Direct and indirect scaling of membership functions of probability phrases

A crucial issue in the empirical measurement of membership functions is whether the degree of fuzziness is invariant under different scaling procedures. In this paper a direct and an indirect procedure, magnitude estimation and graded pair-comparison, are compared in the context of establishing membership functions for probability phrases such as , and so forth. Analyses at the level of individual respondents indicate that: (a) membership functions are stable over time; (b) functions for each phrase differ substantially over people; (c) the two procedures yield similarly shaped functions for a given person-phrase combination; (d) the functions from the two procedures differ systematically, in that those obtained directly dominate, or indicate greater fuzziness than do those obtained indirectly; and (e) where the two differ the indirectly obtained function may be the more accurate one. A secondary purpose of the paper is to evaluate the effects of the modifiers and . has a general intensifying effect that is described by Zadeh's concentration model for 7 subjects and by a shift model for no one. The effects of are unsystematic and not described by any available model

A study of uncertainty expressions in Australian accounting and auditing standards

Australian auditors' interpretation of selected key uncertainty expressions, such as virtual certainty, expected, reasonable assurance and possible, contained in Australian accounting and auditing standards is examined. Auditors demonstrated a reasonably high degree of variability in the interpretation of uncertainty expressions. In view of the proliferation of uncertainty expressions within international and Australian accounting and auditing standards, this lack of consistency in interpretation of uncertainty expressions raises some serious concerns. Compared with the less experienced auditors, the more experienced auditors demonstrated greater variability in their interpretations of uncertainty expressions. Contrary to expectations, the study did not find any difference in judgments between auditors in Big 5 and non-Big 5 firms

The framing of risks and the communication of subjective probabilities for victimizations

What does 'likely' mean, when respondents estimate the risk to become a victim of crime? We apply prospect theory to derive hypotheses of framing-effects on perceptions of risk. Victimization risks can either be interpreted as gains (?being spared of offences?) or as losses (?becoming a victim of crime?). Because losses are perceived as more severe, respondents will state lower subjective victimization probabilities in the loss-frame, compared to the gain-frame. We demonstrate such a framing-effect with data from an experimental survey. Furthermore, we show that the meaning of vague quantifiers varies with the frequency and the severity of the event. Respondents assign to the same vague quantifiers (e.g. 'unlikely') higher likelihoods in terms of percentages for frequent and for less severe events than for infrequent and for severe events. Because respondents do not use vague quantifiers consistently, it is problematic to compare subjective risks for different victimizations