that all valid values of quantitative attributes are applicable for calculation.

Reference[36]used the B′ezier curves to construct a set of EEFs that were flexible to suit many different domains.We believe the method is applicable for mostcases of C4ISR capability efficiency evaluation.

Definition 2A B′ezier curve with n+1 control points

3.2 Estimation method

In this section,we demonstrate,through an example,that the EEF constructed with the B′ezier curves is flexible and adaptive to the change of mission or task.

According to the model shown in Fig.2,the concept“Effectively intercept”describes the efficiency ofthe interception capability.Missile unit plays the role of task performer.There are two kinds of air defense missile unit: shortrange and long range,respectively for operating different tasks.For the short range air defense missile,the domain experts construct the EEF of“Effectively intercept”(EEFEI)as follows,with the sample data shown in Table 1.

Table 1 Sample data for short range air defense missile

The efficiency curve is shown in Fig.3.It shows that the beststriking range of shortrange air defense missile is 15 km,where the interception capability reaches the maximum efficiency.

Fig.3 The efficiency curve for short range air defense missile

For another task,the long range air defense missile is used.Whatthe domain experts need to do is to modify the EEFEI with a new set of sample data to produce a new EEFEIas follows:

The new sample data are shown in Table 2.Fig.4 gives a comparison of the two efficiency curves for the different capabilities(shortrange and long range).

Table 2 Sample data for long range air defense missile

From the drawing,we can see the two curves meet on the pointwhere the EEF value is 0.9 and the attribute value is 17 km,which may lead to an assumption thatthis point is the best chance for capability replacement where one efficiency begins to decline and another efficiency nearly reaches its peak.This assumption is quite reasonable because itis fully in accord with our domain knowledge that when a flying target is within 17 km,a shortrange air defense missile is usually applied,otherwise a long range air defense missile applied.

Fig.4 Comparison of the two efficiency curves

4.Rationality analysis based on DL

4.1 f-SHIN

DL is a logicalreconstruction of the so-called frame-based knowledge representation languages,with the aim of providing a simple well-established Tarski-style declarative semantics.Essentially,DL is the theoreticalcounterpartof the web ontology language(OWL)DL,and plays a particularrole in the representation and inference ofontologies. In order to deal with the knowledge vagueness,some researchers have extended the DL with fuzzy logic[29].We choose f-SHIN,the subsystem off-DL,to describe the performance requirements because it is powerful in expressability and decidability,and allows making use of some handy reasoners like Pelletand Racer.

The background about f-SHIN is briefed here.Let NC, NR,and NIbe pair-wise disjointsets ofatomic fuzzy concepts,atomic fuzzy relations and individuals.The fuzzy concepts of f-SHIN are inductively defined as follows:

Forall A∈NC,A is a fuzzy concept;

Forall o∈NI,{o}is also a fuzzy concept;

Let C,D be fuzzy concepts,R∈NR,S∈NRbe simple,then?C,C∪D,C∩D,?R.C,?R.C,≥pS,?p S, are fuzzy concepts,where p∈N.

The fuzzy interpretation of f-SHIN is defined as I=〈ΔI,·I〉,whereΔIis a nonempty setas the domain and·Iis a fuzzy interpretation function mapping:

Every abstract individual o into an element of the domain(o)I∈ΔI;

Every atomic fuzzy concept into a membership degree function AI:ΔI→(0,1];

Every atomic fuzzy relation R into a membership degree function RI:ΔI×ΔI→(0,1];

·Imaps fuzzy concepts and roles into subsets ofΔIand,which can be seen in[29].

The f-SHIN knowledge base is a tripleIn fuzzy Tbox T,the fuzzy conceptaxiom is an expression in the form of C?D or C≡D.For any fuzzy interpretation I,I satisfies C?D(C≡D)iff?a∈ΔI, CI(a)?DI(a)(CI(a)=DI(a)).The detailed descriptions of H and A can be referenced in[29].

4.2 Modeltransformation

To verify performance requirements with a DL reasoning engine,itis necessary to transform requirements models in fuzzy UML into requirements ontology in f-DL.

Assume that the domain model and the application modelhave been built.The requirements ontology can be established in two steps:(i)mapping all classes of the fuzzy-UML domain model into f-DL concept set and all associations into f-DL axiom set;(ii)mapping all objects and their relations of the fuzzy-UML application models into f-DL assertion set.The following algorithm provides the details of the transformation.

Input:Domain model,application model

Output:Requirements ontology

Step 1Creating axioms in Tbox T

Step 1.1Creating concepts

For every class C in the domain model,create a same name DL concept C in Tbox T.

Step 1.2Creating axioms For every generalization between subclass C and superclass D in the domain model,create a DL axiom C∩∪D in Tbox T.

For every association R between class C and class D in the domain model,create a DL axiom C∩∪?R.D in Tbox T.

Step 2Creating assertions in Abox A

Step 2.1Creating from instances Forevery object c in the application model,with its class C and membership degree n,create a DL assertion＜c: C＞??n in Abox A.

Step 2.2Creating from instance links Forevery link l in the application modelbetween objects a and b,create a DL assertion＜a,b＞??n in Abox A, where??∈{=,＜,?,＞,≥}and n∈[0,1].

The requirements ontology built by the algorithm may contain numericalnumbers and hence cannotbe accepted by the available DL reasoners like Pelletand Racerthatdo not support mathematical calculation on numerical numbers.To solve the problem,we use the crisping technique suggested by[37]to transform fuzzy concepts further into crisp ones.

The principle of the transformation is explained as follows around the example of the city air defense system. In the domain model shown in Fig.2,the capability concept“Interception”is described by the efficiency concept“Effectively intercept”.In the application model,the concept“Effectively intercept”is instantiated,with a membership value 0.9 assigned to it.To constructthe requirements ontology,the concepts“Interception”and“Effectively intercept”and their associations are created in Tbox,while their instances and links between instances are created in Abox.Then,the axiom“Interception??described by Effectively intercept”is created in Tbox,and the assertion“ei1:Effectively intercept=0.9”is created in Abox.To transform fuzzy concepts further into crisp ones,a crisp concept“Effectively intercept=0.9”is created in Tbox to extend the fuzzy concept“Effectively intercept”,and a crisp concept“Interception=1”is created to extend the definite concept“Interception”.Then,the above axiom is replaced by“Interception=1??described by Effectively intercept=0.9”,and the above assertion is replaced by“ei1: Effectively intercept=0.9”.Othertransformation results are summarized in Section 5.

4.3 Rationality verification

The rationality problem arises when requirements models specifying functionalrequirements cannot satisfy the efficiency requirements of a mission.

Such rationality problem can be checked through the following steps:(i)transform the fuzzy-UML models into the f-DL ontology using the algorithm introduced in Section 4.2;(ii)add rationality constraint rules expressed in SWRL[38]into the ontology;(iii)check consistency and completeness of the ontology with a popular DL reasoner.

The followings provide two examples for the rules definition in SWRL.

Rule 1If a capability C1depends on another capability C2,the efficiency E1of C1mustbe nothigher than the efficiency E2of C2.

The rule is specified in SWRL as follows:

where swrlb:greaterThan is one ofthe predicates defined by SWRL to compare two numbers.

Rule 2If a capability C is composed of a set of sub capability C1,...,Cn,the efficiency E of C must be not higher than the minimum efficiency Eiof Ci(1?i?n).

The rule is specified in SWRL as follows:

Capability=1(c)∧Capability=1(c1)∧Efficiency≥m(e)∧Efficiency≥n(e1)∧described by=1(c,e)∧

described by=1(c1,e1)∧aggregation=1(c,c1)→swrlb:greaterThan(n,m).

5.A case study

Continuing on the example,the application model of performance requirements ofcity airdefense is built,as shown in Fig.5,to capture the following requirementsstatements.

Fig.5 Application model of C4ISR capability requirements of the city air defense system

“......Two tasks,air warning and target interception, are assigned for the mission‘City air defense’.To accomplish the tasks,two capabilities‘Warning’and‘Interception’are applied.‘Detection’,a component capability of‘Warning’,should be operated effectively to find air targets as early as possible.The other component‘Identification’should be operated effectively to identify the type of the air target and possible threatas accurately as possible.Any low efficiency in detection or identification may results in failure of interception.An effective interception shall destroy the target or make it lose power.Two types of missiles,short range and long range,are applied in the mission.They have different interception capabilities depending on the distance between the missile unit and the air target......”

For performance requirements analysis,the requirements are modeled in the following way.Three concepts“Effectively intercept”,“Early detect”and“Accurately identify”are modeled to describe the desired efficiency of the capabilities“Interception”,“Detection”and“Identification”respectively,as shown in Fig.2.As the two types of missile are applied in the mission,there are two interception capabilities instantiated accordingly,and two instances of“Effectively intercept”created to describe the capability operation efficiency.The fuzzy attribute of“Effectively intercept”can be calculated by the EFFs introduced in Section 3.

The built models suffer from a rationality problem.The efficiency of interception(evaluated to be 0.9)operated by the short range missile is higher than the efficiency of detection(evaluated to be 0.85),which breaks the rules R1 and R2.The domain explanation to the conflict is:the capability“Detection”,applied to detectair target7 min before it being a threat,does not support the performance requirementof“Effective interception”that requires 90% possible enemy targets to be destroyed ormade lose power.

The above analysis result is made upon rationality verification,reasoning through the requirements ontology that is builtfrom the domain modeland the application model. Table 3 shows the contents of Tbox and Abox after crisping transformation.

The reasoning is processed as follows:

Step 1A new assertion a13“intercept1:Capability=1”can be deduced from assertion a1 and axiom A1.

Step 2A new assertion a14“ei1:Efficiency=0.9”can be deduced from assertion a2 and axiom A2.

Step 3A new assertion a15“we:Efficiency=w”can be deduced from assertion a10 and axiom A10.

Step 4Anew assertion a16“w1:Capability=1”can be deduced from assertion a4 and axiom A1.

Table 3 Axioms and assertions in the requirements ontology

Step 5A new assertion a17“swrlb:greaterThan(w, 0.9)”can be deduced from assertion a13,a14,a15,a16, a3,a9,a12 and the rationality constraintrule R1.

Step 6A new assertion a18“d1:Capability=1”can be deduced from assertion a5 and axiom A1.

Step 7A new assertion a19“ed1:Efficiency=0.85”can be deduced from assertion a6 and axiom A13.

Step 8A new assertion a20“swrlb:greaterThan(w, 0.85)”can be deduced from assertion a15,a16,a18,a19, a11,a12,a8 and the rationality constraintrule R2.

Step 9A new assertion a21“swrlb:greaterThan(0.85, 0.9)”can be deduced from assertion a17 and a 20.Itis apparently a wrong assertion,and hence the reasoning process terminates.

The above case is deliberately cutin order to give a simple example for understanding.But for a practical IT program,there may be thousands of concepts in the models, and it is hard to check all the rationality problems manually.

6.Conclusions

The main contribution of the paper is presenting a method of modeling and verification for both functional and performance requirements analysis,which would decrease the cost and risk of the SoS development.It suggests thatthe popular UML is extended by fuzzy constructs to model the uncertain and vague concepts that are important for analyzing performance requirements.In order to determine whether system capabilities are sufficient for a task to achieve the mission goal with a desired efficiency,the SoS performance requirements need to be modeled and then formally specified.A modeltransformation algorithm is provided to convert the fuzzy-UML model into a f-DL ontology so thatthe verification can be automated with the help of a poplar DL reasonersuch as Pellet.

The current research focuses on requirements analysis,and it considers only the capability viewpoint of the C4ISR architecture.The further research will be extended to the architectural design by covering more viewpoints, such as operationalviewpointand system viewpointof the DoDAF.And,we willintend to develop a domain-specific rules description language based on SWRL.Such language may relieve the domain expertsfromlack offormaldomain knowledge and allow them to define rationality constraint rules with their familiar terms.

Acknowledgments

We acknowledge allauthors ofthe literature referenced for theirvaluable research results,especially the DM2 Groups forthe meta-modelthatprovides a basis for our research.

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Biographies

Yudong Qiwas born in 1973.He is an associate professor of Aeronautical and Astronautical University.He received his Ph.D.degree from Aeronautical and Astronautical University.His research interests are software engineering,semantic web, theory and technology of command information system,currently focusing on conception modeling and information system design.

E-mail:qiyudong@sina.comZhixue Wangwas born in 1961.He is a professor of Institute of Command Information System,PLA University of Science and Technology.He received his M.S.degree from National University of Defense and Technology,and was a visiting researcher in Faculty of Information Technology,University of Brighton,England.His research interests are software engineering,requirements engineering,theory and technology of command automation,currently focusing on domainspecific modeling and formalverification.

E-mail:wzxcx@163.com

Qingchao Dongwas born in 1982.He is a lecturer of Naval Aeronautical and Astronautical University. He received his Ph.D.degree from PLA University of Science and Technology.His research interests are requirements engineering,focusing on specification and formalverification.

E-mail:dongqingchao001@163.com

Hongyue Hewas born in 1985.He is a lecturer of Institute of Command Information System,PLA University of Science and Technology University, where he received his M.S.and Ph.D.degrees.His research interest is requirements engineering,currently focusing on specification and formalverification.

E-mail:hehy2008@sina.com

10.1109/JSEE.2015.00084

Manuscript received June 27,2014.

*Corresponding author.

This work was supported by the National Natural Science Foundation of China(61273210).