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When some existing intuitionistic fuzzy aggregation operators are used to aggregate certain special intuitionistic fuzzy values, the results are counter-intuitive. We first introduce two intuitionistic fuzzy aggregation operators and a method for comparing intuitionistic fuzzy values. Then some examples are given to illustrate the intuitionistic fuzzy aggregation operators which lead to some counter-intuitive results. We also propose new intuitionistic fuzzy aggregation operators based on ε-amended, and investigate the influence the values of e on aggregating results. A decision making method based on ε-amended intuitionistic fuzzy aggregation operators is constructed. Finally, a practical example is given to compare the aggregating results that aggregated by the existing intuitionistic fuzzy aggregation operators and ε-amended intuitionistic fuzzy aggregation operators respectively, which proves that ε-amended intuitionistic fuzzy aggregation operators can amend counter-intuitive results. And ε-amended intuitionistic fuzzy aggregation operators can also extend the range of use of the existing intuitionistic fuzzy aggregation operators. [ABSTRACT FROM AUTHOR]

Based on OpenGL, this paper presented a local 3D scene reconstruction from the frame buffers (including color buffer and depth buffer) after 3D scene rendered. According to projection principles and depth buffer characteristics, it discussed an inverse prooection processing and obtained theoretically a 3D vertex reconstruction method. As a result, it transformed a l valid pixels within frame buffers and generated a 3D vertex set which was a point cloudy model in the camera space in the conducted experiments. Obviously, this cloudy model was a kind of a sample of the original 3D scene in current camera system and named as virtual vision model(VVM). Secondly, it analyzed the point-wise precision of VVM detailed. The results of experiments show that VVM appears very high relative accuracy to the original 3D scene. Above all, the reconstruction method appears natural multi-resolution feature with respect to the resolution of frame buffers and supports scene simplification and streaming transmission. On the other hand, this method is capable of abstracting VVM real-time from the common 3D software easily without any details of 3D scene known previously, which provides a new approach acquiring 3D data efficiently. [ABSTRACT FROM AUTHOR]

The virtual 3D space is a digital one of real world and the human stereo visional space is a 3D reconstruction of the real world or virtual scene through human visional system. Traditionally, human views the environment around himself directly and the geometric relationship between the human stereo visional space and the real world exists undoubtedly. How about the relations of stereo visional space to the virtual 3D space are？ According to the principle of binocular disparity, a geometric model of stereo vision is established for the virtual 3D scene and the corresponding visional 3D model is constructed too. And the screen disparity and retina disparity are analyzed with respect to an arbitrary spatial point. As a result, the geometric mapping between the point of virtual space and the one in visional space is established with matrix algebra, indicating that the 3D visional model can be mapped to a virtual 3D model unambiguously and the metric capability of human visional system is intrinsic. The main contribution of this paper is that a wholesome visional 3D model is proposed, which lays down a quantitative analysis foundation for the traditional stereo vision. The results are useful theory explorations for the stereo presence, the virtual interaction and the metric applications. [ABSTRACT FROM AUTHOR]

The basic argument of this paper is that the unusual form of natural economy (i.e. trading without money) in China during the 3rd-6th centuries was an inevitable outcome of the collapse of the monetary system in the Eastern Han Dynasty (1st-3rd centuries). This collapse was mainly caused by long-term inflation, and extensive archeological evidence is used here to corroborate this contention. There were two institutional shortcomings which caused this monetary breakdown. First, monopoly of coinage encouraged the government to over-issue currency during the Eastern Han in order to increase seignorage profit. Second, the inappropriate “Money Circulation Law” allowed bad money to circulate, driving out good money in accordance with Gresham’s Law. [ABSTRACT FROM AUTHOR]

The satisfiability problem (SAT) refers to whether there is a set of boolean variable assignments that make at least one literal in each clause of the conjunctive normal form (CNF) formula true. The multi literal SAT problem refers to whether there is a set of boolean variable assignments that make at least two literals in each clause of the CNF formula true. Obviously, this problem is still an NP difficult problem. Defining as the ratio of the number of clauses in the CNF formula to the number of variables, we study the upper bound α* of phase transition point of the problem. If α strictly exceeds α*, the multi literal satisfaction problem is almost certainly unsatisfiable. A simple inference of the first moment can be used to prove α* =-ln 2/ln1-(k+1)/2k). α* =1 when k=3. The local maximum technique proposed by Kirousis et al is used to improve the upper bound α* of phase transition point of the multi literal 3-SAT problem to 0.719 3. Finally, a large amount of data is selected for experimental verification, and the results show that the theoretical results are consistent with the experimental results [ABSTRACT FROM AUTHOR]