Logic-Based Fuzzy Neurocomputing With Unineurons

In this paper, we introduce a new category of logic neurons- unineurons that are based on the concept of uninorms. As uninorms form a certain generalization of the generic categories of fuzzy set operators such as t-norms and t-conorms, the proposed unineurons inherit their logic processing capabilities which make them flexible and logically appealing. We discuss several fundamental categories of uninorms (such as UNI_or, UNI_and, and alike). In particular, we focus on the interpretability of networks composed of unineurons leading to several categories of rules to be exploited in rule-based systems. The learning aspects of the unineurons are presented along with detailed optimization schemes. Experimental results tackle two categories of problems such as: (a) a logic approximation of fuzzy sets, and (b) a design of associations between information granules where the ensuing development schemes directly relate to the fundamentals of granular (fuzzy) modeling

[1]  Konstantinos G. Margaritis,et al.  The MYCIN certainty factor handling function as uninorm operator and its use as a threshold function in artificial neurons , 1998, Fuzzy Sets Syst..

[2]  Ronald R. Yager,et al.  Structure of Uninorms , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[3]  Ronald R. Yager,et al.  Defending against strategic manipulation in uninorm-based multi-agent decision making , 2002, Eur. J. Oper. Res..

[4]  Witold Pedrycz,et al.  Granular Computing - The Emerging Paradigm , 2007 .

[5]  Ronald R. Yager,et al.  Uninorms in fuzzy systems modeling , 2001, Fuzzy Sets Syst..

[6]  Lotfi A. Zadeh,et al.  Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic , 1997, Fuzzy Sets Syst..

[7]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[8]  Bernard De Baets,et al.  The functional equations of Frank and Alsina for uninorms and nullnorms , 2001, Fuzzy Sets Syst..

[9]  W. Pedrycz,et al.  An introduction to fuzzy sets : analysis and design , 1998 .

[10]  Qin Feng Uninorm solutions and (or) nullnorm solutions to the modularity condition equations , 2004, Fuzzy Sets Syst..

[11]  Witold Pedrycz,et al.  Fuzzy neural networks and neurocomputations , 1993 .

[12]  Bernard De Baets,et al.  Van Melle's combining function in MYCIN is a representable uninorm: An alternative proof , 1999, Fuzzy Sets Syst..

[13]  Ronald R. Yager,et al.  Uninorm aggregation operators , 1996, Fuzzy Sets Syst..

[14]  Radko Mesiar,et al.  Continuous generated associative aggregation operators , 2002, Fuzzy Sets Syst..

[15]  Bernard De Baets,et al.  Idempotent uninorms , 1999, Eur. J. Oper. Res..

[16]  Witold Pedrycz,et al.  Granular computing: an introduction , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[17]  Witold Pedrycz,et al.  The genetic development of ordinal sums , 2005, Fuzzy Sets Syst..

[18]  W. Pedrycz,et al.  OR/AND neuron in modeling fuzzy set connectives , 1994, IEEE Trans. Fuzzy Syst..

[19]  Witold Pedrycz,et al.  Heterogeneous fuzzy logic networks: fundamentals and development studies , 2004, IEEE Transactions on Neural Networks.