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Home > Archive>Volume 25, Issue 11, 2014 >2518-2527. DOI:10.13328/j.cnki.jos.004525
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Aggregation and Decomposition of Bipolar Information
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    Abstract:

    Information aggregation is one of the basic means for information processing. This paper mainly discusses about behavior of several aggregation operators. Firstly, from the perspective of generalized adjunction, the properties of generalized aggregation operators are discussed. Given one aggregation operator A, two different methods are adopted to construct new aggregation operators greater (less) than or equal to A. Furthermore, several aggregation operators, such as bipolar t-norms and bipolar implications, are explored, and the condition is provided for bipolar aggregation operators to be decomposed into two unipolar aggregation operators. Under this condition, the aggregation processing for positive as well as negative information is also presented.

    Reference
    [1] Bloch I. Mathematical morphology on bipolar fuzzy sets: General algebraic framework. Int'l Journal of Approximate Reasoning, 2012,53(7):1031-1060. [doi: 10.1016/j.ijar.2012.05.003]
    [2] Dubois D, Prade H. An overview of the asymmetric bipolar representation of positive and negative information in possibility theory. Fuzzy Sets and Systems, 2009,160(10):1355-1366. [doi: 10.1016/j.fss.2008.11.006]
    [3] Wang ZD, Yu YD. Pseudo-t-Norms and implication operators: Direct products and direct product decompositions. Fuzzy Sets and Systems, 2003,139(3):673-683. [doi: 10.1016/S0165-0114(02)00503-1]
    [4] Zadrozny S, Kacprzyk J. Bipolar queries: An aggregation operator focused perspective. Fuzzy Sets and Systems, 2012,196:69-81. [doi: 10.1016/j.fss.2011.10.013]
    [5] Liu HW. On a new class of implications: (g,min)-Implications and several classical tautologies. Int'l Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2012,20(1):1-20.
    [6] Kaci S. Logical formalisms for representing bipolar preferences. Int'l Journal of Intelligent Systems, 2008,23(8):985-997. [doi: 10. 1002/int.20303]
    [7] Bosc P, Pivert O. On a fuzzy bipolar relational algebra. Information Sciences, 2013,219:1-16. [doi: 10.1016/j.ins.2012.07.018]
    [8] Liu HW. Fuzzy implications derived from generalized additive generators of representable uninorms. IEEE Trans. on Fuzzy Systems, 2013,21(3):555-566. [doi: 10.1109/TFUZZ.2012.2222892]
    [9] Wang DH, Jin B, Jia YL. An algorithm of image edge examination based on morphology dual-structural elements. Xihua University Journal, 2010,29(3):42-45 (in Chinese with English abstract).
    [10] Zhang X, Dang JW, Ma HF. Edgr detection method of track images based on mathematical morphology of dual-structure elements. Railway Computer Application, 2011,20(5):28-31 (in Chinese with English abstract).
    [11] Hu XH, Deng MN. Soft morphological edge-detection algorithm based on fuzzy theory. Computer Engineering and Applications, 2010,46(33):155-157 (in Chinese with English abstract).
    [12] Soille P, Worte; Wang XP, et al., Trans. Morphological Image Analysis-Principle and Application. 2nd ed., Beijing: Tsinghua University Press, 2007 (in Chinese).
    [13] Bloch I, Maitre N. Fuzzy mathematical morphologies: A comparative study. Pattern Recognition, 1995,28(9):1341-1387. [doi: 10. 1016/0031-3203(94)00312-A]
    [14] Bloch I. Duality vs. adjunction for fuzzy mathematical morphology and general form of fuzzy erosions and dilations. Fuzzy Sets and Systems, 2009,160(13):1858-1867. [doi: 10.1016/j.fss.2009.01.006]
    [15] Maragos P. Lattice image processing: A unification of morphological and fuzzy algebraic systems. Journal of Mathematical Imaging and Vision, 2005,22(2-3):333-353. [doi: 10.1007/s10851-005-4897-z]
    [16] Sussner P, Valle ME. Classification of mathematical morphologies based on concept of inclusion measure and duality. Journal of Mathematical Imaging and Vision, 2005,32(2):139-159.
    [17] Bloch I. Spatial reasoning under imprecision using fuzzy set theory, formal logics, and mathematical morphology. Int'l Journal of Approximate Reasoning, 2006,41(2):77-95. [doi: 10.1016/j.ijar.2005.06.011]
    [18] Wang ZD, Fang JX. Residual coimplicators of left and right uninorms on a complete lattice. Fuzzy Sets and Systems, 2009,160(14): 2086-2096. [doi: 10.1016/j.fss.2008.10.007]
    [19] Deschrijver G, Cornelis C, Kerre EE. On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE Trans. on Fuzzy Systems, 2004,12(1):45-61. [doi: 10.1109/TFUZZ.2003.822678]
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王国俊,段景瑶.双极信息的聚合与分解.软件学报,2014,25(11):2518-2527

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History
  • Received:February 12,2013
  • Revised:November 05,2013
  • Online: November 05,2014
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