An Evidential Fusion Approach for Activity Recognitionunder Uncertainty in Ambient Intelligence Environments

Faouzi SEBBAK Abdelghani CHIBANI Yacine AMIRAT Farid BENHAMMADI Aicha MOKHTARILISSI, AI, LRIA Laboratory LISSI Laboratry LISSI Laboratry AI Laboratory LRIA Laboratory

UPEC, EMP, USTHB UPEC, Paris, France UPEC, Paris, France EMP, Algiers, Algeria USTHB, Algiers, Algeriafaouzi.sebbak@gmail.com chibani@u-pec.fr amirat@u-pec.fr fbenhammadi2008@gmail.com aissani mokhtari@yahoo.fr

ABSTRACTIn ambient intelligence environments, the information pro-vided by robot’s embedded sensors and physical or logicalentities may be inaccurate and uncertain. The Dempster-Shafer evidence Theory (DST) gives a mathematical conve-nient framework for the evidential fusion representation andinference of uncertain information. However, DST yieldscounterintuitive results in high conflicting ambient intelli-gence situations. This paper aims to provide a new strategyto manage conflict in activity recognition process in the am-bient intelligence applications. It addresses the challenge ofuncertainty and proposes an evidential fusion model basedon the management of conflicting situation to optimize deci-sion making in activity recognition. The proposed approachgives intuitive interpretation for combining multiple sourcesin conflicting situations and avoids the problems of usingThe Dempster-Shafer rule of combination.

Author KeywordsAmbient intelligence, conflict resolution, Dempster-Shafertheory, activity recognition, robotics.

ACM Classification KeywordsH.5.2 Information interfaces and presentation (e.g., HCI):Miscellaneous.

General TermsMeasurement, Theory, Verification.

INTRODUCTIONA lot of works are proposed in the literature to develop in-frastructures allowing applications to be context-aware [7,12]. A context is any information that can be used to char-acterize the situation of an entity. An entity can be a per-son, place, or object which is considered relevant to the in-teraction between a user and an application (including theuser and applications themselves) [7]. Context-aware sys-tems provide mechanisms to develop applications that areaware of their contexts and able to adopt to changing con-

Permission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwise, orrepublish, to post on servers or to redistribute to lists, requires prior specificpermission and/or a fee.UbiComp ’12, Sep 5-Sep 8, 2012, Pittsburgh, USA.

Copyright 2012 ACM 978-1-4503-1224-0/12/09...

texts seamlessly. A context-aware application uses the con-text or the current situation to adapt its behavior to best meetthe user’s need. A context-aware activity recognition is builton surrounding low-level context data. In ambient intelli-gence environments, activity recognition constitutes a cen-tral task. Such environments often rely on sensed informa-tion, where diversity and lack of precision should be com-pensated by advanced evidential fusion and reasoning tech-niques. Over the last decade, a plethora of research hasbeen done on context representation and reasoning to pro-vide context-aware services that can be used in building am-bient intelligence environment. However, Evidence theory isstill less addressed to manage uncertainty in these environ-ments. Based on Dempster-Shafer Theory (DST), the pro-posed evidential fusion techniques typically use separatelythe associated sensed data to recognize user’s activity with-out considering the global conflicting context sensibility. Inpractice, conflict is a natural behavior in ambient intelligenceenvironments since the sensor context can be shared betweendifferent situations and services. in our daily living, openingthe fridge can provide the means to different activities suchas ’Prepare dinner’, ’Prepare breakfast’ and ’Get drink’.

This paper proposes a new approach to support conflict ac-tivities recognition in ambient intelligence environment. Toprovide a conflict management for activity recognition, wepropose a new mapping for conflict evidential fusion to in-crease the efficiency and accuracy of activity recognition.The evidential mapping representation and reasoning capac-ities provide the advantages of combining the sensed infor-mation and commonsense reasoning for activity recognition.This can increases the accuracy of decision making throughactivity conflicts management.

The rest of the paper is structured as follows. Section 2 givesrelated previous work on representation and reasoning ap-proaches about uncertainty in ambient intelligence environ-ments. Section 3 briefly presents the evidence theory. Insection 4, we present a common model used in the field ofactivity recognition and its limitation. Section 5 details theproposed evidential fusion model. Section 6 reports the con-flict resolution for Zadeh paradox problems. Finally, section7 conclude the paper.

RELATED WORKSA lot of works are proposed in the literature in order todevelop infrastructures allowing applications to be context-aware [7, 12]. Context reasoning aims to deduce new knowl-

$15.00.

edge based on existing context data, and provide servicesthat better match current user’s activities. However, uncer-tainty of contextual information and the dynamic and hetero-geneous nature of ambient intelligence environments face tothe challenge of developing such context-aware systems. Inthis way, a multitude of representations and reasoning ap-proaches have been proposed. These approaches can be clas-sified into six categories: case-based, logic-based, ontology-based, probabilistic-based, rule-based and evidential-based.

Case-Based Reasoning aims to solve current problem basedon previous similar cases [1, 14, 29]. Case-Based contextReasoning aims to be adapted to new context situation byremembering similar earlier experienced situations. It is aninteresting method to address context-awareness situationsand the assessment of these situations. However, it lacks inhow to generate automatically cases, and how to measure thesimilarity among them [3].

Rule-based approaches use language rules which provide aformal model for context reasoning. In [8] the authors usethe OWL (The Ontology Web Language) for rules express-ing the user preferences and security constraints. However,the Rule-Based approaches typically cannot handle ambigu-ous and imperfect context information.

Logic-Based Context Reasoning is another popular schemethat involves first-order logic. The context reasoning pre-sented in [18] uses first order logic to represent contextsas first order predicates. It allows the deduction of higher-level context from basic sensed contexts using rule-basedapproaches. The approach in [11] proposes a situation ab-straction based on predicate logic. Loke et al. [15] useProlog-style logic programs to represent contextual informa-tion. The Semantic Context-Aware Access Control Frame-work in [22] uses hybrid reasoning approach of a combina-tion of Logic Description and Logic Programming reason-ing. However, Logic-Based approaches are not suitable forreasoning about probabilistic uncertainty because they aredesigned for exact reasoning.

Probabilistic reasoning approaches try to predicate uncertaincontext by using probability theory. Gandon et al. [8] pro-posed an uncertainty model based on a predicate representa-tion of contexts and associated confidence values. For rea-soning about uncertainty, they incorporated various mecha-nisms in Gaia middleware [19] such as probabilistic logic,fuzzy logic, and Bayesian Network. The uncertainty is mod-eled by attaching a confidence value between 0 and 1 topredicates. In Fuzzy logic, confidence values represent de-grees of membership rather than probability. Bayesian net-works can be used to handle uncertainty by using exist causalrelationships to perform probabilistic fusion and higher-levelcontext aggregation [16]. Van Kastersen et al. [23] applyHidden Markov Model (HMM) to detect the activities of aperson in their home. Crowley2009 et al. [4] use HMMsfor learning and recognition of human behavior models frommultimodal observation in a smart home environment. Themain problem with probabilistic reasoning approaches is thatis not always possible to get training data.

Ontology-based reasoning approaches enable representation,reuse, and sharing of the semantics of context representa-tions. A lot of works have used OWL to represent contextinformation [2, 5, 9, 20, 25]. Agostini et al. [2] suggest com-bining rule-based reasoning with DL reasoning by propos-ing OWL DL ontology for context representation. The rea-soning models introduced in [9, 10] extend web ontologylanguage OWL to allow representing dependency relationsbetween properties. To deal with uncertain context infor-mation in building context-aware applications in ambient in-telligence environments, the authors propose a probabilis-tic extension to an ontology-based model. It represents un-certain contexts by attaching probability values to contextpredicates, and uses Bayesian Network to reason about un-certainty. Then, the formal model [25] integrates BayesianNetwork into OWL to make use of probability and depen-dency annotated OWL to represent uncertain information inBayesian Networks structures. The ontological reasoningpresents two advantages: (1) it ensures a good integrationwith the ontology model; (2) it maintains low computationalcomplexity. However, it has limited capability in dynami-cally inferring contexts [28].

Evidence theory [6] is considered a prominent approach todeal with uncertainty in the ambient intelligence environ-ments. This theory allows inferring from imprecise and in-complete contexts, and has been applied in various domains.Zhang et al. [28] present an evidence selection and conflictresolution strategy. Hong et al. [13] introduce an evidentialfusion of sensors data based on evidence theory. McKeeveret al. [17] incorporate temporal knowledge and extend theevidence over the duration of the activity. All previous worksthat propose evidential fusion techniques typically use sepa-rately the associated sensed data to recognize user’s activitywithout considering the global conflicting context sensibil-ity. The main disadvantage of such techniques is that theydo not take into account the impact of sensor’s beliefs of theconflict activities in conflicting contexts. In order to addressthese limitations, we propose a complementary approach tosupport conflicting activities based on new evidence fusionmodel.

DS THEORYDempster-Shafer Theory (DST) known as Belief FunctionsTheory is a theory of uncertainty that was developed by Demp-ster and further extended by Shafer [21]. In the following,we recall the grounds of the main concepts and principles ofthis theory.The frame of discernment is a set of mutually exclusive andexhaustive hypotheses Hn. From a frame of discernment Θcorrespondingly 2Θ the power set of Θ, a basic belief as-signment (bba) is defined as a mapping m(·) satisfying thefollowing proprieties:

m (∅) = 0 and∑

H∈2Θ

m (H) = 1

The subsets H of Θ is called the focal set elements if m(H) > 0.

Based on Shafer’s model; Dempster’s rule for two sources,m = m1 ⊕m2 is defined by Equation.1:

mDS (H) =m12 (H)

1−m12 (∅) (1)

m12 (H) =∑

H1,H2∈2Θ

H1∩H2=H

m1 (H1)m2 (H2) (2)

where m12(H) represents the conjunctive consensus opera-tor and m12(∅) reflects the conflicting mass (total conflict)of the combination between the two sources. When the con-flict is equal to 1, the sources are totally in conflict and themasses cannot be combined using Dempster’s rule of combi-nation. In addition, some researchers argue that this combi-nation rule has abnormal behavior in high conflicting sources[24, 26] as we shall explain it below.

CONFLICT ACTIVITY REPRESENTATIONS IN AMBIENTINTELLIGENCE ENVIRONMENTSIn ambient intelligence environments, robot’s embedded sen-sors and smart gadgets are data sources providing informa-tion that may be partial imprecise and/or uncertain. Gen-erally, the unreliability and the inaccuracies associated withthese sensors affect reasoning under uncertainty in the deci-sion model. The reliability of sensors can be controlled bythe discounted function mass computed according to the dis-count rate of each sensor [21]. In this section, we describethe general framework for the conflict activity inference.

Consider the example of Figure.1, which visually illustratesa hierarchy tree of binary sensors, contexts and activity usedfor activity recognition in a smart home use case introducedin [13]. In this example, the sensor node (Scup) is directlyconnected to the object context node Cup. The object con-text node Cup in turn is connected to the object compositenode (Cup,water) which is connected to the activity ’DrinkWater’. Sensors Scup , Swater and Ssugar are active becausethey were triggered. The other sensors (Scoffee and Skettle)were not activated. This example motivates the need for fur-ther modeling extensions of the activity inference eviden-tial networks. The activity inference starts from the discountfunction masses of the sensors to the activity. First, evidenceon sensor nodes are represented by mass functions as fol-lows:

mScup ({Scup}) = 1, mSwater ({Swater}) = 1;mScoffee

({¬Scoffee}) = 1, mSkettle({¬Skettle}) = 1;

and mSsugar({Ssugar}) = 1;

Then, the discounted mass function can be calculated by tak-ing into account the discount rate of each sensor (Figure.1).

To take into account the misreading or the malfunctioningof sensors in the evidence aggregation process, Shafer [21]proposed to incorporate the discount rate to control the re-liability of these sensors, and as a consequence the impactof evidence is discounted. The discounted mass function isdefined as follows:

mr (A) =

{(1− r)m (A) A ⊂ Θr + (1− r)m (Θ) A = Θ

(3)

where r is the sensor discount rate that takes a value between0 and 1. When r is equal to zero, the sensor is completelyreliable; when r is equal to one, the sensor is absolutely un-reliable. In our current example, we calculate the discountmass function as follows:

mrScup

({Scup}) = 0.90,

mrScup

({Scup,¬Scup}) = 0.1 ;

mrSwater

({Swater}) = 0.97,mr

Swater({Swater,¬Swater}) = 0.03;

mrScoffee

({¬Scoffee}) = 0.94,

mrScoffee

({Scoffee,¬Scoffee}) = 0.06;

mrSkettle

({¬Skettle}) = 0.98,mr

Skettle({Skettle,¬Skettle}) = 0.02;

mrSsugar

({Ssugar}) = 0.99,

mrSsugar

({Ssugar,¬Ssugar}) = 0.01;

Now, we translate the mass functions from the sensors to theassociated objects using the multivalued mapping [13].

mcup ({cup}) = mrScup

({Scup}) = 0.9,

mcup ({cup,¬cup}) = mrScup

({Scup,¬Scup}) = 0.1;

mwater ({water}) = mrSwater

({Swater}) = 0.97,mwater ({water,¬water}) = mr

Swater({Swater,¬Swater}) = 0.03;

mcoffee ({¬coffee}) = mrScoffee

({¬Scoffee}) = 0.94,

mcoffee ({coffee,¬coffee}) = mrScoffee

({Scoffee,¬Scoffee}) = 0.06;

mkettle ({¬kettle}) = mrSkettle

({¬Skettle}) = 0.98,mkettle ({kettle,¬kettle}) = mr

Skettle({Skettle,¬Skettle}) = 0.02;

msugar ({sugar}) = mrSsugar

({Ssugar}) = 0.99,

msugar ({sugar,¬sugar}) = mrSsugar

({Ssugar,¬Ssugar}) = 0.01;

An Evidential mapping can be used when the relationshipbetween the elements inside two frames of discernments isnot certain [13]. After, we translate the calculated masses tothe composite context node (cup, water) and (cup, water,coffee, kettle) in short (cwck) using the multivalued map-ping as follows:

Figure 1. An example of evidential network in ambient intelligent envi-ronment.

m1(cup,water) ({cup, water}) = mcup ({cup}) = 0.9,m1(cup,water) ({(cup, water),¬(cup, water)}) =mcup ({cup,¬cup}) = 0.1;

m2(cup,water) ({cup, water}) = mwater ({water}) = 0.97,m2(cup,water) ({(cup, water),¬(cup, water)}) =mwater ({water,¬water}) = 0.03;

m1(cwck) ({cwck}) = m(cup,water) ({(cup, water)}) = 0.935,m1(cwck) ({cwck,¬cwck}) =m(cup,water) ({(cup, water) ,¬ (cup, water)}) = 0.065;

m2(cwck) ({cwck}) = mcoffee ({coffee}) = 0,m2(cwck) ({¬cwck}) = mcoffee ({¬coffee}) = 0.94,m2(cwck) ({cwck,¬cwck}) = mcoffee ({coffee,¬coffee}) = 0.06;

m3(cwck) ({cwck}) = mkettle ({kettle}) = 0,m3(cwck) ({¬cwck}) = mkettle ({¬kettle}) = 0.98,m3(cwck) ({cwck,¬cwck}) = m ({kettle,¬kettle}) = 0.02;

The contexts (cup, water) and cwck cannot be aggregatedusing Dempster’s combination rule, because the belief dis-tributions are not independent. An equally weighted sumoperator is used in [13] to sum belief distributions on a com-posite node. It is defined as follows:

m (A) = m1⊕ · · · ⊕mN (A) =1

N

N∑i=1

mi (A) (4)

where A ⊆ ΘFinally, using Dempster’s rule of combination for combiningmasses of context cwck and sugar, we obtain the activitiesmasses as:

m(Drinkwater) ({Drinkwater}) = m(cup,water) ({(cup, water)})= 0.935m(Drinkwater) ({Drinkwater,¬Drinkwater}) =m(cup,water) ({(cup, water) ,¬ (cup, water)}) = 0.065

m(Drinkcofee) ({Drinkcoffe}) = m(Cwck) ({Cwck}) = 0.981m(Drinkcofee) ({Drinkcoffe}) = m(Cwck) ({Cwck}) = 0.017m(Drinkcoffe) ({Drinkcoffe,¬Drinkcoffe})= m(Cwck) ({Cwck,¬Cwck}) = 0.002

We calculate the belief and the plausibility over Drink waterand Drink coffee as follows:

Bel ({Drinkwater}) = m(Drinkwater) ({Drinkwater}) = 0.935Pls ({Drinkwater}) = m(Drinkwater) ({Drinkwater})+m(Drinkwater) ({Drinkwater,¬Drinkwater}) = 1;

Bel ({Drinkcoffee}) = m(Drinkcoffee) ({Drinkcoffee}) = 0.981Pls ({Drinkcoffee}) = m(Drinkcoffee) ({Drinkcoffee})+m(Drinkcoffee) ({Drinkcoffee,¬Drinkcoffee}) = 0.983

Using DST, the belief values on Drink coffee and Drink wa-ter activities are 0.981 and 0.935 respectively. These beliefvalues are close to one and the belief value on Drink coffee isbigger with a value of 0.046 than that on Drink water in spiteof the inactivity of the Scoffee and Skettle sensors. Thus wecannot identify each activity performed in smart home. Ob-viously, this evidential inference produces counterintuitivedecision making process for activity recognition in ambient

environments. Such a mistake arises from the fact that theevidential mapping and inference are inadequate from thecomposite objects to the activity. This is due to the omissionto take into account the activation/desactivation of the sen-sors associated to the conflict in the evidence computationof the activities. To address this problem, further evidentialmapping and inference improvements are needed for effec-tive activity decision-making. This improvement is based onthe conflict activities management.

PROPOSED EVIDENCE FUSION MODELIn most if works dealing with activity recognition in am-bient intelligence environments [13, 17, 28], the proposedevidential fusion techniques use separately the associatedsensed data to recognize user’s activity without consideringthe global conflicting context sensibility. The mass compu-tation of each activity is given by combining only masseson the associated object contexts. A disadvantage of suchtechniques is that they do not take into account the impactof sensor’s mass of the conflict activities. In order to ad-dress these limitations, we propose a new evidence fusionmodel to support conflicting activities. First, we aim to pro-vide some definitions to manage the conflict of the sensedinformation.

DEFINITION 1. Let Ac = {A1, · · · , An} be a set of con-flict activities, and let OAj = {o1, · · · , on} be the set of ob-ject context associated to the activity Aj . We define the con-flict associated to the activity Ai as:

CAi=

{oj

∣∣ oj ∈ OAj

}(5)

We exemplify the above definition with the following sim-plified illustration of activity recognition in the smart homeof Figure.1. According to the previous definition, we obtainthe following activity conflicts sets:CDrinkwater = {cup, water, coffee, kettle, sugar}CDrinkcoffee = {cup, water}

For each generated activity Ai, we compute its conflict masswhich is based on the object context nodes of the conflictactivities using the next definition.

DEFINITION 2. Let CAi = {o1, · · · , oN} be a set of con-flict associated to the activity Ai. We define the average con-flict mass of the activity Ai denoted by m(CAi) as:

m(CAi) =1

N

n=N∑n=1

(1−m(on)) (6)

Once the average conflict mass of each activity is computed,the novel activity masses can be obtained by applying thefollowing equation:

mAi =1

K

l=L∑l=1

mlAi

∗m(CAi) (7)

Sensor Activity DS Proposed model

kettle coffee Bel(DW ) Bel(DC) Bel(DW ) Bel(DC)0 0 0,935 0,981 0,825 0,1750 1 0,935 0,994 0,681 0,3191 0 0,935 0,995 0,672 0,3281 1 0,935 0,999 0,246 0,754

Table 1. Belief on ’Drink water’ and ’Drink coffee’ activities accordingto the combinations of ’coffee’ and ’kettle’ sensors.

where L represents the number of multiple independent as-sociated objects related to the activity Ai. To normalizethe conflict masses of the activities, we used the constant

K =n∑

i=1

mAi which is computed over the entire set of con-

flict evidence of the activity.Reconsider our example. The average conflicts of user’s ac-tivities are:

m(CDrink water) =15 ((1−mcup ({cup}) + (1−mwater ({water})

+(1−mcoffee ({coffee}) + (1−mkettle ({kettle})+(1−msugar ({sugar}))=15 ((1− 0.9) + (1− 0.97) + (1− 0) + (1− 0) + (1− 0.99))

= 0.428

m(CDrink coffee)=12 ((1−mcup ({cup}) + (1−mwater ({water}))

= 12 ((1− 0.9) + (1− 0.97)) = 0.065

The novel activities masses are:

mcDrink water = m(cup, water) ({cup, water}) ∗m(CDrink water)

0.935× 0.428 = 0, 400mc

Drink coffee= m1(Cwck) ({Cwck}) ∗m(CDrink coffee)+m2(Cwck) ({Cwck}) ∗m(CDrink coffee)= 0, 312× 0.065 + 0.99× 0.065 = 0.085

The constant of normalization is:k = mc

Drink water +mcDink coffee = 0, 400 + 0, 085

= 0, 485

As result, we obtain the masses of the conflict activities

mDrink water =mc

Drink water

k = 0.4000.485 = 0.825

mDrink coffee =mc

drink coffee

k = 0.0850.485 = 0.175

From these results Bel(Drink water) - Bel(Drink coffee) =0.825− 0.175 = 0.650 is bigger than those calculated usingDempster’s combination rule. So the Drink water activitycan be identified.

Table 1 reports the belief values of performing an activityrelated to different combinations of the Scoffee and Skettle

sensors. A sensor with zero value is inactive sensor. Us-ing the Dempster-Shafer evidence theory, it can be seen thatin all cases the Bel(Drink coffee) is bigger than Bel(Drinkwater) when the Skettle and/or Scoffee sensors are inactive.These results are considered as a counterintuitive interpreta-tion for combining information of the two sensors. In ourcase, when Skettle and Scoffee sensors are active, the Drinkcoffee activity has been performed. In addition, the proposedapproach gives a better believe values in all cases which rep-resent the intuitive inference.

Figure 2. Example of the Zadeh paradox

CONFLICT RESOLUTION OF WELL-KNOWN CONFLICTPROBLEMSIn this section, we apply the proposed conflict resolutionstrategy to two well-known conflict problems.

Zadeh paradoxThe problem of combining conflicting evidences is largelystudied in the literature. Researchers argue that Dempster’srule is catastrophically counter-intuitive when the conflict issignificant [27]. In this section, we focus on two problemsprovided by the Zadeh paradox using our conflict resolutionapproach.

Figure.2 illustrates a well-known example of the Zadeh para-dox. Activity B supported by a little evidence will get abelief equal to 1 when applying the Dempster’s rule of com-bination. Furthermore, activity A and activity C that werestrongly supported by respectively ’source 1’ and ’source 2’,will get the belief as 0 which is a counterintuitive result. Inorder to avoid the Zadeh paradox, we use the proposed evi-dential model.

The set of conflicting activities is given as follows.CA = {¬S1, S2, ¬S2}CB = {S1, S2}CC = {S1, ¬S1, ¬S2}where S1 and S2 refer to source1 and source2 respectively.The average conflict mass for each activity is computed us-ing equation (6) as follows:

m(CA)=1n

i=n∑i=1

(1−m(oi))

= 13 ((1− 0.01) + (1− 0.99) + (1− 0.01)) = 0.6633

m(CB)=1n

i=n∑i=1

(1−m(oi))

= 12 ((1− 0.99) + (1− 0.99)) = 0.01

m(CC)=1n

i=n∑i=1

(1−m(oi))

= 13 ((1− 0.99) + (1− 0.01) + (1− 0.01)) = 0.6633

The novel activities masses are:mc

A= m1 ({S1}) ∗m(CA) = 0.99 ∗ 0.663333 = 0, 6567mc

B= m1 ({¬S1}) ∗m(CB) +m2 ({¬S2}) ∗m(CB)= 0.01 ∗ 0.01 + 0.01 ∗ 0.01 = 0, 0002

mcC= m2 ({S2}) ∗m(CC) = 0.99 ∗ 0.663333 = 0, 6567

After normalization, we obtain:

mA =mc

A

mcA+mc

B+mcC= 0.6567

1.3136 = 0.49992

mB =mc

B

mcA+mc

B+mcC= 0.0002

1.3136 = 0.00016

mC =mc

C

mcA+mc

B+mcC= 0.6567

1.3136 = 0.49992

As a result, the obtained masses are entirely consistent withintuition.

Total conflict situationThe second problem is the situation when the total conflictvalue is equal to one (ie: 1 − K = 0). Let’s assume thatwe have conflicting evidences due to the belief conflictingof two experts. The first expert assumes that situation A ishappening with a probability p1, situation B with probabil-ity 1 − p1, situation C and D with a zero probability. Thesecond expert assumes that the probabilities are distributedas follow: Both situations A and B have a zero probabil-ity, Situation C and D with probabilities of p2 and 1 − p2respectively.

Let p1 = 0.01 and p2 = 0.8. Using Dempster’s rule ofcombination to calculate masses for each situation, we getdividing by zero problem, because of the value of 1−K:1 − K = 1 − ∑

A∩B=Φ

m1 (A) m2 (B) = 1 − 0 + 0.008 +

0.002 + 0 + 0.792 + 0.198 + 0 + 0 + 0 + 0 + 0 + 0 = 0So, we cannot compute any masses about these four situa-tions. However, our conflict resolution approach avoids thissituation.

From the conflict activity sets:CA = {S1 (B) , S1 (C) , S1 (D) , S2 (B) , S2 (C) , S2 (D)}CB = {S1 (A) , S1 (C) , S1 (D) , S2 (A) , S2 (C) , S2 (D)}CC = {S1 (A) , S1 (B) , S1 (D) , S2 (A) , S2 (B) , S2 (D)}CD = {S1 (A) , S1 (B) , S1 (D) , S2 (A) , S2 (B) , S2 (D)}

Ac = {A, B, C, D}we compute the average conflict mass for each activity usingequation 6:m(CA) = 0.6683; m(CB) = 0.8316; m(CC) = 0.8;m(CD) = 0.7.

The novel activities masses are:mc

A= m1 ({S1 (A)}) ∗m(CA) +m2 ({S2 (A)}) ∗m(CA)= 0.01× 0, 6683 + 0× 0.6683 = 0, 00668

mcB= m1 ({S1 (B)}) ∗m(CB) +m2 ({S2 (B)}) ∗m(CB)= 0.99 ∗ 0, 8316 + 0 ∗ 0.8316 = 0, 8233

mcC= m1 ({S1 (C)}) ∗m(CC) +m2 ({S2 (C)}) ∗m(CC)= 0 ∗ 0, 8 + 0, 8 ∗ 0.8 = 0, 64

mcD= m1 ({S1 (D)}) ∗m(CD) +m2 ({S2 (D)}) ∗m(CD)= 0 ∗ 0, 7 + 0.2 ∗ 0.7 = 0, 14

After normalization, we obtain the value of the constant k:k = mc

A +mcB +mc

C +mcD = 0, 6100

As result, the combined masses are:

mA =mc

A

k = 0,006681.6100 = 0.0042

mB =mc

B

k = 0,82331.6100 = 0.5113

mC =mc

C

k = 0,641.6100 = 0, 3975

mD =mc

D

k = 0,141.6100 = 0.0870

As conclusion, the obtained results satisfy the practical situ-ations, and avoid the problem of Dempster’s rule of combi-nation. In addition, the proposed approach gives an intuitivesolution in high conflictiong situation (Zadeh paradox andTotal conflicting situation).

CONCLUSIONThe present paper presents an evidential fusion of sensor in-formation modeling to support the conflicting activity deci-sion making process in ambient intelligence environments.The novelty of our approach is that it can model uncertaintyusing activity conflict credibility and a new rule combina-tion to infer context-aware activities based on sensor data.The present model building on the new evidential fusionmethod can better support the activity decision making pro-cess. It uses conflicting contexts to calculate the global com-bined masses of the activities. The obtained results demon-strate that activity recognition in ambient intelligence envi-ronments using the proposed model is feasible and can pro-vide a better results in terms of efficiency. Compared toapproaches using Dempster’s rule of combination, the pro-posed model gives intuitive interpretation for combining mul-tiple sources information.

ADDITIONAL AUTHORSREFERENCES1. A. Aamodt and E. Plaza. Case-based reasoning:

foundational issues, methodological variations, andsystem approaches. AI Communications, 7(1):39–59,1994.

2. A. Agostini, C. Bettini, and D. Riboni. Looselycoupling ontological reasoning with an efficientmiddleware for context-awareness. In MobiQuitous,pages 175–182. IEEE Computer Society, 2005.

3. A. Bikakis, T. Patkos, G. Antoniou, andD. Plexousakism. A survey of semantics-basedapproaches for context reasoning in ambientintelligence. In Proceedings of the Workshop ArtificialIntelligence Methods for Ambient Intelligence, pages15–24. Springer, 2007.

4. O. Brdiczka, M. Langet, J. Maisonnasse, and J. L.Crowley. Detecting human behavior models frommultimodal observation in a smart home. IEEE T.Automation Science and Engineering, 6(4):588–597,2009.

5. H. Chen, T. W. Finin, A. Joshi, L. Kagal, F. Perich, andD. Chakraborty. Intelligent agents meet the semanticweb in smart spaces. IEEE Internet Computing,8(6):69–79, 2004.

6. A. P. Dempster. A generalization of Bayesian inference.Journal of the Royal Statistical Society, Series B,30:205–247, 1968.

7. Dey, A. K., Abowd, G. D., and D. Salber. A conceptualframework and a toolkit for supporting the rapidprototyping of context-aware applications.Human-Computer Interaction, 16(2/4):97–166, 2001.

8. F. L. Gandon and N. M. Sadeh. Semantic webtechnologies to reconcile privacy and contextawareness. J. Web Sem, 1(3):241–260, 2004.

9. T. Gu, H. K. Pung, and D. Zhang. Toward anOSGi-based infrastructure for context-awareapplications. IEEE Pervasive Computing, 3(4):66–74,2004.

10. T. Gu, H. K. Pung, and D. Q. Zhang. A bayesianapproach for dealing with uncertain contexts, Apr. 162004.

11. K. Henricksen and J. Indulska. Developingcontext-aware pervasive computing applications:Models and approach. Pervasive and MobileComputing, 2(1):37–64, 2006.

12. Hong, J. I., Landay, and J. A. An infrastructureapproach to context-aware computing.Human-Computer Interaction, 16(2/4):287–303, 2001.

13. X. Hong, C. D. Nugent, M. D. Mulvenna, S. I.McClean, B. W. Scotney, and S. Devlin. Evidentialfusion of sensor data for activity recognition in smarthomes. Pervasive and Mobile Computing,5(3):236–252, 2009.

14. O. B. Kwon and N. M. Sadeh. Applying case-basedreasoning and multi-agent intelligent system tocontext-aware comparative shopping. Decision SupportSystems, 37(2):199–213, 2004.

15. S. W. Loke. Logic programming for context-awarepervasive computing: Language support, characterizingsituations,and integration with the web. In WebIntelligence, pages 44–50. IEEE Computer Society,2004.

16. Y. Ma, D. V. Kalashnikov, and S. Mehrotra. Towardmanaging uncertain spatial information for situationalawareness applications. IEEE Trans. Knowl. Data Eng,20(10):1408–1423, 2008.

17. S. McKeever, J. Ye, L. Coyle, C. J. Bleakley, andS. Dobson. Activity recognition using temporalevidence theory. JAISE, 2(3):253–269, 2010.

18. A. Ranganathan, J. Al-Muhtadi, and R. H. Campbell.Reasoning about uncertain contexts in pervasivecomputing environments. IEEE Pervasive Computing,3(2):62–70, 2004.

19. M. Roman, C. Hess, R. Cerqueira, A. Ranganathan,R. H. Campbell, and K. Nahrstedt. A middlewareinfrastructure for active spaces. IEEE PervasiveComputing, 1(4):74–83, 2002.

20. F. Sebbak, Y. Amirat, A. Chibani, and A. Mokhtari.Context-aware ubiquitous framework services usingjade-osgi integration framework. In InternationalConference on Machine and Web Intelligence(ICMWI), pages 48–53, 2010.

21. G. Shafer. A mathematical theory of evidence.Princeton university press, 1976.

22. A. Toninelli, R. Montanari, L. Kagal, and O. Lassila. Asemantic context-aware access control framework forsecure collaborations in pervasive computingenvironments. In International Semantic WebConference, volume 4273 of Lecture Notes inComputer Science, pages 473–486. Springer, 2006.

23. T. van Kasteren, A. K. Noulas, G. Englebienne, andB. J. A. Krose. Accurate activity recognition in a homesetting. In UbiComp, volume 344 of ACM InternationalConference Proceeding Series, pages 1–9. ACM, 2008.

24. F. Voorbraak. On the justification of Dempster’s rule ofcombination. Artificial Intelligence, 48:171–197, 1991.

25. Y. Yang and J. Calmet. Ontobayes: An ontology-drivenuncertainty model. In CIMCA/IAWTIC, pages 457–463.IEEE Computer Society, 2005.

26. L. Zadeh. On the validity of Dempster’s rule ofcombination of evidence. Memorandum UCB/ERL-M.Electronics Research Laboratory, Univ. of California,1979.

27. L. A. Zadeh. A mathematical theory of evidence (bookreview). AI Magazine, 5(3):81–83, 1984.

28. D. Zhang, M. Guo, J. Zhou, D. Kang, and J. Cao.Context reasoning using extended evidence theory inpervasive computing environments. Future GenerationComp. Syst, 26(2):207–216, 2010.

29. A. Zimmermann. Context-awareness in user modelling:Requirements analysis for a case-based reasoningapplication. In K. D. Ashley and D. G. Bridge, editors,ICCBR, volume 2689 of Lecture Notes in ComputerScience, pages 718–732. Springer, 2003.