Fuzzy qualitative trigonometry

AbstractThis paper presents a fuzzy qualitative representation of conventional trigonometry with the goal of bridging the gap between symbolic cognitive functions and numerical sensing & control tasks in the domain of physical systems, especially in intelligent robotics. Fuzzy qualitative coordinates are defined by replacing a unit circle with a fuzzy qualitative circle; a Cartesian translation and orientation are defined by their normalized fuzzy partitions. Conventional trigonometric functions, rules and the extensions to triangles in Euclidean space are converted into their counterparts in fuzzy qualitative coordinates using fuzzy logic and qualitative reasoning techniques. This approach provides a promising representation transformation interface to analyze general trigonometry-related physical systems from an artificial intelligence perspective.Fuzzy qualitative trigonometry has been implemented as a MATLAB toolbox named XTRIG in terms of 4-tuple fuzzy numbers. Examples are given throughout the paper to demonstrate the characteristics of fuzzy qualitative trigonometry. One of the examples focuses on robot kinematics and also explains how contributions could be made by fuzzy qualitative trigonometry to the intelligent connection of low-level sensing & control tasks to high-level cognitive tasks

Qualitative kinematics of planar robots: Intelligent connection

AbstractThis paper proposes a qualitative representation for robot kinematics in order to close the gap, raised by the perception–action problem, with a focus on intelligent connection of qualitative states to their corresponding numeric data in a robotic system. First, qualitative geometric primitives are introduced by combining a qualitative orientation component and qualitative translation component using normalisation techniques. A position in Cartesian space can be mathematically described by the scalable primitives. Secondly, qualitative robot kinematics of an n-link planar robot is derived in terms of the qualitative geometry primitives. Finally, it shows how to connect quantitativeness and qualitativeness of a robotic system. On the one hand, the integration of normalisation and domain knowledge generates normalised labels to introduce the meaningful parameters into the proposed representation. On the other hand, the normalised labels of this representation can be converted to a quantitative description using aggregation operators, whose numeric outputs can be used to generate desired trajectories based on mature interpolation techniques

Guide to the Richard C. Heyser Collection

This guide describes the organization and scope of the Richard C. Heyser archival collection, housed within the College Archives & Special Collections at Columbia College Chicago. Richard C. Heyser (1931-1987) was a pioneer in research relating to audio and acoustic measurement techniques

Some applications of possibilistic mean value, variance, covariance and correlation

In 2001 we introduced the notions of possibilistic mean value and variance of fuzzy numbers. In this paper we list some works that use these notions. We shall mention some application areas as wel

Variability reduction in stencil printing of solder paste for surface mount technology

Competition in stencil printing to produce excellence in the finished product is intense. Faults in the printing process are a major source of board failure. Studies have shown that over 63% of defects identified after reDow originated from the solder paste printing ( A. Lotfi ,1998 ) . However. understanding these failures are a challenging problem as the printing process has a large number of non linearly dependent variables such as factors relating to paste (formulation. viscosity), the environment (temperature, humidity) and machine parameter (alignment, pressure and speed of squeegee, blade hardness etc). The process engineer is challenged to widen the process window so that future modifications to the process, such as the addition of a new component, can be achieved with little. if any, change in materials or process parameters. This thesis reports the effect of temperature and humidity variation from the manufacturing environment on the solder paste consistency and optimization of the essential parameters of squeegee pressure, squeegee speed. separation speed and print gap. The outcome of variation in temperature and humidity to the solder paste viscosity were analyzed and tests were done to determine the characteristic of the solder paste. The tests results indicate that the temperature and humidity has an impact on the solder paste printability. thus some attempts must be taken to control these variables. For parameter optimization. the analysis was carried out using statistical optimization. The main aim was to combine these parameters with three main pitch categories to produce the acceptable print formation. The results showed that. the ideal print result requires optimum statistical combinations of four parameters essentially related to a particular pitch. It is also shown that there is a diversity and contrasts of the combination of the parameters for each category of pitch. Detailed explanations as to the phenomenon are outlined in the thesis

A survey of qualitative spatial representations

Representation and reasoning with qualitative spatial relations is an important problem in artificial intelligence and has wide applications in the fields of geographic information system, computer vision, autonomous robot navigation, natural language understanding, spatial databases and so on. The reasons for this interest in using qualitative spatial relations include cognitive comprehensibility, efficiency and computational facility. This paper summarizes progress in qualitative spatial representation by describing key calculi representing different types of spatial relationships. The paper concludes with a discussion of current research and glimpse of future work