A Dynamic Programming Algorithm Based Clustering Model and Its Application to Interval Type-2 Fuzzy Large-Scale Group Decision-Making Problem
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This article focuses on employing the dynamic programming algorithm to solve the large-scale group decision-making problems, where the preference information takes the form of linguistic variables. Specifically, considering the linguistic variables cannot be directly computed, the interval type-2 fuzzy sets are employed to encode them. Then, new distance model and similarity model are respectively developed to measure the relationships between the interval type-2 fuzzy sets. After that, a dynamic programming algorithm-based clustering model is proposed to cluster the decision-makers from the overall perspective. Moreover, by taking both the cluster center and the group size into consideration, a new model is introduced to determine the weights of clusters and decision-makers, respectively. Finally, a centroid-based ranking method is developed to compare and rank the alternatives, and two illustrative experiments are provided to illustrate the effectiveness of the proposed method. Comparisons and discussions are also conducted to verify its superiority.Keywords:
Rank (graph theory)
Centroid
Similarity (geometry)
Group Decision Making
The program centroid takes as input a set of variables and a grouping variable, which is designated groupvar. Groupvar indicates into which group each case falls. As output, it generates a set of group centroids, which are means of each variable in varlist, and a set of distances, which indicate how far each case is from each centroid.
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Detecting and calculating accuracy of centroid of light spot is an important factor which affects the detecting accuracy of Hartmann wavefront sensor. The influence of window selection on centroid detection error is great. The Prieto's method of progressively reducing window size is analysed, and the template matching method is adopted according to the feature of the light spots of Hartmann sensor. With template matching, the accuracy of centroid detection is improved. The computer simulation of the centroid calculations of spot array shows that the centroid's rms error can be decreased by 53.7%. In addition, the template matching method avoides iterative centroid calculations and reduces computer time consumption.
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Abstract In constrained mixture experiments the centroid of a constraint region has traditionally been defined as the average of all extreme vertices of the region. This differs from the classical physics definition of a centroid as the center of mass (or volume) of a region. An algorithm for calculating a centroid based on the center of mass definition is discussed and illustrated with an example. This centroid calculation technique can be used to calculate centroids of various dimensional faces and edges of the constraint region as well as of the overall centroid. Results of the center-of-mass and averaged-extreme-vertices centroid computation techniques are compared using examples from the literature. KEY WORDS: Centroid calculationConstraint regionMixture experiments
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The program centroid takes as input a set of variables and a grouping variable, which is designated groupvar. Groupvar indicates into which group each case falls. As output, it generates a set of group centroids, which are means of each variable in varlist, and a set of distances, which indicate how far each case is from each centroid.
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Abstract In the design of gears, the most important task is to obtain centroids. Features of selection of centroids of round and non-round gears obtained by means of functions of harmonious form are considered, process of its formation is shown. Analytical dependencies are presented describing the geometry of the centroid of a round and non-round gearwheel. An example of an implementation of a mechanism based on dependencies describing the construction of a centroid is given.
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First moment spot centroid calculation in a sliding window with a threshold is proposed. The global centroid is computed in the image first. At this center a certain size window is used,and then the centroid again is calculated. Whether the difference value of the two adjacent centroids meets the given centroid convergence condition is estimated,if not the window slides to the new centroid position and the centroid again is computed until convergent. Compare the method with the traditional first moment centroid calculation method under different system conditions on the calculation accuracy,the simulation and experiment results show that the method is of higher calculation accuracy which can be used in the high precision adaptive optics system.
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In constrained mixture experiments the centroid of a constraint region has traditionally been defined as the average of all extreme vertices of the region. This differs from the classical physics definition of a centroid as the center of mass (or volume) of a region. An algorithm for calculating a centroid based on the center of mass definition is discussed and illustrated with an example. This centroid calculation technique can be used to calculate centroids of various dimensional faces and edges of the constraint region as well as of the overall centroid. Results of the center-of-mass and averaged-extreme-vertices centroid computation techniques are compared using examples from the literature.
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In order to simulate the adaptability and the fluctuation resistance ability of simulation inspection device and hanging ladder on ground, simulation inspection device and multi-grade centroid adjusting mechanism are designed in this paper. In the process of centroid adjusting, modification of the centroid position is transformed by means of mathematical model into a certain centroid adjusting mechanism, which is relative to displacement of Y Axis in calculating coordinate system and angle alternation between the adjustable centroid lever and the main rocker. The results show that the calculation is in good agreement with the analysis.
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The article considers the design of noncircular wheels, which serve as centroids in the design of gears. Centroids consist of congruent arcs of a given symmetric curve. The number of these arcs, that is the elements of the centroid, is determined by the type of gearing (internal or external). In external gearing, the number of elements of both centroids can be arbitrary, starting with one element. In the case of internal gearing, the number of elements of the internal centroid must be one less than the number of elements of the external centroid. If the number of elements is the same, then the centroids coincide. Rolling centroids one by one occurs in the absence of sliding. This is possible provided that the lengths of the arcs of the individual elements of both centroids are equal to each other. The construction of a centroid is carried out in a polar coordinate system. Both centroids are formed by rotating its element, that is the arc of the curve, at a given angle around the pole. The magnitude of the angle depends on the number of elements of the centroid. When rolling one centroid on the other, the pole of the moving centroid must describe the circle. In this case, the rolling of a moving centroid on a stationary one can be replaced by the rotational motion of both centroids around the fixed centers (poles). The point of contact of the centroids during their rotation is on the segment connecting the centers of rotation and which is called the center-to-center distance. This point for non-circular wheels when they rotate makes a certain movement along the specified segment, and for round wheels remains stationary. The length of the arc of an element of one centroid is determined by the magnitude of the central angle on which it rests. The same applies to the element of the second centroid. If the lengths of the arcs of the elements of the centroid are equal, then the values of the corresponding angles are not equal and are in a certain functional dependence. Finding this dependence is reduced to the integration of the expression obtained on the basis of the equality of the differentials of the arcs of the corresponding centroid elements. This expression may not be integrated for all curves from which the arcs of the original or leading centroid are formed. If the expression cannot be integrated, then the construction of the driven centroid must be carried out by numerical methods. The article considers a curve based on the hyperbolic cosine, for which the obtained expression is integrated. The parametric equations of the curves of which the arcs of both the leading and the driven centroids consist are given. It is shown that for a centroid with a given ratio of elements the intercenter distance is determined unambiguously. Centroid drawings with different number of elements for internal and external gearing are constructed.
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The heavy-ion experiments at the Heavy Ion Research Facility in Lanzhou (HIRFL) and the future High-Intensity Heavy-Ion Accelerator Facility (HIAF) in China drives the development of Monolithic Active Pixel Sensor (MAPS) for particle tracking detectors. To reduce the data volume from the MAPS based detectors, a centroid finder that can calculate the geometric centroid of the region of the energy deposition quickly has been designed. The centroid calculation is realized by distance screening among the coordinates of the pixels in the fired region. Performance study with the data from heavy-ion experiments in HIRFL proves that the centroid finder can accurately find the centroids and reduce the data volume from the MAPS by approximately one order of magnitude.
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