Research article

Fuzzy gradient descent for the linear fuzzy real number system

  • Received: 11 July 2019 Accepted: 31 July 2019 Published: 09 August 2019
  • MSC : 00A69

  • Many problems in education, finance, and engineering design require that decisions be made under uncertainty. In these fields, Machine Learning is often used to search for patterns and information from data. To find patterns in Fuzzy Data, Fuzzy Machine Learning techniques can be used. In this paper, we focus on solving and manipulating Fuzzy Nonlinear problems in the Linear Fuzzy Real (LFR) number system using the Gradient Descent. The Gradient Descent is the most often used learning algorithm in Machine Learning. Thus, we propose the LFR Gradient Descent method for solving nonlinear equations in the LFR number system.

    Citation: Frank Rogers. Fuzzy gradient descent for the linear fuzzy real number system[J]. AIMS Mathematics, 2019, 4(4): 1078-1086. doi: 10.3934/math.2019.4.1078

    Related Papers:

  • Many problems in education, finance, and engineering design require that decisions be made under uncertainty. In these fields, Machine Learning is often used to search for patterns and information from data. To find patterns in Fuzzy Data, Fuzzy Machine Learning techniques can be used. In this paper, we focus on solving and manipulating Fuzzy Nonlinear problems in the Linear Fuzzy Real (LFR) number system using the Gradient Descent. The Gradient Descent is the most often used learning algorithm in Machine Learning. Thus, we propose the LFR Gradient Descent method for solving nonlinear equations in the LFR number system.


    加载中


    [1] R. E. Bellman, L. A. Zadeh, Decision making in a fuzzy environment, Manage. Sci., 17 (1970), 141-164. doi: 10.1287/mnsc.17.4.B141
    [2] J. Cheng, Data-Mining Research in Education, Report, International School of Software, Wuhan University, 2017.
    [3] D. Dubois, H. Prade, System of linear fuzzy constraints, Fuzzy Set. Syst., 3 (1980), 37-48. doi: 10.1016/0165-0114(80)90004-4
    [4] B. Monk, A Proposed Theory of Fuzzy Random Variables, Dissertation, University of Alabama, 2001.
    [5] A. C. Muller, S. Guido, Introduction to Machine Learning with Python: A Guide for Data Scientists, O'Reilly Media, 2016.
    [6] J. Neggers, H. Kim, Fuzzy posets on sets, Fuzzy Set. Syst., 117 (2001), 391-402. doi: 10.1016/S0165-0114(98)00249-8
    [7] J. Neggers, H. Kim, On Linear Fuzzy Real Numbers, Manuscript for book under development, 2007.
    [8] C. V. Negoita, Fuzziness in management, OPSA/TIMS, Miami, 1970.
    [9] R. Prevo, Entropies of families of fuzzy random variables: an introduction to an in-depth exploration of several classes of important examples, Dissertation, University of Alabama, 2002.
    [10] F. Rogers, Optimal Choices in an LFR System, Dissertation, University of Alabama, 2005.
    [11] F. Rogers, Y. Jun, Fuzzy Nonlinear Optimization for the Linear Fuzzy Real Number System, International Mathematical Forum, 4 (2009), 587-596.
    [12] N. V. Sahindas, Optimization under uncertainty: state-of-the-art and opportunities, Comput. Chem. Eng., 28 (2004), 971-983. doi: 10.1016/j.compchemeng.2003.09.017
    [13] H. Tanaka, K. Asai, Fuzzy linear programming problems with fuzzy numbers, Fuzzy Set. Syst., 13 (1984), 1-10. doi: 10.1016/0165-0114(84)90022-8
    [14] H. J. Zimmermann, Fuzzy mathematical programming, Comput. Oper. Res., 10 (1983), 291-298. doi: 10.1016/0305-0548(83)90004-7
  • Reader Comments
  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3453) PDF downloads(545) Cited by(0)

Article outline

Figures and Tables

Figures(1)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog