New structures for uninorms on bounded lattices
Pages 2019 - 2030
Abstract
In this article, we present new methods for constructing uninorms on bounded lattices under the additional constraints and prove that some of these constraints are sufficient and necessary for the uninorms. Moreover, some illustrative examples for the construction of uninorms are provided. At last, we show that the additional constraints on t-norms (t-conorms) and t-subnorms (t-subconorms) of some uninorms in the literature are exactly sufficient and necessary.
References
[1]
Aşıcı E. and Mesiar R., On the construction of uninorms on bounded lattices, Fuzzy Sets and Systems 408 (2021), 65–85.
[2]
Birkhoff G., Lattice theory, 3rd Edition, Amer. Math. Soc., Rhode Island, 1967.
[3]
Bodjanova S. and Kalina M., Construction of uninorms on bounded lattices, in: IEEE 12th International Symposium on Intelligent Systems and Informatics, SISY 2014, September 11–13, Subotica, Serbia, 61–66
[4]
Baczyński M. and Jayaram B., Fuzzy Implications, Springer, Berlin, 2008.
[5]
Dombi J., Basic concepts for a theory of evaluation: The aggregative operator, European Journal of Operational Research 10 (1982), 282–293.
[6]
Çaylı G.D., New methods to construct uninorms on bounded lattices, International Journal of Approximate Reasoning 115 (2019), 254–264.
[7]
Çaylı G.D., On the structure of uninorms on bounded lattices, Fuzzy Sets and Systems 357 (2019), 2–26.
[8]
Çaylı G.D., Uninorms on bounded lattices with the underlying t-norms and t-conorms, Fuzzy Sets and Systems 395 (2020), 107–129.
[9]
Çaylı G.D., New construction approaches of uninorms on bounded lattices, International Journal of General Systems 50 (2021), 139–158.
[10]
Çaylı G.D. and Karaçal F., Construction of uninorms on bounded lattices, Kybernetika 53 (2017), 394–417.
[11]
Çaylı G.D., Karaçal F. and Mesiar R., On a new class of uninorms on bounded lattices, Information Sciences 367 (2016), 221–231.
[12]
Dan Y.X. and Hu B.Q., A new structure for uninorms on bounded lattices, Fuzzy Sets and Systems 386 (2020), 77–94.
[13]
Dan Y.X., Hu B.Q. and Qiao J.S., New constructions of uninorms on bounded lattices, International Journal of Approximate Reasoning 110 (2019), 185–209.
[14]
De Baets B. and Van Fodor J., Melle’s combining function in MYCIN is a representable uninorm: an alternative proof, Fuzzy Sets and Systems 104 (1999), 133–136.
[15]
Grabisch M., Marichal J.L., Mesiar R. and Pap E., Aggregation functions, Cambridge University Press, 2009.
[16]
Grabisch M., Marichal J.L., Mesiar R. and Pap E., Aggregation functions: construction methods, conjunctive, disjunctive and mixed classes, Information Sciences 181 (2011), 23–43.
[17]
Goguen J., L-fuzzy sets, Journal of Mathematical Analysis and Applications 18 (1967), 145–147.
[18]
Höhle U., Commutative, residuated l-monoids, in: U. Höhle, E.Klement (Eds.), Non-Classical Logics and Their Applications to Fuzzy Subsets: A Handbook on the Mathematical Foundations of Fuzzy Set Theory, Kluwer, Dordrecht, 1995.
[19]
Hua X.-J. and Ji W., Uninorms on bounded lattices constructed by t-norms and t-subconorms, Fuzzy Sets and Systems 427 (2022), 109–131.
[20]
Hua X.-J., Zhang H.-P. and Ouyang Y., Note on “Construction of uninorms on bounded lattices”, Kybenetika 57(2) (2021), 372–382.
[21]
He P. and Wang X.-P., Constructing uninorms on bounded lattices by using additive generators, International Journal of Approximate Reasoning 136 (2021), 1–13.
[22]
Ji W., Constructions of uninorms on bounded lattices by means of t-subnorms and t-subconorms, Fuzzy Sets and Systems 403 (2021), 38–55.
[23]
Karaçal F. and Mesiar R., Uninorms on bounded lattices, Fuzzy Sets and Systems 261 (2015), 33–43.
[24]
Klement E.P., Mesiar R. and Pap E., Triangular norms. Position paper I: basic analytical and algebraic properties, Fuzzy Sets and Systems 143 (2004), 5–26.
[25]
Liang X. and Pedrycz W., Logic-based fuzzy networks: a study in system modeling with triangular norms and uninorms, Fuzzy Sets and Systems 160 (2009), 3475–3502.
[26]
Menger K., Statistical metrics, Proc Natl Acad Sci USA 8 (1942), 535–537.
[27]
Ouyang Y. and Zhang H.P., Constructing uninorms via closure operators on a bounded lattice, Fuzzy Sets and Systems 395 (2020), 93–106.
[28]
Pedrycz W. and Hirota K., Uninorm-based logic neurons as adaptive and interpretable processing constructs, Soft Computing 11 (2007), 41–52.
[29]
Quesada F.J., Palomares I. and Martinez L., Managing experts behavior in large-scale consensus reaching processes with uninorm aggregation operators, Applied Soft Computing 35 (2015), 873–887.
[30]
Schweizer B. and Sklar A., Statistical metric spaces, Pacific Journal of Mathematics 10 (1960), 313–334.
[31]
Schweizer B. and Sklar A., Associative functions and statistical triangular inequalities, Publicationes mathematicae 8 (1961), 169–186.
[32]
Schweizer B. and Sklar A., Probabilistic Metric Spaces, North-Holland, New York, 1983.
[33]
Saminger S., On ordinal sums of triangular norms on bounded lattices, Fuzzy Sets and Systems 157 (2006), 1403–1416.
[34]
Wang Z., TL-filters of integral residuated l-monoids, Information Sciences 177 (2007), 887–896.
[35]
Xie A.F. and Li S.J., On constructing the largest and smallest uninorms on bounded lattices, Fuzzy Sets and Systems 386 (2020), 95–104.
[36]
Xiu Z.Y. and Zheng X., New construction methods of uninorms on bounded lattices via uninorms, Fuzzy Sets and Systems 2023. doi.org/10.1016/j.fss.2023.108535.
[37]
Yager R.R. and Rybalov A., Uninorm aggregation operators, Fuzzy sets and systems 80 (1996), 111–120.
[38]
Zhang H.P., Wu M., Wang Z., Ouyang Y. and De Baets B., A characterization of the classes Umin and Umax of uninorms on a bounded lattice, Fuzzy Sets and Systems 423 (2021), 107–121.
[39]
Zhao B. and Wu T., Some further results about uninorms on bounded lattices, International Journal of Approximate Reasoning 130 (2021), 22–49.
[40]
Zimmermann H.J., Fuzzy Set Theory and Its Applications, fourth ed., Kluwer, Aachen, 2001.
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Published: 01 January 2023
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