Interpretations on Quantum Fuzzy Computing: Intuitionistic Fuzzy Operations × Quantum Operators

Quantum processes provide a parallel model for fuzzy connectives. Calculations of quantum states may be simultaneously performed by the superposition of membership and non-membership degrees of each element regarding the intuitionistic fuzzy sets. This work aims to interpret Atanassov's intuitionistic fuzzy logic through quantum computing, where not only intuitionistic fuzzy sets, but also their basic operations and corresponding connectives (negation, conjuntion, disjuntion, difference, codifference, implication, and coimplication), are interpreted based on the traditional quantum circuit model.

[1]  George Gargov,et al.  Elements of intuitionistic fuzzy logic. Part I , 1998, Fuzzy Sets Syst..

[2]  David W. Roberts.  An anticommutative difference operator for fuzzy sets and relations , 1987 .

[3]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[4]  Vladik Kreinovich,et al.  Formalizing the informal, precisiating the imprecise: How fuzzy logic can help mathematicians and physicists by formalizing their intuitive ideas , 2015, 2015 Annual Conference of the North American Fuzzy Information Processing Society (NAFIPS) held jointly with 2015 5th World Conference on Soft Computing (WConSC).

[5]  Chris Cornelis,et al.  Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application , 2004, Int. J. Approx. Reason..

[6]  Marek A. Perkowski,et al.  Quantum Robots for Teenagers , 2007, 37th International Symposium on Multiple-Valued Logic (ISMVL'07).

[7]  Jarosław Pykacz,et al.  Fuzzy quantum logic I , 1993 .

[8]  Vladik Kreinovich,et al.  Fuzzy Xor Classes from Quantum Computing , 2015, ICAISC.

[9]  K. Atanassov.  New operations defined over the intuitionistic fuzzy sets , 1994 .

[10]  Marek A. Perkowski,et al.  Fuzzy quantum circuits to model emotional behaviors of humanoid robots , 2010, IEEE Congress on Evolutionary Computation.

[11]  Mirco Mannucci,et al.  Quantum Fuzzy Sets: Blending Fuzzy Set Theory and Quantum Computation , 2006, ArXiv.

[12]  Michal Baczynski.  On some properties of intuitionistic fuzzy implications , 2003, EUSFLAT Conf..

[13]  Vladik Kreinovich,et al.  Aggregation operations from quantum computing , 2013, 2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[14]  Krassimir T. Atanassov.  Elements of Intuitionistic Fuzzy Logics , 1999 .

[15]  Sandor Imre,et al.  Quantum Computing and Communications: An Engineering Approach , 2005 .

[16]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[17]  J. Fodor.  On fuzzy implication operators , 1991 .

[18]  Isaac L. Chuang,et al.  Quantum Computation and Quantum Information (10th Anniversary edition) , 2011 .

[19]  Vladik Kreinovich,et al.  Relation between polling and Likert-scale approaches to eliciting membership degrees clarified by quantum computing , 2013, 2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[20]  Raymond Laflamme,et al.  An Introduction to Quantum Computing , 2007, Quantum Inf. Comput..