Conjunctive Rule Research Articles

Combination of partially non-distinct beliefs: The cautious-adaptive rule

The combination rule is critical in an evidence based fusion process. The conjunctive rule is most common eventhough when the cognitive independence – distinctness – assumption is often questionable. A new combination rule is tested here in both discrete and continuous cases, accounting for a partial non-distinctness between evidences. It is based on ‘generalized discounting’, that we define for separable basic belief assignments (bbas) or basic belief densities (bbds), to be applied to the source correlation derived from the cautious rule. This correlation can be specified in both considered cases of consonant bbas/bbds (as proposed by Dubois et al.) and separable bbas/bbds (as proposed by Denœux). Then, the so-called ‘cautious-adaptive’ rule varies between the conjunctive rule and the cautious one, depending on the discounting level. In the Gaussian case with standard deviation σ, the evidence non-distinctness will be parameterized by a factor ϱ∈[0,1] dividing σ. It leads to the generalized discounting needed in the cautious-adaptive formulation.

SWRL: Rule Acquisition Using Ontology

SWRL: Rule Acquisition Using Ontology Nowadays rule-based systems are very common. The use of ontology-based systems is becoming ever more popular, especially in addition to the rule-based one. The most widely used ontology development platform is Protégé. Protégé provides a knowledge acquisition tool, but still the main issue of the ontology-based rule system is rule acquisition. This paper presents an approach to using SWRL rules Tab, a plug-in to Protégé, for rule acquisition. SWRL rules Tab transforms conjunctive rules to Jess rules in IF…THEN form.

A Model of Error Propagation in Conjunctive Decisions and its Application to Database Quality Management

This study centers on the accuracy dimension of information quality and models the relationship between input accuracy and output accuracy in a popular class of applications. These applications consist of dichotomous decisions that are implemented through conjunction of selected criteria. In particular, the model provides the tools for quantifying the effect of errors in each decision input on the accuracy of a decision. Application of the model is illustrated through the example of a residential real estate database, where users’ preferences are captured by conjunctive decision rules. This example demonstrates how the new model can be utilized for quantifying the aggregate damage that errors in different database attributes inflict on property selection decisions. Finally, this paper reports on an initial empirical validation of the proposed model through a series of Monte Carlo simulations. Numerical estimates of the model that have been developed through this inquiry can be useful for data and information quality assessments or policy-making purposes. Mainly, they can be integrated into cost-benefit analyses that assess alternative data accuracy enhancements or process and system designs.

Ontology-based curriculum content sequencing system with semantic rules

Curriculum content sequencing involves managing a learning route to help users achieve learning goals. A conventional learning route consists of ordered content and is primarily based on a single course material. In an e-learning system, amount of similar course contents are available. These contents are expected to mutually substitute for one another in creating flexible learning routes. Owing to inconsistency in materials editing and cataloging, composing contents based on multiple sources leads to sequencing complexity. Most significantly, most e-learning systems lack a sequencing mechanism for dominating content composition. This study utilizes a knowledge-intensive approach to create a general sequencing knowledge base. This approach includes two components: (1) ontology is used to represent abstract views of content sequencing and course materials and (2) added semantic rules are used to represent relationships between individuals. Following knowledge base creation, both practical curriculum sequences and course materials can be inserted as factual knowledge. A reliable knowledge base can be established using inference power. An example involving mathematics course in elementary school education is designed using Web Ontology Language (OWL) and Semantic Web Rule Language (SWRL). Experimental lessons demonstrate that semantic rules in conjunction with ontologies not only solve sequencing problems but also achieve a durable knowledge base and a reliable system.

Fallacies in probability judgments for conjunctions and disjunctions of everyday events

AbstractThe conjunction fallacy occurs when people judge a conjunction B‐and‐A as more probable than a constituent B, contrary to probability theory's ‘conjunction rule’ that a conjunction cannot be more probable than either constituent. Many studies have demonstrated this fallacy in people's reasoning about various experimental materials. Gigerenzer objects that from a ‘frequentist’ standpoint probability theory is not valid for these materials, and so failure to follow the conjunction rule is not a fallacy. This paper describes three experiments showing that the conjunction fallacy occurs as consistently for conjunctions where frequentist probability theory is valid (conjunctions of everyday weather events) as for other conjunctions. These experiments also demonstrate a reliable correlation between the occurrence of the conjunction fallacy and the disjunction fallacy (which arises when a disjunction B‐or‐A is judged less probable than a constituent B). This supports a probability theory + random variation account of probabilistic reasoning. Copyright © 2008 John Wiley & Sons, Ltd.

The conjunction fallacy and the many meanings of and

According to the conjunction rule, the probability of A and B cannot exceed the probability of either single event. This rule reads and in terms of the logical operator ∧, interpreting A and B as an intersection of two events. As linguists have long argued, in natural language “and” can convey a wide range of relationships between conjuncts such as temporal order (“I went to the store and bought some whisky”), causal relationships (“Smile and the world smiles with you”), and can indicate a collection of sets rather than their intersection (as in “He invited friends and colleagues to the party”). When “and” is used in word problems researching the conjunction fallacy, the conjunction rule, which assumes the logical operator ∧, therefore cannot be mechanically invoked as a norm. Across several studies, we used different methods of probing people’s understanding of and-conjunctions, and found evidence that many of those respondents who violated the conjunction rule in their probability or frequency judgments inferred a meaning of and that differs from the logical operator ∧. We argue that these findings have implications for whether judgments involving ambiguous and-conjunctions that violate the conjunction rule should be considered manifestations of fallacious reasoning or of reasonable pragmatic and semantic inferences.

Robust combination rules for evidence theory

Dempster’s rule of combination in evidence theory is a powerful tool for reasoning under uncertainty. Since Zadeh highlighted the counter-intuitive behaviour of Dempster’s rule, a plethora of alternative combination rules have been proposed. In this paper, we propose a general formulation for combination rules in evidence theory as a weighted sum of the conjunctive and disjunctive rules. Moreover, with the aim of automatically accounting for the reliability of sources of information, we propose a class of robust combination rules (RCR) in which the weights are a function of the conflict between two pieces of information. The interpretation given to the weight of conflict between two BPAs is an indicator of the relative reliability of the sources: if the conflict is low, then both sources are reliable, and if the conflict is high, then at least one source is unreliable. We show some interesting properties satisfied by the RCRs, such as positive belief reinforcement or the neutral impact of vacuous belief, and establish links with other classes of rules. The behaviour of the RCRs over non-exhaustive frames of discernment is also studied, as the RCRs implicitly perform a kind of automatic deconditioning through the simple use of the disjunctive operator. We focus our study on two special cases: (1) RCR-S, a rule with symmetric coefficients that is proved to be unique and (2) RCR-L, a rule with asymmetric coefficients based on a logarithmic function. Their behaviours are then compared to some classical combination rules proposed thus far in the literature, on a few examples, and on Monte Carlo simulations.

On the nature of the conjunction fallacy

In a seminal work, Tversky and Kahneman showed that in some contexts people tend to believe that a conjunction of events (e.g., Linda is a bank teller and is active in the feminist movement) is more likely to occur than one of the conjuncts (e.g., Linda is a bank teller). This belief violates the conjunction rule in probability theory. Tversky and Kahneman called this phenomenon the “conjunction fallacy”. Since the discovery of the phenomenon in 1983, researchers in psychology and philosophy have engaged in important controversies around the conjunction fallacy. The goal of this paper is to explore the most important of these controversies, namely, the controversy about the nature of the conjunction fallacy. Is the conjunction fallacy mainly due to a misunderstanding of the problem by participants (misunderstanding hypothesis) or is it mainly due to a genuine reasoning bias (reasoning bias hypothesis)? A substantial portion of research on the topic has been directed to test the misunderstanding hypothesis. I review this literature and argue that a stronger case can be made against the misunderstanding hypothesis. Thus, I indirectly provide support for the reasoning bias hypothesis.

Fusion of Vegetation Indices Using Continuous Belief Functions and Cautious-Adaptive Combination Rule

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The goal of this paper is to propose a methodology based on vegetation index fusion to provide an accurate estimation of the fraction of vegetation cover (fCover). Because of the partial and imprecise nature of remote-sensing data, we opt for the evidential framework that allows us to handle such kind of information. The defined fCover belief functions are continuous with the interval [0, 1] as a discernment space. Since the vegetation indices are not independent (e.g., perpendicular vegetation index and weighted difference vegetation index are linearly linked), we define a new combination rule called “cautious adaptive” to handle the partial “nondistinctness” between the sources (vegetation indices). In this rule, the “nondistinctness” is modeled by a factor <formula formulatype="inline"><tex>$\varrho$</tex> </formula> varying from zero (distinct sources) to one (totally correlated sources), and the fusion rule varies accordingly from the conjunctive rule to the cautious one. In terms of results, both in the cases of simulated data and actual data, we show the interest of the combination of two or three vegetation indices to improve either the accuracy of fCover estimation or its robustness. </para>

SOLUTION OF CONTACT PROBLEM FOR AN ARC CRACK USING HYPERSINGULAR INTEGRAL EQUATION

This paper investigates the contact problem for an arc crack, for example, under a remote compression. A hypersingular integral equation (HSIE) for curved cracks in plane elasticity is suggested. It is found that the direct usage of HSIE cannot solve the mentioned contact problem. For the contact problem, one must take necessary modifications for solving the HSIE. The main modified points are as follows. First, one should assume some portion along the crack under contact. The margin or the end of the contacted portion is determined by the vanishing normal contact stress at the margin point. In addition, it is found that a suggested quadrature rule in conjunction with the curve length method provides a very effective way to solve the HSIE. Finally, several numerical examples are given.

Modeling of Texture Evolution during Hot Forging of Alpha/Beta Titanium Alloys

Texture development during the subtransus hot forging of alpha/beta titanium alloys with an equiaxed-alpha microstructure was modeled using the Los Alamos polycrystalline plasticity (LApp) code and a \( {\left\langle {111} \right\rangle } \)pencil-glide polycrystalline plasticity code coupled with the finite-element-method (FEM) program DEFORM. The methodology treated the partitioning of the imposed strain between the alpha and beta phases, and thus enabled the prediction of the distinct deformation textures developed in the primary alpha and beta matrix during hot working. Two variant selection rules in conjunction with the beta deformation texture were also examined to establish a method for predicting the transformation texture of secondary alpha developed as a result of beta decomposition during cooldown following forging or heat treatment. The approach was validated via an industrial-scale trial comprising hot pancake forging of Ti-6Al-4V.

Emotions and decision rules in discrete choice experiments for valuing health care programmes for the elderly

The evaluation of health care programmes is commonly approached with stated preference methods such as contingent valuation or discrete choice experiments. These methods provide useful information for policy decisions involving health regulations and infrastructures for health care. However, econometric modelling of these data usually relies on a number of maintained assumptions, such as the use of the compensatory or random utility maximization rule. On the other hand, health policy issues can raise emotional concerns among individuals, which might induce other types of choice behaviour. In this paper we consider potential deviations from the general compensatory rule, and how these deviations might be explained by the emotional state of the subject. We utilized a mixture econometric model which allows for various potential decisions rules within the sample, such as the complete ignorance, conjunctive rule and satisfactory rules. The results show that deviations from the full linear compensatory decision rule are predominant, but they are significantly less observed for those subjects with a medium emotional state about the issue of caring for the health state of the elderly. The implication is that the emotional impact of health policy issues should be taken into account when making assumptions of individual choice behaviour in health valuation methods.

Evolution of a Negative-Rule Fuzzy Obstacle Avoidance Controller for an Autonomous Vehicle

A fuzzy obstacle avoidance controller is designed for an autonomous vehicle. The controller is given the capability for obstacle avoidance by using negative fuzzy rules in conjunction with traditional positive ones. Negative fuzzy rules prescribe actions to be avoided rather than performed. A rule base of positive rules is specified by an expert for directing the vehicle to the target in the absence of obstacles, while a rule base of negative rules is experimentally determined from expert operation of the vehicle in the presence of obstacles. The consequents of the negative-rule system are codified into a chromosome, and this chromosome is evolved using an evolutionary algorithm. The resulting fuzzy system has far fewer rules than would be necessary for an obstacle avoidance controller using purely positive rules, while in addition retaining greater interpretability.

Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence

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

Considerations in the Design and Analysis of an ASME Section VIII, Div. 2 Reactor Support Skirt

This paper describes the considerations employed in the finite element analysis of a relatively “short” support skirt on a hydrocarbon reactor vessel. The analysis is accomplished in accordance with ASME B&amp;PV Code, Section VIII, Division 2 alternate rules in conjunction with the guidelines outlined in WRC Bulletin 429. This provides a sound basis for the classification of the calculated stress intensities. The support skirt is capable of sustaining the deadweight load in addition to resisting the effects of thermal displacements, wind loadings, overturning moments from external piping loads on the attached hydrocarbon reactor vessel, and friction between the skirt base plate and concrete foundation. The displacement and thermal boundary conditions are well defined and discussed in detail. The effects of multiple scenarios for the displacement boundary conditions are examined. The skirt design also employs a hot-box arrangement whereby the primary mode of heat transfer is by radiation. A discussion of the two-part analysis is included and details the interaction between the heat transfer analysis and the subsequent structural analysis. The heat transfer finite element analysis is utilized to determine the temperatures throughout the bottom of the vessel shell and head, as well as the integrally attached support skirt. Of prime importance during the analysis is the axial thermal gradient present in the skirt from the base plate up to and slightly beyond the skirt-to-shell junction. While the geometry of the subject vessel and skirt is best described as axisymmetric, the imposed loadings are a mixture of axisymmetric and non-axisymmetric. This combination lends itself to the judicious selection and utilization of the harmonic finite element and properly chosen Fourier series representation of the applied loads. Comparison of the thermally induced axial stress gradient results from the FEA to those obtained by the closed form beam-on-elastic-foundation are also tendered and discussed. Finally, recommendations are included for the design and analysis of critical support skirts for large, heavy-wall vessels.

Reliable conjunctive use rules for sustainable irrigated agriculture and reservoir spill control

We develop optimal conjunctive use water management strategies that balance two potentially conflicting objectives: sustaining irrigated agriculture during droughts and minimizing unnecessary spills and resulting water losses from the reservoir during wet periods. Conjunctive use is specified by a linear operating rule, which determines the maximum surface water release as a function of initial reservoir storage. Optimal strategies are identified using multiobjective interannual optimization for sustainability and spill control, combined with gradient‐based annual profit maximization. Application to historical conditions in the irrigated system of the Yaqui Valley, Mexico, yields a Pareto curve of solutions illustrating the trade‐off between sustaining agriculture and minimizing spills and water losses. Minimal water losses are obtained by maximizing surface water use and limiting groundwater pumping, such that reservoir levels are kept sufficiently low. Maximum agricultural sustainability, on the other hand, results from increased groundwater use and keeping surface water reservoir levels high during wet periods. Selected optimal operating rules from the multiobjective optimization are tested over a large number of equally probable streamflow time series, generated with a stochastic time series model. In this manner, statistical properties, such as the mean sustainability and sustainability percentiles, are determined for each optimal rule. These statistical properties can be used to select rules for water management that are reliable over a wide range of streamflow conditions.

The Conjunction Effect and Clinical Judgment

Judgments made by clinicians may sometimes violate an axiom of probability theory, which dictates that neither the probability of event A, P(A) nor the probability of event B, P(B), can be less than the probability of the conjunction of events A and B, P(A [.intersection] B). In the following study, 40 psychologists and psychology interns estimated the probability of one of their clients obtaining (a) a particular result on the Personality Assessment Inventory (PAI; Morey, 1991), (b) a particular result on the Minnesota Multiphasic Personality Inventory–2 (MMPI–2; Butcher, Dahlstrom, Graham, Tellegen, & Kaemmer, 1989), and (c) the same specified results on both the PAI and MMPI–2. Violations of the conjunction rule occurred for 58% of the clinicians and were relatively large in size.

Estimating Heterogeneous EBA and Economic Screening Rule Choice Models

Consumer choice in surveys and in the marketplace reflects a complex process of screening and evaluating choice alternatives. Behavioral and economic models of choice processes are difficult to estimate when using stated and revealed preferences because the underlying process is latent. This paper introduces Bayesian methods for estimating two behavioral models that eliminate alternatives using specific attribute levels. The elimination by aspects theory postulates a sequential elimination of alternatives by attribute levels until a single one, the chosen alternative, remains. In the economic screening rule model, respondents screen out alternatives with certain attribute levels and then choose from the remaining alternatives, using a compensatory function of all the attributes. The economic screening rule model gives an economic justification as to why certain attributes are used to screen alternatives. A commercial conjoint study is used to illustrate the methods and assess their performance. In this data set, the economic screening rule model outperforms the EBA and other standard choice models and provides comparable results to an equivalent conjunctive screening rule model.

Constructing a 3D trunk model from two images

Trees stand for a key component in the natural environment, thus modeling realistic trees has received much attentions of researchers in computer graphics. However, most trees in computer graphics are generated according to some procedural rules in conjunction with some random perturbations, thus they are generally different from the real trees in the natural environment. In this paper, we propose a systematic approach to create a 3D trunk graphical model from two images so that the created trunk has a similar 3D trunk structure to the real one. In the proposed system, the trunk is first segmented from the image via an interactive segmentation tool and its skeleton is then extracted. Some points on the skeleton are selected and their context relations are established for representing the 2D trunk structure. A camera self-calibration algorithm appropriate for the two-view case is developed, and a minimum curvature constraint is employed to recover the 3D trunk skeleton from the established 2D trunk structure and the calibrated camera. The trunk is then modeled by a set of generalized cylinders around the recovered 3D trunk skeleton. A polygonal mesh representing the trunk is finally generated and a textured 3D trunk model is also produced by mapping the image onto the surface of the 3D trunk model. We have conducted some experiments and the results demonstrated that the proposed system can actually yield a visually plausible 3D trunk model which is similar to the real one in the image.

How Initiation Factors Maximize the Accuracy of tRNA Selection in Initiation of Bacterial Protein Synthesis

During initiation of bacterial protein synthesis, messenger RNA and fMet-tRNAfMet bind to the 30S ribosomal subunit together with initiation factors IF1, IF2, and IF3. Docking of the 30S preinitiation complex to the 50S ribosomal subunit results in a peptidyl-transfer competent 70S ribosome. Initiation with an elongator tRNA may lead to frameshift and an aberrant N-terminal sequence in the nascent protein. We show how the occurrence of initiation errors is minimized by (1) recognition of the formyl group by the synergistic action of IF2 and IF1, (2) uniform destabilization of the binding of all tRNAs to the 30S subunit by IF3, and (3) an optimal distance between the Shine-Dalgarno sequence and the initiator codon. We suggest why IF1 is essential for E. coli, discuss the role of the G-C base pairs in the anticodon stem of some tRNAs, and clarify gene expression changes with varying IF3 concentration in the living cell.