Fuzzy Structure of Complex Belief Systems: Fuzzy Relations and Fuzzy Belief Sets

In previous work, Nescolarde-Selva and Usó-Doménech (2014a, b) discussed the theory that complex belief systems have a topological structure. In this article it is suggested that this structure is also fuzzy. We introduce the concepts of fuzzy sets in the context of beliefs (substantive and derived), and between derived beliefs themselves. Also introduced are the concepts of fuzzy covering and fuzzy invariance and the relationships between them.

[1]  Josep Lluis Usó-Doménech,et al.  An introduction to alysidal algebra (IV) , 2013, Kybernetes.

[2]  Josep Lluis Usó-Doménech,et al.  An introduction to alysidal algebra (III) , 2012, Kybernetes.

[3]  L. Goble.  The Blackwell guide to philosophical logic , 2001 .

[4]  M. Eliade,et al.  History of Religious Ideas, Volume 1: From the Stone Age to the Eleusinian Mysteries , 1979 .

[5]  F. Heider,et al.  Principles of topological psychology , 1936 .

[6]  Miguel Lloret-Climent,et al.  Coverage, invariability and orbits by structural functions , 2006 .

[7]  J. L. Usó-Doménech,et al.  Reality, Systems and Impure Systems , 2014 .

[8]  Jean-Yves Béziau,et al.  What is many-valued logic? , 1997, Proceedings 1997 27th International Symposium on Multiple- Valued Logic.

[9]  Miguel Lloret-Climent,et al.  Coverage and invariability by structural functions , 2006, Int. J. Gen. Syst..

[10]  Josep Lluis Usó-Doménech,et al.  Topological structures of complex belief systems , 2013, Complex..

[11]  Peter Gärdenfors,et al.  On the logic of theory change: Partial meet contraction and revision functions , 1985, Journal of Symbolic Logic.

[12]  Grzegorz Malinowski,et al.  Many-Valued Logics , 1994 .

[13]  D. Michael Miller,et al.  Multiple Valued Logic: Concepts and Representations , 2008, Multiple Valued Logic.

[14]  Daniel Berend,et al.  An introduction to alysidal algebra (II) , 2012, Kybernetes.

[15]  Ying-ming Liu,et al.  Fuzzy Topology , 1998, Advances in Fuzzy Systems - Applications and Theory.

[16]  Josep Lluis Usó-Doménech,et al.  Topological structures of complex belief systems (II): Textual materialization : Textual Materialization , 2013, Complex..

[17]  J. Usó-Doménech,et al.  Truth Values in t-norm based Systems Many-valued FUZZY Logic , 2014 .

[18]  T. V. Dijk,et al.  Ideology: A Multidisciplinary Approach , 1998 .

[19]  Josep Lluis Usó-Domènech,et al.  Mathematic and Semiotic Theory of Ideological Systems , 2012 .

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

[21]  A sociology of belief , 1976 .

[22]  Daniel Berend,et al.  An introduction to alysidal algebra (I) , 2012, Kybernetes.

[23]  Peter Gärdenfors,et al.  Knowledge in Flux , 1988 .

[24]  Mircea Eliade,et al.  A history of religious ideas , 1986 .

[25]  Josué Antonio Nescolarde-Selva,et al.  Semiotic Vision of Ideologies , 2014 .

[26]  Josué-Antonio Nescolarde-Selva,et al.  Coverage and invariability in fuzzy systems , 2014, Int. J. Gen. Syst..

[27]  Charles C. Lemert,et al.  A Sociology of Belief , 1976 .

[28]  D. Mundici,et al.  Algebraic Foundations of Many-Valued Reasoning , 1999 .