@article{reamer_ivy_vila-parrish_young_2015, title={Understanding the evolution of mathematics performance in primary education and the implications for STEM learning: A Markovian approach}, volume={47}, ISSN={["1873-7692"]}, DOI={10.1016/j.chb.2014.09.037}, abstractNote={National reports have documented deficiencies in the vertical alignment of mathematical learning in K-12 education. Many students fail to master requisite concepts before advancing to more complex ideas, leaving them ill-prepared to succeed in higher level Science, Technology, Engineering, and Mathematics (STEM) coursework. In this paper, we model elementary and middle school students’ performance in mathematics over time as a stochastic process to forecast their proficiency by the eighth grade. We conduct an extensive examination of tens of thousands of student records and extract useful information. We use this data to present a longitudinal analysis of student performance on the North Carolina End-of-Grade mathematics exam and use Markov chain models to probabilistically characterize the movement of students’ scores from one grade level to the next. This work is the first step in developing a framework to forecast individual students’ development of mathematical knowledge over time.}, journal={COMPUTERS IN HUMAN BEHAVIOR}, author={Reamer, Amy Craig and Ivy, Julie S. and Vila-Parrish, Anita R. and Young, Robert E.}, year={2015}, month={Jun}, pages={4–17} }
 @article{carrano_taylor_young_lemaster_saloni_2004, title={Fuzzy knowledge-based modeling and statistical regression in abrasive wood machining}, volume={54}, number={5}, journal={Forest Products Journal}, author={Carrano, A. L. and Taylor, J. B. and Young, R. E. and Lemaster, R. L. and Saloni, D. E.}, year={2004}, pages={66–72} }
 @article{loetamonphong_fang_young_2002, title={Multi-objective optimization problems with fuzzy relation equation constraints}, volume={127}, ISSN={["1872-6801"]}, DOI={10.1016/S0165-0114(01)00052-5}, abstractNote={This paper studies a new class of optimization problems which have multiple objective functions subject to a set of fuzzy relation equations. Since the feasible domain of such a problem is in general non-convex and the objective functions are not necessarily linear, traditional optimization methods may become ineffective and inefficient. Taking advantage of the special structure of the solution set, a reduction procedure is developed to simplify a given problem. Moreover, a genetic-based algorithm is proposed to find the “Pareto optimal solutions”. The major components of the proposed algorithm together with some encouraging test results are reported.}, number={2}, journal={FUZZY SETS AND SYSTEMS}, author={Loetamonphong, H and Fang, SC and Young, RE}, year={2002}, month={Apr}, pages={141–164} }
 @article{zukin_young_2001, title={Applying fuzzy logic and constraint networks to a problem of manufacturing flexibility}, volume={39}, ISSN={["0020-7543"]}, DOI={10.1080/00207540110053570}, abstractNote={The primary contribution is to present an application of fuzzy logic and constraint networks to a problem of manufacturing flexibility. The paper begins with a literature review showing the different approaches when measuring manufacturing flexibility. Next, it provides a brief review of fuzzy logic and its applications, explaining how it enhances the ability to model flexibility strategies. Then, the application is presented and its utility is demonstrated with an example from the production of printed circuit boards. Finally, the paper concludes with comments on how this model could be expanded to other applications.}, number={14}, journal={INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH}, author={Zukin, M and Young, RE}, year={2001}, month={Sep}, pages={3253–3273} }
 @article{ress_young_1998, title={A distributed fuzzy constraint satisfaction system with context-based reasoning}, volume={48}, ISSN={["1071-5819"]}, DOI={10.1006/ijhc.1997.0177}, abstractNote={This paper presents a fuzzy constraint satisfaction system which can be used in a distributive environment and, through an example, identifies contexts which exist within the constraint satisfaction system. The fuzzy constraint satisfaction system utilizes value propagation on constraints through the use of formal logic and theorem proving. The system has been designed to work in a distributive environment such that large problems can be broken down into smaller constraint networks for easier processing. Context-based reasoning is identified both within and among constraint networks. The paper begins with the motivation behind this research, followed by a description of the fuzzy constraint satisfaction system FuzCon. It concludes by identifying three mappings of the context-based reasoningistoperator to fuzzy constraints and by showing an example of designing a printed wiring board.}, number={3}, journal={INTERNATIONAL JOURNAL OF HUMAN-COMPUTER STUDIES}, author={Ress, DA and Young, RE}, year={1998}, month={Mar}, pages={393–407} }
 @article{giachetti_young_roggatz_eversheim_perrone_1997, title={A methodology for the reduction of imprecision in the engineering process}, volume={100}, ISSN={["0377-2217"]}, DOI={10.1016/S0377-2217(96)00290-1}, abstractNote={Engineering design is characterized by a high level of imprecision, vague parameters, and ill-defined relationships. In design, imprecision reduction must occur to arrive at a final product specification. Few design systems exist for adequately representing design imprecision, and formally reducing it to precise values. Fuzzy set theory has considerable potential for addressing the imprecision in design. However, it lacks a formal methodology for system development and operation. One repercussion of this is that imprecision reduction is, at present, implemented in a relatively ad-hoc manner. The main contribution of this paper is to introduce a methodology called precision convergence for making the transition from imprecise goals and requirements to the precise specifications needed to manufacture the product. A hierarchy of fuzzy constraint networks is presented along with a methodology for creating transitional links between different levels of the hierarchy. The solution methodology is illustrated with an example within which an imprecision reduction of 98% is achieved in only three stages of the design process. The imprecision reduction is measured using the coefficient of imprecision, a new measure introduced to quantify imprecision.}, number={2}, journal={EUROPEAN JOURNAL OF OPERATIONAL RESEARCH}, author={Giachetti, RE and Young, RE and Roggatz, A and Eversheim, W and Perrone, G}, year={1997}, month={Jul}, pages={277–292} }
 @article{giachetti_young_1997, title={A parametric representation of fuzzy numbers and their arithmetic operators}, volume={91}, ISSN={["0165-0114"]}, DOI={10.1016/S0165-0114(97)00140-1}, abstractNote={Direct implementation of extended arithmetic operators on fuzzy numbers is computationally complex. Implementation of the extension principle is equivalent to solving a nonlinear programming problem. To overcome this difficulty many applications limit the membership functions to certain shapes, usually either triangular fuzzy numbers (TFN) or trapezoidal fuzzy numbers (TrFN). Then calculation of the extended operators can be performed on the parameters defining the fuzzy numbers, thus making the calculations trivial. Unfortunately the TFN shape is not closed under multiplication and division. The result of these operators is a polynomial membership function and the triangular shape only approximates the actual result. The linear approximation can be quite poor and may lead to incorrect results when used in engineering applications. We analyze this problem and propose six parameters which define parameterized fuzzy numbers (PFN), of which TFNs are a special case. We provide the methods for performing fuzzy arithmetic and show that the PFN representation is closed under the arithmetic operations. The new representation in conjunction with the arithmetic operators obeys many of the same arithmetic properties as TFNs. The new method has better accuracy and similar computational speed to using TFNs and appears to have benefits when used in engineering applications.}, number={2}, journal={FUZZY SETS AND SYSTEMS}, author={Giachetti, RE and Young, RE}, year={1997}, month={Oct}, pages={185–202} }
 @article{giachetti_young_1997, title={Analysis of the error in the standard approximation used for multiplication of triangular and trapezoidal fuzzy numbers and the development of a new approximation}, volume={91}, ISSN={["0165-0114"]}, DOI={10.1016/S0165-0114(96)00118-2}, abstractNote={Triangular and trapezoidal fuzzy numbers are commonly used in many applications. It is well known that the operators used for the non-linear operations such as multiplication, division, and inverse are approximations to the actual operators. It is also commonly assumed that the error introduced by the approximations is small and acceptable. This paper examines the error of approximation for repeated use of the multiplication operand and shows it can be sufficiently large in simple circumstances to produce erroneous results. The computational complexity of the multiplication operation is analyzed and shown to be sufficiently complex that a computationally simpler approximation is needed. As a consequence, the error produced by the approximation for the multiplication operation is analyzed and a new approximation developed that is accurate for a large range of problems. An error expression is developed for the new approximation that can be used to determine when it is producing unacceptable results.}, number={1}, journal={FUZZY SETS AND SYSTEMS}, author={Giachetti, RE and Young, RE}, year={1997}, month={Oct}, pages={1–13} }