The Soft Sets and Fuzzy Sets-Based Neural Networks and Application

This paper reviews and compares theories of fuzzy sets and soft sets from the perspective of transformation, and a machine learning model—SF-ANN (the soft sets and fuzzy sets based artificial neural network) is proposed. Liu et al. proved that every fuzzy set on a universe $U$ can be considered as a soft set, and show that any soft set can be regarded as even a fuzzy set. Inspired by this idea, we construct a neuron-like structure based on soft sets and fuzzy sets, and we get a more practical fuzzy learning model—SF-ANN. In practical applications, it can be used as a general methodology for establishing the membership function of fuzzy sets, and it also can be applied to pattern recognition, decision-making, etc. In general, it provides a new perspective to observe the relationship between soft sets and fuzzy sets, and it is easy to relate soft set theory and fuzzy set theory to machine learning methods. To a certain extent, it reveals that the research of fuzzy sets and artificial neural networks do lead to the same destination.

[1]  Zheng Pei,et al.  The relationship between soft sets and fuzzy sets and its application , 2019, J. Intell. Fuzzy Syst..

[2]  Jin Liu,et al.  On Induced Soft Sets and Topology for the Parameter Set of a Soft Set , 2015, 2015 IEEE International Conference on Computer and Information Technology; Ubiquitous Computing and Communications; Dependable, Autonomic and Secure Computing; Pervasive Intelligence and Computing.

[3]  José Carlos Rodriguez Alcantud,et al.  Some formal relationships among soft sets, fuzzy sets, and their extensions , 2016, Int. J. Approx. Reason..

[4]  Dimitrios Zissis,et al.  A cloud based architecture capable of perceiving and predicting multiple vessel behaviour , 2015, Appl. Soft Comput..

[5]  Patrick van der Smagt,et al.  Introduction to neural networks , 1995, The Lancet.

[6]  José Carlos Rodriguez Alcantud,et al.  Glaucoma Diagnosis: A Soft Set Based Decision Making Procedure , 2015, CAEPIA.

[7]  Zhi Xiao,et al.  A combined forecasting approach based on fuzzy soft sets , 2009 .

[8]  Onur Oktay,et al.  Reduced soft matrices and generalized products with applications in decision making , 2018, Neural Computing and Applications.

[9]  Yiyu Yao,et al.  A Comparative Study of Fuzzy Sets and Rough Sets , 1998 .

[10]  Samanthe M. Lyons,et al.  Changes in cell shape are correlated with metastatic potential in murine and human osteosarcomas , 2016, Biology Open.

[11]  Jianming Zhan,et al.  A survey of decision making methods based on certain hybrid soft set models , 2016, Artificial Intelligence Review.

[12]  Gustavo Santos-García,et al.  Using Artificial Neural Networks to Identify Glaucoma Stages , 2011 .

[13]  Anna Kolesárová.  Limit properties of quasi-arithmetic means , 2001, Fuzzy Sets Syst..

[14]  D. Molodtsov.  Soft set theory—First results , 1999 .

[15]  Sven Rahmann,et al.  Application of Neural Networks in Diagnosing Cancer Disease using Demographic Data , 2010 .

[16]  Goutam Saha,et al.  Lung sound classification using cepstral-based statistical features , 2016, Comput. Biol. Medicine.

[17]  LiMin Fu,et al.  Neural networks in computer intelligence , 1994 .

[18]  Mustafa Mat Deris,et al.  A soft set approach for association rules mining , 2011, Knowl. Based Syst..

[19]  Young Bae Jun,et al.  An adjustable approach to fuzzy soft set based decision making , 2010, J. Comput. Appl. Math..

[20]  Tutut Herawan,et al.  On If-Then Multi Soft Sets-Based Decision Making , 2014, ICT-EurAsia.

[21]  W S McCulloch,et al.  A logical calculus of the ideas immanent in nervous activity , 1990, The Philosophy of Artificial Intelligence.

[22]  Michael Egmont-Petersen,et al.  Image processing with neural networks - a review , 2002, Pattern Recognit..

[23]  Francisco Herrera,et al.  A Historical Account of Types of Fuzzy Sets and Their Relationships , 2016, IEEE Transactions on Fuzzy Systems.

[24]  José Carlos Rodriguez Alcantud,et al.  A New Criterion for Soft Set Based Decision Making Problems under Incomplete Information , 2017, Int. J. Comput. Intell. Syst..

[25]  Samanthe M. Lyons,et al.  Measuring systematic changes in invasive cancer cell shape using Zernike moments. , 2016, Integrative biology : quantitative biosciences from nano to macro.

[26]  Jianming Zhan,et al.  A survey of parameter reduction of soft sets and corresponding algorithms , 2019, Artificial Intelligence Review.

[27]  José Carlos Rodriguez Alcantud,et al.  A social choice approach to graded soft sets , 2017, 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[28]  L. Bottaci,et al.  Artificial neural networks applied to outcome prediction for colorectal cancer patients in separate institutions , 1997, The Lancet.

[29]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[30]  Wei Xu,et al.  Financial ratio selection for business failure prediction using soft set theory , 2014, Knowl. Based Syst..

[31]  Naim Çagman,et al.  Soft sets and soft groups , 2007, Inf. Sci..

[32]  Tutut Herawan,et al.  Soft Solution of Soft Set Theory for Recommendation in Decision Making , 2014, SCDM.

[33]  Xueling Ma,et al.  Applications of rough soft sets in BCI-algebras and decision making , 2015, J. Intell. Fuzzy Syst..

[34]  Yong Yang,et al.  Interval-valued Hesitant Fuzzy Soft Sets and their Application in Decision Making , 2015, Fundam. Informaticae.

[35]  Vicenç Torra,et al.  Decomposition theorems and extension principles for hesitant fuzzy sets , 2018, Inf. Fusion.

[36]  Witold Pedrycz,et al.  Soft set based association rule mining , 2016, Knowl. Based Syst..

[37]  Michael Negnevitsky,et al.  Artificial Intelligence: A Guide to Intelligent Systems , 2001 .

[38]  Radko Mesiar,et al.  Hesitant L ‐Fuzzy Sets , 2017, Int. J. Intell. Syst..