Uncertainty vagueness

This book presents systematic and comprehensive modeling of uncertainty, vagueness, or imprecision through fuzzy principles and procedures for problem solving in engineering. There are several chapters for introduction to fuzzy logic... 

The typical risk properties are random and epistemic uncertainties (epistemic uncertainties = vagueness). If we want to manage risk, we must identify, analyse, assess it and after this to decide what we can do, in dependence on our possibihties—knowledge, staff, technical means and finance sources. For this, we must use a lot of different methods, tools and techniques and also principles of good practice (good engineering practice). 

Conventional computers initially were not conceived to handle vague data. Human reasoning, however, uses vague information and uncertainty to come to a decision. In the mid-1960 this discrepancy led to the conception of fuzzy theory [14]. In fuzzy logic the strict scheme of Boolean logic, which has only two statements true and false), is extended to handle information about partial truth, i.e., truth values between "absolutely true" and absolutely false". It thus gives a mathematical representation of uncertainty and vagueness and provides a tool to treat them. 

The problem is defined during process development as information becomes available and decisions are made. Initially, the definition is limited, vague, and brief and economic analysis involves a high level of uncertainty. As the project evolves, the definition becomes more complete, more highly specific, and lengthier. At the same time, the economic assessment tends to exhibit less uncertainty. 

Manufacturers often feel compelled to be very vague about how well a battery will perform because of the uncertainty about how the batteiy will be used. Technology manufacturers invest heavily m marketing research before deciding what type of batteiy to provide with a new product. Sometimes it is a clear-cut decision other times there is no one best choice for all potential users. Perhaps the most important issue is whether a product will be used continuously or intermittently. For instance, selecting a battery for a DVD player is much easier than a cellular phone. The DVD player is likely to be used continuously by... 

There are no indications, or only vague ones, of the size of the various battery separator markets in the literature 131. A rough estimate can be deduced from the sales figures for battery systems by a rule of thumb the sales value of separators is roughly 2-5% of the sales for the battery producers. Even the data for battery markets are not uniformly gathered, however, and contain considerable uncertainties. 

The rest of the atom is sparsely populated but also vibrant and dynamic. The ghostly electrons are arranged in vague clouds and have no clearly defined position. Heisenberg s Uncertainty Principle (1927) tells us that we can t pin-point their positions. Instead, we have to talk in terms of the probability of there being electrons of a certain energy in certain positions (or orbits) around the nucleus at certain times. 

However, a main defect of the Unified Environmental Code of 1998 and its accompanying explanations remains. Left unanswered is what degree of certainty (or uncertainty) is required to trigger actions based on the vague PP. Another serious shortcoming of the Swedish legislation is that it makes anyone who undertakes any action that may have a potential impact on health or the environment responsible for implementation of the PP. 

QUALITATIVE COMMENTS (with 150 mg) At most, there was a bare threshold over the course of the afternoon. A vague unreal feeling, as if I had not had quite enough sleep last night. By late afternoon, even this had disappeared and 1 was left with an uncertainty that anything at all had occurred. ... 

Estimates of the level of anthropogenic impact on global climate contained in IPCC documents are vague. As Reilly et al. (2001) justly noted, the reason for this is the absence of quantitative estimates of the uncertainty of the results obtained (e.g., the supposed increase of SAT within 1.5°C-4.5°C). What is worse, trying to make decisions fit with ecological policy (e.g., to the Kyoto Protocol)... 

All these uncertainties about the uses to be made of, and the demands to be placed on, an infrastructure exacerbate the problems of designing for dependability. Design decision-making often has to be based on very vague evidence and statistics, and very suspect assumptions, much more than is the case with systems that are designed for an identified owner and set of users. 

Fuzzy methods are suitable for approximate reasoning (Isukapalli Georgopoulos, 2001), especially for analysis of systems where uncertainty arises due to vagueness or fuzziness or... 

Consequently, risk managers, as transmitters of information to the public, want to avoid vagueness and press for precise statements (without uncertainty), as otherwise they must decide and act under uncertainty. One task of the exposure assessment step is to articulate the main arguments for restrictions with respect to the interpretation together and propose what could and should be done to enhance the scientific basis for a refined analysis that would result in less uncertainty. 

The quotient NdN2 is the ratio of the probabilities of finding the electron in the infinitesimally small volume elements dv around points 1 and 2. For example, if the value of the ratio N,/N2 is 100, the electron is 100 times more likely to be found at position 1 than at position 2. The model gives no information concerning when the electron will be at either position or how it moves between the positions. This vagueness is consistent with the concept of the Heisenberg uncertainty principle. 

The rough set concept is a mathematical approach to deal with data imprecision, fuzziness, vagueness, and uncertainty. The theory of rough sets is complex mathematically and often considered to be too obscure for widespread implementation in engineering applications. The purpose of this section is to present rough sets as a MOO method that can be easily understood and implemented. The objective of RSM is to assess... 

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