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Researchers should hear saturated factor correlations and entirely free measurement error variances as shouting THEORY IMPRECISION regarding the latent-level causal structure.
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This inclines the researcher toward theory-imprecision merely to reduce the possibility that the data will speak against their theory.
Making a theory imprecise does indeed make it more difficult for the data to detect problems in the theory – but that same imprecision makes it easier for the discipline to disregard the researcher's work!
Since Aristotle often calls attention to the imprecision of ethical theory (see e.g. 1104a1 7), it comes as a surprise to many readers of the Ethics that he begins Book VI with the admission that his earlier statements about the mean need supplementation because they are not yet clear (saphes).
Model selection was guided primarily by theory and biological plausibility, parameter imprecision obtained from non-parametric bootstrap 39 (100 replicates during model development and 500 replicates for the final model) and prediction-corrected visual predictive checks (pcVPCs) 40.
Zadeh [45] proposed the concept of fuzzy set theory and successfully used to handle imprecision (or uncertainty) in decision making problems, to solve the ambiguity and vagueness in information from human judgements and preferences.
Fuzzy set theory is developed for handing uncertainty, imprecision and complexity in the real world; for example, we say "driving speed is high" wherein speed is a fuzzy variable and high is a fuzzy set, which uses the membership function to indicate the degree of a element belonging to the set (words in Italics to denote fuzzy variables or fuzzy sets).
The increasing number of successful applications of fuzzy logic and fuzzy sets theory to dealing with the uncertainty, imprecision and subjectivity inherent to environmental quality assessments, and the recent development of new procedures based on fuzzy logic for the design of environmental quality indexes open new ways to carry out more rigorous and realistic estimations of soil quality.
Random Set Theory is used to cope with both imprecision and dissonance affecting the available information.
Fuzzy goal programming utilizes fuzzy set theory to deal with a level of imprecision in the goal programming model.
The problem of frequent imprecision can be solved by probability theory, while the problem of linguistic imprecision can be tackled by possibility theory.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com