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...kings is the degree of uncertainty of the information sources about their expressed opinions. Possibility theory addresses uncertainty through the necessity and possibility measures. Subjective logic =-=[21]-=-, an extension to Dempster-Shafer theory of evidence [15], is also able to explicitly address uncertainty. It defines uncertainty as one of the dimensions of belief in its three dimensional belief str...

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... to overall behavior of the information source throughout a period of observation called reliability. Under different contexts researchers have employed terms such as trustworthiness [14], reputation =-=[20]-=-, confidence [28], and others to refer to the same issue. We formalize the reliability of the source of a belief base as a subjective opinion that represents the degree of belief in the fact that the ...

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... that they occur when the hypothesis space is not exhaustive [45]. In a different approach, Yager proposes the assignment of conflict masses to θ, and interprets it as the degree of overall ignorance =-=[49]-=-. Within the framework of Subjective logic, the combination operation is performed through the application of the Consensus operator. Definition 10 Let χAx = (b A x , d A x , u A x ) and χ B x = (b B ...

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...f information sources that may contain mutual inconsistencies, how can a coherent set of information be developed which is a fair representative of the content conveyed by all the information sources =-=[27]-=-. Several researchers have approached this issue as a multi-stage game [27, 13, 39]. The game is a competition between the information sources where the weakest information sources are considered as t...

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...of acceptable arguments can be developed from the framework, which can be considered as the required results. Other merging models based on possibilistic theory can be found in the related literature =-=[29, 40, 33, 32, 38]-=-. 10.2. Collaborative Modeling A survey conducted in the United States revealed that seventy percent of the people involved in the modeling and design divisions of their company believe that sequentia...

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...g functions more difficult in these frameworks. Several models have been proposed which exploit priority relationships between the belief bases and their constituting formulae in the process of merge =-=[8, 10, 11]-=-. The priorities provide essential information with regards to the degree of formulae importance. They can be helpful in deciding which formulae need to be discarded in order to restore consistency. P...

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...hat are allowed are compatibility, multiplicity, and reachability. χbel is another inconsistency management framework that provides means for reasoning over multiple inconsistent state machine models =-=[16]-=-. The models are annotated with Quasi-Boolean logic values and a model checker called χchek performs an evaluation over the defined properties. Moreover, AGORA is a goal-oriented discrepancy identific...

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...ually reliable. Furthermore, epistemic uncertainty (also known as partial ignorance) is an indispensable element of human judgments that makes them even more susceptible to inaccuracy and imprecision =-=[43]-=-. There is no guarantee that the received information coming from various human sources be consonant or consistent. They may be in many cases arbitrarily (with very few common elements) or disjointedl...

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...ous rounds. More recently, a class of general belief merge operators called DA2 have been proposed that encode many previous merging operators (both model-based and syntax-based) as its special cases =-=[26]-=-. The general DA2 framework is defined using a distance function d and two aggregation function ⊕ ands. The major shortcoming of the mentioned models is that they function over pure propositional logi...

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...The specifications provided for the overlapping segments of each model may be inconsistent, and therefore, require meticulous methods for addressing their integration. According to the definitions in =-=[46]-=-, the inconsistencies between software models can be formally defined based on the overlap relationships between the interpretations assigned to domain models by the experts. Definition 33 The interpr...

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...he intention of combining information is to meaningfully summarize and simplify a corpus of data elements coming from various sources in order to develop a consensus between the participating sources =-=[22]-=-. There exist several possible techniques for aggregating multiple belief mass assignments in Dempster-Shafer theory of evidence. The base combination rule for multiple mass assignment functions is De...

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... 4. Basics of Evidence Theory Evidence theory is one of the theoretical models, which is able to numerically quantify the lack of knowledge with regards to a certain phenomenon in an effective manner =-=[44]-=-. It is a potentially useful tool for the evaluation of the reliability of information sources. Dempster-Shafer (DS) theory of evidence is one of the most widely used models that provides means for ap...

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... θ, β 6= ø when ∑ ϕ,ψ⊆θ,ϕ∩ψ=øm1(ϕ)m2(ψ) 6= 1. Dempster’s rule redistributes the conflicting masses over the non-conflicting masses and therefore insists on the mutual agreements and removes conflicts =-=[31]-=-. This approach to belief integration has been criticized due to its counter-intuitive results under highly conflicting belief expressions [50]. Several authors have proposed models to overcome this p...

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...o overcome this problem. For instance, Smets has proposed the assignment of the conflicting masses to φ. His interpretation of conflicts is that they occur when the hypothesis space is not exhaustive =-=[45]-=-. In a different approach, Yager proposes the assignment of conflict masses to θ, and interprets it as the degree of overall ignorance [49]. Within the framework of Subjective logic, the combination o...

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...archers believe that inconsistency is totally undesirable and should be removed after merging [10, 9]. The second approach claims that inconsistencies are unavoidable and they can exist after merging =-=[1, 7, 11]-=-. Qi et al. [39] propose a prioritized belief negotiation model that merges information sources represented by possibilistic belief bases. They introduce several negotiation and weakening functions th...

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...e information sources that are furthest away from the coalition. The rationality for such an approach under the reliability assumption for the information sources is based on Condorcet’s Jury theorem =-=[30]-=-. This theorem argues that in most cases listening to the majority of the members of the jury (coalition) is the most rational decision. Each stage of the merging game is known as rounds of negotiatio...

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...ef mass assignments in Dempster-Shafer theory of evidence. The base combination rule for multiple mass assignment functions is Dempster’s rule of combination, which is a generalization of Bayes’ rule =-=[36]-=-. This combination operator ignores the conflicts between the functions and emphasizes on their agreements. Definition 9 Let m1 and m2 be two belief mass assignments defined on a frame of discernments...

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...h the employment of information from different sources. Here, the sources of information are human experts that are in most cases cooperating to develop a unique model for a given domain of discourse =-=[48]-=-. The model developed by each expert can be considered as an information source and their integration can be viewed as a belief merging process. The factor distinguishing collaborative modeling from t...

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... B x )/κ u A,B x = 0 INTEGRATING SUBJECTIVE KNOWLEDGE... 9 The Consensus operator has been shown to have a stable behavior under various conditions and even while merging conflicting dogmatic beliefs =-=[23]-=-. It satisfies two important algebraic properties i.e. commutativity (A ⊕ B = B ⊕ A), and associativity (A ⊕ [B ⊕ C] = [A ⊕ B] ⊕ C), which are of great significance while merging two peer information ...

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...t provides its users with the possibility of defining pluggable algorithms called strategies. JDiff is a tool that compares two object-oriented programs and identifies differences and correspondences =-=[3]-=-. For this purpose, JDiff reduces this problem to a hammock matching problem in a graph. UMLDiff is a model specific differencing tool that operates on two UML class models reverse engineered from Jav...

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...alition) is the most rational decision. Each stage of the merging game is known as rounds of negotiation or competition. Konieczny’s belief negotiation model [27] and Booth’s belief negotiation model =-=[13, 12]-=- are among the most popular frameworks for belief merging, which are defined for a pure propositional logic setting. In these models, in each round of negotiation, some of the information sources are ...

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...rencing tool that operates on two UML class models reverse engineered from Java code, and produces a structural change tree depicting the additions, removals, refactorings, and etc [19]. Furthermore, =-=[42]-=- introduces a distributed consistency checking tool that given a set of models and the mappings between them, it first merges the models and then verifies the derived product against consistency const...

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...g approach is BS−C=C∪D. The authors have also proposed two splitting methods, namely: upper-free-degree based splitting and the free-formula based splitting. In a different approach, Amgoud and Prade =-=[2]-=- propose an argumentation framework for merging conflicting prioritized belief bases. In this model, the preference orderings between the arguments makes it possible to distinguish different types of ...

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...certainty function corresponding with mθ, a belief mass assignment on θ, is a function u : 2θ → [0, 1] defined as: u(ψ) = ∑ ϕ∩ψ 6=∅,ϕ 6⊆ψmθ(ϕ), ϕ, ψ ∈ 2θ. With the above definitions, Subjective logic =-=[24]-=- extends Dempster-Shafer theory of evidence. A belief expression in Subjective logic is defined as a 3-tuple χAx = (bAx , d A x , u A x ) also known as the opinion of expert A about hypothesis x (χ A ...

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...g functions more difficult in these frameworks. Several models have been proposed which exploit priority relationships between the belief bases and their constituting formulae in the process of merge =-=[8, 10, 11]-=-. The priorities provide essential information with regards to the degree of formulae importance. They can be helpful in deciding which formulae need to be discarded in order to restore consistency. P...

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...eted as the belief that one of the atomic sets in ψ is true, but uncertainty rules out the possibility of pinpointing the exact atomic set. Definition 4 A belief mass assignment is a mapping m : 2θ → =-=[0, 1]-=- that assigns mθ(ψ) to each subset ψ ∈ 2θ such that: (1) mθ(ψ) ≥ 0, (2) mθ(∅) = 0, (3) ∑ ψ∈2θ mθ(ψ) = 1. 6 EBRAHIM BAGHERI mθ(ψ) is then called the belief mass of ψ. A belief mass assignment is called...

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...e insists on the mutual agreements and removes conflicts [31]. This approach to belief integration has been criticized due to its counter-intuitive results under highly conflicting belief expressions =-=[50]-=-. Several authors have proposed models to overcome this problem. For instance, Smets has proposed the assignment of the conflicting masses to φ. His interpretation of conflicts is that they occur when...

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... from the mentioned fields is that it directly interacts with human participants. Humans usually make conception errors due to risk aversion, short-term memory or even framing and perceptual problems =-=[37]-=-. This implies that not all asserted information from the sources are correct or equally reliable. Furthermore, epistemic uncertainty (also known as partial ignorance) is an indispensable element of h...

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...ty theory [34]. There are two approaches to possibilistic belief base merging. In the first approach, researchers believe that inconsistency is totally undesirable and should be removed after merging =-=[10, 9]-=-. The second approach claims that inconsistencies are unavoidable and they can exist after merging [1, 7, 11]. Qi et al. [39] propose a prioritized belief negotiation model that merges information sou...

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...ercent of the people involved in the modeling and design divisions of their company believe that sequential engineering products are insufficient and that they will need collaborative design software =-=[18]-=-. Despite the growing need for collaborative modeling tools, INTEGRATING SUBJECTIVE KNOWLEDGE... 23 only recently has this domain gained attention. There are two major models of collaboration, namely:...

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...odel specific differencing tool that operates on two UML class models reverse engineered from Java code, and produces a structural change tree depicting the additions, removals, refactorings, and etc =-=[19]-=-. Furthermore, [42] introduces a distributed consistency checking tool that given a set of models and the mappings between them, it first merges the models and then verifies the derived product agains...

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...g functions more difficult in these frameworks. Several models have been proposed which exploit priority relationships between the belief bases and their constituting formulae in the process of merge =-=[8, 10, 11]-=-. The priorities provide essential information with regards to the degree of formulae importance. They can be helpful in deciding which formulae need to be discarded in order to restore consistency. P...

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...be a normalization factor. Ambiguity is a function ζ : F → [0, 1], defined as: ζ(φ) = − ( 1 e1−(bφ+dφ) − 1 ) /. Ambiguity is similar to the belief entropy metric in the generalized entropy criterion =-=[47]-=-. Furthermore, the indecisiveness property is a measure of the ability of the information source to firmly state a given formula. The further away the degree of belief and disbelief of a given formula...

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...us kinds of models, and to integrate them into a unique representation. The Epsilon Merging Language is a rule-based language that provides tools for merging models designed using diverse meta-models =-=[17]-=-. It provides its users with the possibility of defining pluggable algorithms called strategies. JDiff is a tool that compares two object-oriented programs and identifies differences and correspondenc...

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...of acceptable arguments can be developed from the framework, which can be considered as the required results. Other merging models based on possibilistic theory can be found in the related literature =-=[29, 40, 33, 32, 38]-=-. 10.2. Collaborative Modeling A survey conducted in the United States revealed that seventy percent of the people involved in the modeling and design divisions of their company believe that sequentia...

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... in many cases the reliability value that dynamically changes as a result of the rounds of negotiation is not very much different from the initial reliability value that was ascribed to a belief base =-=[5]-=-; therefore, reliability is a static subjective opinion in our model. We have also introduced several choice and enhancement functions. The CB enhancement function is demonstrates enduring behavior, w...

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...rces about their expressed opinions. Possibility theory addresses uncertainty through the necessity and possibility measures. Subjective logic [21], an extension to Dempster-Shafer theory of evidence =-=[15]-=-, is also able to explicitly address uncertainty. It defines uncertainty as one of the dimensions of belief in its three dimensional belief structure. Logic-based merging approaches have been employed...

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... annotated with Quasi-Boolean logic values and a model checker called χchek performs an evaluation over the defined properties. Moreover, AGORA is a goal-oriented discrepancy identification framework =-=[25]-=-. The framework computes two metrics, vertical and diagonal variances, that allow the identification of cross-perspective inconsistency. Finally, the Integration Suite [6, 4] is a collaborative concep...

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...of acceptable arguments can be developed from the framework, which can be considered as the required results. Other merging models based on possibilistic theory can be found in the related literature =-=[29, 40, 33, 32, 38]-=-. 10.2. Collaborative Modeling A survey conducted in the United States revealed that seventy percent of the people involved in the modeling and design divisions of their company believe that sequentia...

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...cy identification framework [25]. The framework computes two metrics, vertical and diagonal variances, that allow the identification of cross-perspective inconsistency. Finally, the Integration Suite =-=[6, 4]-=- is a collaborative conceptual modeling framework that employs belief theory to capture the uncertainty in the expressions of multiple experts. Uncertainty is employed in this framework to formally gu...

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...cy identification framework [25]. The framework computes two metrics, vertical and diagonal variances, that allow the identification of cross-perspective inconsistency. Finally, the Integration Suite =-=[6, 4]-=- is a collaborative conceptual modeling framework that employs belief theory to capture the uncertainty in the expressions of multiple experts. Uncertainty is employed in this framework to formally gu...

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...of acceptable arguments can be developed from the framework, which can be considered as the required results. Other merging models based on possibilistic theory can be found in the related literature =-=[29, 40, 33, 32, 38]-=-. 10.2. Collaborative Modeling A survey conducted in the United States revealed that seventy percent of the people involved in the modeling and design divisions of their company believe that sequentia...

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...herent set of information be developed which is a fair representative of the content conveyed by all the information sources [27]. Several researchers have approached this issue as a multi-stage game =-=[27, 13, 39]-=-. The game is a competition between the information sources where the weakest information sources are considered as the losers of the game and should make appropriate concessions. The basic idea of th...

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...of acceptable arguments can be developed from the framework, which can be considered as the required results. Other merging models based on possibilistic theory can be found in the related literature =-=[29, 40, 33, 32, 38]-=-. 10.2. Collaborative Modeling A survey conducted in the United States revealed that seventy percent of the people involved in the modeling and design divisions of their company believe that sequentia...

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...ider the role of formulae priorities while merging belief bases. Some researchers have defined formulae priorities through the employment of the necessity degree of each formula in possibility theory =-=[34]-=-. There are two approaches to possibilistic belief base merging. In the first approach, researchers believe that inconsistency is totally undesirable and should be removed after merging [10, 9]. The s...

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...dividual weakening (contraction) function. The belief negotiation model has its roots in belief revision, which is defined in terms of two primary operations: belief contraction, and belief expansion =-=[35]-=-. Additionally, the Belief Game Model (BGM) has been proposed by Konieczny [27]. Analogous to BNM, BGM consists of two base functions: choice function, which selects from every belief profile in E , a...

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...ees of the formulae and employ the conjunctive operator (that can have a reinforcement effect) over the obtained consistent belief bases for combination. The split-combination (S-C) merging operators =-=[41]-=- are another set of operators that effectively employ possibilistic information to merge belief bases. The basic idea of the S-C approach is that it initially splits the belief profile into two subpro...