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Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 18

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Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 18 studies the combination of various methods of designing for reliability, availability, maintainability and safety, as well as the latest techniques in probability and possibility modelling, mathematical algorithmic modelling, evolutionary algorithmic modelling, symbolic logic modelling, artificial intelligence modelling, and object-oriented computer modelling, in a logically structured approach to determining the integrity of engineering design. . | 3.3 Analytic Development of Reliability and Performance in Engineering Design 153 These modifiers change the shape of a fuzzy set using mathematical operations on each point of the set. In the above table the variable y represents each membership value in the fuzzy set and A represents the entire fuzzy set i.e. the term very A applies the very modifier to the entire set where the modifier descriptiony 2 squares each membership value . When a modifier is used in descriptive expressions it can be used in upper or lower case i.e. NOT or not . c Uncertainty Uncertainty occurs when one is not absolutely sure about an element of information. The degree of uncertainty is usually represented by a crisp numerical value on a scale from 0 to 1 where a certainty factor of 1 indicates that the assessment of a particular fact is very certain that the fact is true and a certainty factor of 0 indicates that the assessment is very uncertain that the fact is true. A fact is composed of two parts the statement of the fact in non-fuzzy reasoning and its certainty factor. Only facts have associated certainty factors. In general a factual statement takes the following form fact CF certainty factor The CF acts as the delimiter between the fact and the numerical certainty factor and the brackets indicate an optional part of the statement. For example pressure high CF 0.8 is a fact that indicates a particular system attribute of pressure will be high with a certainty of 0.8. However if the certainty factor is omitted as in a non-fuzzy fact pressure high then the assumption is that the pressure will be high with a certainty of 1 or 100 . The term high in itself is fuzzy and relates to a fuzzy set. The fuzzy term high also has a certainty qualification through its certainty factor. Thus uncertainty and fuzziness can occur simultaneously. d Fuzzy Inference Expression of fuzzy knowledge is primarily through the use of fuzzy rules. However there is no unique type of fuzzy knowledge nor is there