Generalized Rough Sets (Preclusivity Fuzzy-Intuitionistic (BZ) Lattices)

The standard Pawlak approach to rough set theory, as an approximation space consisting of a universe U and an equivalence (indiscernibility) relation R U x U, can be equivalently described by the induced preclusivity ("discernibility") relation U x U \ R, which is irreflexive and symmetric.We generalize the notion of approximation space as a pair consisting of a universe U and a discernibility or preclusivity (irreflexive and symmetric) relation, not necessarily induced from an equivalence relation. In this case the "elementary" sets are not mutually disjoint, but all the theory of generalized rough sets can be developed in analogy with the standard Pawlak approach. On the power set of the universe, the algebraic structure of the quasi fuzzy-intuitionistic "classical" (BZ) lattice is introduced and the sets of all "closed" and of all "open" definable sets with the associated complete (in general nondistributive) ortholattice structures are singled out.The rough approximation of any fixed subset of the universe is the pair consisting of the best "open" approximation from the bottom and the best "closed" approximation from the top. The properties of this generalized rough approximation mapping are studied in the context of quasi-BZ lattice structures of "closed-open" ordered pairs (the "algebraic logic" of generalized rough set theory), comparing the results with the standard Pawlak approach. A particular weak form of rough representation is also studied.     

On the discriminability of stimulus duration.

The performance of pigeons trained to detect differences in the duration of stimuli was analysed using a matching model of signal detection. Two white stimuli, S1 and S2, differing in duration, were arranged with equal probability on the center key of a three-key chamber. S1 was systematically varied from 5 seconds to 25 seconds while S2 remained constant at 30 seconds. On completion of the center-key stimulus, a peck on the center key turned on the two red side keys. A left-key response was "correct" when S1 had been in effect on the center key and a right-key response was "correct" on S2 trials. A correct response produced a 3-second magazine light accompanied intermittently by food. Incorrect responses produced 3-second blackouts. Detection performance was measured under two procedures. In the first, the obtained reinforcement ratio was uncontrolled by allowing the number of food reinforcements obtained for correct left- and right-key responses to vary as the stimuli were changed. In the second procedure, the presentation of food reinforcement was controlled by holding the obtained reinforcement ratio constant. Discriminability changed as a function of stimulus differences under both procedures. No such trend was found in response bias.     

Covariance structure analysis in several populations

This paper is concerned with the study of covariance structural models in several populations. Estimation theory of the parameters that are subject to general functional restraints is developed based on the generalized least squares approach. Asymptotic properties of the constrained estimator are studied; and asymptotic chi-square tests are presented to evaluate appropriate model comparisons. The method of multipliers and the standard reparametrization technique are discussed in obtaining the estimates. The methodology is demonstrated by a set of real data.Computer facilities were provided by the Computer Services Center, The Chinese University of Hong Kong. The authors are indebted to several anonymous reviewers for suggestions for improvement of this paper.     

Stimulus discriminability in free-operant and discrete-trial detection procedures.

Six pigeons were trained to discriminate different light intensities in four experimental procedures. Experiment 1 compared stimulus discriminability in a yes-no signal-detection task with discriminability measures obtained from two free-operant procedures. Discriminability estimates were significantly lower in the detection procedure. Experiment 2 showed this lowered discriminability to be a function of the delay between stimulus presentation and the availability of the choice-response keys in the standard detection task. In addition, reinforcement sensitivity was lowest when correct choice responses were intermittently, rather than continuously, reinforced.     

Stopping rules for multi-category computerized classification testing

Computerized classification testing (CCT) aims to classify persons into one of two or more possible categories to make decisions such as mastery/non-mastery or meet most/meet all/exceed. A defining feature of CCT is its stopping criterion: the test terminates when there is enough confidence to make a decision. There is abundant research on CCT with a single cut-off, and two common stopping criteria are the sequential probability ratio test (SPRT) statistic and the generalized likelihood ratio statistic (GLR). However, there is a relative scarcity of research extending the SPRT to the multi-hypothesis case for when there is more than one cut-off. In this paper, we propose a new multi-category GLR (mGLR) statistic as well as a stochastically curtailed version of the CCT with three or more categories. A simulation study was conducted to show that the mGLR statistic outperformed the existing stopping rules by generating shorter average test length without sacrificing classification accuracy. Results also revealed that the stochastically curtailed mGLR successfully increased test efficiency in certain testing conditions.     

Information Processing and Decision-Making in Pathological Worriers and their Potential Role in Mechanisms of Generalized Anxiety Disorder

Systematic information processing and decision-making under uncertainty are key constructs of new conceptions explaining the severity of pathological worry. The current study attempted to analyze their usefulness in subclinical and clinical groups. In the first phase of the study (N = 251) participants were examined with the Penn State Worry Questionnaire (PSWQ), a GP consultationrelated survey, and a screening survey for generalized anxiety disorder (GAD). In the second phase (N = 220), the State-Trait Anxiety Inventory, the PSWQ, and tasks measuring systematic information processing (SIP) versus heuristic reasoning (HR) were applied. In the third phase (N = 60), GAD (n = 30) and healthy control (n = 30) groups were examined with the above methods and the Iowa Gambling Task (IGT). In the low risk group, a relationship between mood and the representativeness heuristic (ρ = 0.50), as well as anchoring and adjustment heuristic (anxiety-related stimuli) was found (ρ = −0.53). In the GAD group, significant correlations between the PSWQ score, the IGT loss avoidance score (ρ = 0.40), and total IGT score (ρ = 0.48) were found. The results did not confirm a particular usefulness of the systematic/heuristic information processing construct in subclinical and clinical groups. Theory-consistent results were rather found in the nonclinical groups. Nevertheless, the data revealed some interesting findings supporting potential explanatory power of some theoretical models.     

Treating a Chronically Depressed Adolescent Female Using the Cognitive Behavioral Analysis System of Psychotherapy: A Case Study

A case is presented of an adolescent female with double depression who was treated using the Cognitive Behavioral Analysis System of Psychotherapy (CBASP). CBASP is designed to teach a social problem-solving procedure called Situational Analysis (SA). Generalized treatment effects were measured through monitoring of diagnostic status, two administrations of the Minnesota Multiphasic Personality Inventory-Adolescent, weekly administrations of the Child Depression Inventory, and acquisition performance ratings on the SA task. The results showed that CBASP appeared to be an effective treatment. The double depressive disorder remitted, and the patient learned to identify behavioral consequences as well as target and attain her interpersonal goals. CBASP can be effective for adolescents, although modifications of the adult form of the therapy may be necessary.     

The Beck Anxiety Inventory in Older Adults With Generalized Anxiety Disorder

The authors investigated the psychometric properties of the Beck Anxiety Inventory (BAI) in a sample of 75 older generalized anxiety disorder (GAD) patients and a comparison group of 32 older adults without significant psychopathology. Internal consistency was above .80, and the BAI showed evidence of convergent validity in both groups. Evidence for discriminant validity with respect to measures of depression was weaker. Two items, fearing the worst and nervousness, correctly distinguished 86.5% of patients with GAD and 93.8% of the normal controls. Medical comorbidity was associated with somatic but not cognitive anxiety symptoms in the normal older sample. Overall, results indicate the limitations of the BAI in assessing anxiety symptoms in older adults and suggest the need for use of an instrument focusing on cognitive aspects of anxiety.     

Effectiveness of the Hamilton Anxiety Rating Scale with Older Generalized Anxiety Disorder Patients

To expand the collection of instruments available for assessment of anxiety in the elderly, this report examined the original and revised Hamilton anxiety scales in a sample of 50 older adults diagnosed with Generalized Anxiety Disorder (GAD) and 93 normal community participants (ages 55–82). Although the revised anxiety scale had better discriminant validity (lower correlation with the revised Hamilton depression scale) than the original anxiety and depression scales, a considerable amount of shared variance still existed (41% shared variance, GAD sample alone; 17% control sample alone; 74% shared variance, both samples combined). Near-perfect group classification was possible using 7 items from the original anxiety scale and 10 items from the revised anxiety scale. Results are discussed in light of their implications for use of the Hamilton anxiety rating scale with older anxiety-disordered patients.     

Asymptotic Standard Errors of Generalized Partial Credit Model True Score Equating Using Characteristic Curve Methods

In this study, the delta method was applied to estimate the standard errors of the true score equating when using the characteristic curve methods with the generalized partial credit model in test equating under the context of the common-item nonequivalent groups equating design. Simulation studies were further conducted to compare the performance of the delta method with that of the bootstrap method and the multiple imputation method. The results indicated that the standard errors produced by the delta method were very close to the criterion empirical standard errors as well as those yielded by the bootstrap method and the multiple imputation method under all the manipulated conditions.