Development of Fuzzy Trigonometric Functions to Support Design and Manufacturing
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Date
2010-03-11
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Abstract
It is a well established fact that design undergoes stages from imprecision to precision. In the early design stages, fuzzy logic is a natural tool for modeling since it is by definition an imprecise representation. The mathematics behind fuzzy numbers have been well developed and defined in literature; yet, very little research exists in the form of fuzzy trigonometric functions. Two design problems are presented to support the motivation behind this research followed by a review of fuzzy set theory. Several approaches for mapping Y = cos(X) into the fuzzy realm are then discussed followed by the development of special purpose fuzzy trigonometric functions and fuzzy inverse trigonometric functions which are computationally simple and easy to implement. With these functions, 8 forward and 6 inverse trigonometric identities are shown to exist in the fuzzy realm. The proposal concludes by examining three engineering problems. The first problem involves the design of a fuzzy truss bridge with fuzzy forces. The second problem analyzes fuzzy forces on a block positioned on an inclined plane. The last example utilizes the fuzzy inverse trigonometric functions to calculate fuzzy bond angles within a chemical compound.
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Keywords
fuzzy sets, fuzzy trigonometric functions, fuzzy mathematics, fuzzy logic
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Degree
PhD
Discipline
Industrial Engineering
