Archive
Special Issues
Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms and Implications Satisfying the Order Property
Applied and Computational Mathematics
Volume 6, Issue 1, February 2017, Pages: 45-53
Received: Jan. 8, 2017; Accepted: Jan. 19, 2017; Published: Feb. 23, 2017
Authors
Zhudeng Wang, School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, People's Republic of China
Yuan Wang, College of Information Engineering, Yancheng Teachers University, Yancheng, People's Republic of China
Keming Tang, College of Information Engineering, Yancheng Teachers University, Yancheng, People's Republic of China
Article Tools Abstract PDF (266KB) HTML
Abstract
We firstly give out the formulas for calculating the upper and lower approximation strict left (right)-conjunctive left (right) semi-uninorms of a binary operation. Then, we lay bare the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation. Finally, we reveal the relationships between the upper approximation strict left (right)-conjunctive left (right) arbitrary ˅-distributive left (right) semi-uninorms and lower approximation right arbitrary ˄-distributive implications which satisfy the order property.
Keywords
Fuzzy Logic, Fuzzy Connective, Left (Right) Semi-Uninorm, Implication, Strict Left (Right)-Conjunctive
Zhudeng Wang, Yuan Wang, Keming Tang, Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms and Implications Satisfying the Order Property, Applied and Computational Mathematics. Vol. 6, No. 1, 2017, pp. 45-53. doi: 10.11648/j.acm.20170601.13
References

J. Fodor and M. Roubens, “Fuzzy Preference Modelling and Multicriteria Decision Support”, Theory and Decision Library, Series D: System Theory, Knowledge Engineering and Problem Solving, Kluwer Academic Publishers, Dordrecht, 1994.

G. J. Klir and B. Yuan, “Fuzzy Sets and Fuzzy Logic, Theory and Applications”, Prentice Hall, New Jersey, 1995.

E. P. Klement, R. Mesiar and E. Pap, “Triangular Norms”, Trends in Logic-Studia Logica Library, Vol. 8, Kluwer Academic Publishers, Dordrecht, 2000.

J. Fodor and T. Keresztfalvi, “Nonstandard conjunctions and implications in fuzzy logic”, International Journal of Approximate Reasoning, 12, 69-84, 1995.

J. Fodor, “Srict preference relations based on weak t-norms”, Fuzzy Sets and Systems, 43, 327-336, 1991.

Z. D. Wang and Y. D. Yu, “Pseudo-t-norms and implication operators on a complete Brouwerian lattice”, Fuzzy Sets and Systems, 132, 113-124, 2002.

Y. Su and Z. D. Wang, “Pseudo-uninorms and coimplications on a complete lattice”, Fuzzy Sets and Systems, 224, 53-62, 2013.

Z. D. Wang and J. X. Fang, “Residual operators of left and right uninorms on a complete lattice”, Fuzzy Sets and Systems, 160, 22-31, 2009.

H. W. Liu, “Semi-uninorm and implications on a complete lattice”, Fuzzy Sets and Systems, 191, 72-82, 2012.

Y. Ouyang, “On fuzzy implications determined by aggregation operators”, Information Sciences, 193, 153-162, 2012.

R. R. Yager and A. Rybalov, “Uninorm aggregation operators”, Fuzzy Sets and Systems, 80, 111-120, 1996.

J. Fodor, R. R. Yager and A. Rybalov, “Structure of uninorms”, Internat. J. Uncertainly, Fuzziness and Knowledge-Based Systems, 5, 411-427, 1997.

M. Mas, M. Monserrat and J. Torrens, “On left and right uninorms”, Internat. J. Uncertainly, Fuzziness and Knowledge-Based Systems, 9, 491-507, 2001.

M. Mas, M. Monserrat and J. Torrens, “On left and right uninorms on a finite chain”, Fuzzy Sets and Systems, 146, 3-17, 2004.

Z. D. Wang and J. X. Fang, “Residual coimplicators of left and right uninorms on a complete lattice”, Fuzzy Sets and Systems, 160, 2086-2096, 2009.

Y. Su, Z. D. Wang and K. M. Tang, “Left and right semi-uninorms on a complete lattice”, Kybernetika, 49, 948-961, 2013.

S. Jenei and F. Montagna, “A general method for constructing left-continuous t-norms”, Fuzzy Sets and Systems, 136, 263-282, 2003.

Z. D. Wang, “Generating pseudo-t-norms and implication operators”, Fuzzy Sets and Systems, 157, 398-410, 2006.

Y. Su and Z. D. Wang, “Constructing implications and coimplications on a complete lattice”, Fuzzy Sets and Systems, 247, 68-80, 2014.

X. Y. Hao, M. X. Niu and Z. D. Wang, “The relations between implications and left (right) semi-uninorms on a complete lattice”, Internat. J. Uncertainly, Fuzziness and Knowledge-Based Systems, 23, 245-261, 2015.

M. X. Niu, X. Y. Hao and Z. D. Wang, “Relations among implications, coimplications and left (right) semi-uninorms”, Journal of Intelligent and Fuzzy Systems, 29, 927-938, 2015.

Z. D. Wang, “Left (right) semi-uninorms and coimplications on a complete lattice”, Fuzzy Sets and Systems, 287, 227-239, 2016.

X. Y. Hao, M. X. Niu, Y. Wang and Z. D. Wang, “Constructing conjunctive left (right) semi-uninorms and implications satisfying the neutrality principle”, Journal of Intelligent and Fuzzy Systems, 31, 1819-1829, 2016.

Z. D. Wang, M. X. Niu and X. Y. Hao, “Constructions of coimplications and left (right) semi-uninorms on a complete lattice”, Information Sciences, 317, 181-195, 2015.

G. Birkhoff, “Lattice Theory”, American Mathematical Society Colloquium Publishers, Providence, 1967.

M. Baczynski and B. Jayaram, “Fuzzy Implication”, Studies in Fuzziness and Soft Computing, Vol. 231, Springer, Berlin, 2008.

H. Bustince, P. Burillo and F. Soria, “Automorphisms, negations and implication operators”, Fuzzy Sets and Systems, 134, 209-229, 2003.

B. De Baets and J. Fodor, “Residual operators of uninorms”, Soft Computing, 3, 89-100, 1999.
PUBLICATION SERVICES 