Development of Fuzzy Trigonometric Functions to Support Design and Manufacturing

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dc.contributor.advisorDr. Steven R. LeClair, Committee Memberen_US
dc.contributor.advisorDr. James C. Lester, Committee Memberen_US
dc.contributor.advisorDr. Yuan-Shin Lee, Committee Memberen_US
dc.contributor.advisorDr. Shu-Cherng Fang, Committee Memberen_US
dc.contributor.advisorDr. Robert E. Young, Committee Chairen_US
dc.contributor.authorRess, David Andressen_US
dc.date.accessioned2010-04-02T18:48:11Z
dc.date.available2010-04-02T18:48:11Z
dc.date.issued2010-03-11en_US
dc.degree.disciplineIndustrial Engineeringen_US
dc.degree.leveldissertationen_US
dc.degree.namePhDen_US
dc.description.abstractIt 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.en_US
dc.identifier.otheretd-03112010-104230en_US
dc.identifier.urihttp://www.lib.ncsu.edu/resolver/1840.16/4176
dc.rightsI hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dis sertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.en_US
dc.subjectfuzzy setsen_US
dc.subjectfuzzy trigonometric functionsen_US
dc.subjectfuzzy mathematicsen_US
dc.subjectfuzzy logicen_US
dc.titleDevelopment of Fuzzy Trigonometric Functions to Support Design and Manufacturingen_US

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