Kafesler Üzerinde Nullnormların Bir Farklı Ailesinin İnşaası

Bu çalışmada sınırlı bir ? kafesinin bir alt aralığı üzerinde hareket eden nullnormlar ve üçgensel normlar temel alınarak ? üzerinde bir yutan elemanlı nullnormları elde etmek için yeni bir inşaa yöntemi önerilmektedir. Bu inşaa yöntemi ile ilgili bazı temel özellikler araştırılmaktadır. Ayrıca, önerilen yöntemin sınırlı kafesler üzerinde nullnormları inşa eden mevcut yöntemlerden farklı olduğu örnekle gösterilmektedir.

Building A Different Family of Nullnorms on Lattices

In this paper, we introduce a new method for obtaining nullnorms on ? having an annihilator based onthe existence of triangular norms and nullnorms acting on a subinterval of a bounded lattice ?. Somebasic properties concerning this construction method are investigated. Furthermore, it is exemplifiedthe fact that the proposed method differs from the existing methods for constructing nullnorms onbounded lattices.

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Birkhoff, G., 1967. Lattice Theory. American Mathematical Society Colloquium Publishers, Providence, RI.
Calvo, T., De Baets, B. and Fodor, J., 2001. The functional equations of Frank and Alsina for uninorms and nullnorm. Fuzzy Sets and Systems, 120, 385-394.
Çaylı, G.D., 2018. On a new class of t-norms and tconorms on bounded lattices. Fuzzy Sets and Systems, 332, 129-143.
Çaylı, G.D. and Karaçal, F., 2018a. Idempotent nullnorms on bounded lattices. Information Sciences, 425, 154- 163.
Çaylı, G.D. and Karaçal, F., 2018b. A survey on nullnorms on bounded lattices. In: J. Kacprzyk et al. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT 2017, IWIFSGN 2017. Advances in Intelligent Systems and Computing, Springer, Cham, 641, 431- 442.
Çaylı, G.D., Karaçal, F. and Mesiar, R., 2016. On a new class of uninorms on bounded lattices. Information Sciences, 367–368, 221–231.
Drygaś, P., 2004a. A characterization of idempotent nullnorms. Fuzzy Sets and Systems, 145, 455-461.
Drygaś, P., 2004b. Isotonic operations with zero element in bounded lattices. in: K. Atanassov, O. Hryniewicz, J. Kacprzyk (Eds.), Soft Computing Foundations and Theoretical Aspect, EXIT Warszawa, 181–190.
Drygaś, P., Qin, F. and Rak, E., 2017. Left and right distributivity equations for semi-t-operators and uninorms. Fuzzy Sets and Systems, 325, 21-34.
Dubois, D. and Prade, H., 2000. Fundamentals of Fuzzy Sets. Kluwer Academic Publishers, Boston, MA.
Ertuğrul, Ü., 2018. Construction of nullnorms on bounded lattices and an equivalence relation on nullnorms. Fuzzy Sets and Systems, 334, 94–109.
Ertuğrul, Ü., Karaçal, F. and Mesiar, R., 2015. Modified ordinal sums of triangular norms and triangular conorms on bounded lattices. International Journal of Intelligent Systems, 30, 807-817.
Grabisch, M., Marichal, J.L., Mesiar, R. and Pap, E., 2009. Aggregation Operations. Cambridge University Press Cambridge.
Karaçal, F., İnce, M.A. and Mesiar, R., 2015. Nullnorms on bounded lattices. Information Sciences, 325, 227–236.
Klement, E.P., Mesiar, R. and Pap, E., 2000. Triangular Norms. Kluwer Academic Publishers, Dordrecht.
Mas, M., Mayor, G. and Torrens, J., 1999. t-operators. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 7, 31-50.
Mas, M., Mayor, G. and Torrens, J., 2002. The distributivity condition for uninorms and t-operators. Fuzzy Sets and Systems, 128, 209-225.
Sun, F., Wang, X.P. and Qu, X.B., 2017. Uni-nullnorms and null-uninorms. Journal of Intelligent & Fuzzy Systems, 32, 1969-1981.
Takács, M., 2008. Uninorm-based models for FLC systems. Journal of Intelligent & Fuzzy Systems, 19, 65-73.