Araştırma Makalesi
BibTex RIS Kaynak Göster

Unidefiners

Yıl 2025, Cilt: 29 Sayı: 1, 220 - 227, 25.04.2025

Selim Çetin

https://doi.org/10.19113/sdufenbed.1666339

Öz

In this study, we examine the concept of a unidefiner, defined on the interval [0,∞], which provides a unified framework for both t-definer and t-codefiner structures. Similar to the approach of uninorms on [0,1], a unidefiner is a binary operation on [0,∞], with a neutral element e∈[0,∞],, which is associative, commutative, and monotonic. Consequently, when e = 0, it yields a t-definer, and when e =∞, it yields a t-codefiner. This paper discusses the theoretical properties of unidefiners and explores their relationship with t-definer and t-codefiner examples. In conclusion, it emphasizes that unidefiners can serve as a “generalized connective” analogous to uninorms for a “proper” identity value (i.e., e ≠ 0, e≠∞) in the [0,∞] range.

Anahtar Kelimeler

Unidefiner t-definer t-codefiner identity element monoid

Kaynakça

  • [1] Aşıcı E., Mesiar R. 2021. On the direct product of uninorms on bounded lattices. Kybernetika 57(6), 989–1004
  • [2] Aşıcı E., Mesiar R. 2024. Some investigations on the U-partial order induced by uninorms. Aequa-tiones mathematicae 1-14.
  • [3] Cao M., Du WS. 2023. On residual implications derived from 2-uninorms. International Journal of Approximate Reasoning 159, 108926.
  • [4] Çaylı GD. 2023. An alternative construction of uninorms on bounded lattices. International Journal of General Systems 52(5), 574–596.
  • [5] Çaylı GD. 2024. Constructing uninorms on bounded lattices through closure and interior op-erators. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 32(1), 109–129.
  • [6] Çaylı GD., Ertuğrul U., Karaçal F. 2023. Some fur-ther construction methods for uninorms on bounded lattices. International Journal of General Systems 52(4), 414–442.
  • [7] Csiszar O, Pusztahazi LS., Denes-Fazakas L., Gashler MS., Kreinovich V, Csisz´ar G. 2023. Un-inorm-like parametric activation functions for human-understandable neural models. Knowledge-Based Systems 260, 110095.
  • [8] Dan Y. 2023. A unified way to studies of t-seminorms, t-semiconorms and semi-uninorms on a complete lattice in terms of behaviour oper-ations. International Journal of Approximate Rea-soning 156, 61–76.
  • [9] Dan Y., Hu BQ., De Baets B. 2022. Nullnorms on bounded lattices constructed by means of closure and interior operators. Fuzzy Sets and Systems 439, 142–156.
  • [10] De Campos Souza PV., Lughofer E. 2022. An ad-vanced interpretable fuzzy neural network model based on uni-nullneuron constructed from n-uninorms. Fuzzy Sets and Systems 426, 1–26.
  • [11] Dvorak A., Holcapek M., Paseka J. 2022. On ordi-nal sums of partially ordered monoids: A unified approach to ordinal sum constructions of t-norms, t-conorms and uninorms. Fuzzy Sets and Systems 446, 4–25.
  • [12] Fodor J., De Baets B. 2007. Uninorm basics. In Fuzzy Logic: A Spectrum of Theoretical & Practical Issues 49–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 15s.
  • [13] Fodor JC., Yager RR., Rybalov A. 1997. Structure of uninorms. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 5(4), 411–427.
  • [14] Gürdal U., Oğur O., Çetin S. Unima on [0,1]. Manu-script submitted for publication.
  • [15] He SY., Xie LH., Yan PF. 2022. On ⋆-metric spaces. Filomat 36(18), 6173–6185.
  • [16] Hlinena D., Kalina M. 2011. Characterization of uninorms on bounded lattices and pre-order they induce. International Journal of Computational In-telligence Systems 14(1), 148–158.
  • [17] İnce MA., Karaçal F. 2023. Determination of the smallest-greatest uni-nullnorms and null-uninorms on an arbitrary bounded lattice L. Inter-national Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 31(1), 103–119.
  • [18] Jiang DX., Liu HW. 2024. Migrativity of uninorms not internal on the boundary over continuous t-(co)norms. Iranian Journal of Fuzzy Systems 21(3), 103–121.
  • [19] ] Jocic D., Stajner-Papuga I. 2023. Distributivity of a uni-nullnorm with continuous and Archimedean underlying T-norms and T-conorms over an arbi-trary uninorm. Mathematica Slovaca 73(6), 1527–1544.
  • [20] Karaçal F., Ertuğrul U., Arpacı S., Kesicioğlu MN. 2023. Congruence relations and direct decomposi-tion of uninorms on bounded lattices. Interna-tional Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 31(6), 1033–1059.
  • [21] Karaçal F., Ertuğrul U., Kesicioğlu M. 2021. Gener-ating methods for principal topologies on bound-ed lattices. Kybernetika 57(4), 714-736.
  • [22] Karaçal F., Köroğlu T. 2022. A principal topology obtained from uninorms. Kybernetika 58(6), 863–882.
  • [23] Khatami SMA., Mirzavaziri M. 2020. Yet another generalization of the notion of a metric space. arXiv preprint. arXiv:2009.00943
  • [24] Mesiarova-Zemankova A., Mesiar R., Su Y., Wang ZD. 2024. Idempotent uninorms on bounded lat-tices with at most single point incomparable with the neutral element: Part I. International Journal of General Systems 1-34.
  • [25] Ouyang Y., Zhang HP., De Baets B. 2024. Decom-position and construction of uninorms on the unit interval. Fuzzy Sets and Systems 493–494, 109083.
  • [26] Wang SM. 2019. The logic of pseudo-uninorms and their residua, Symmetry 11(3), 368-380.
  • [27] Wen H., Wu X., Çaylı GD. 2023. Characterizing some types of uninorms on bounded lattices. In-ternational Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 31(4), 533–549.
  • [28] Xie A., Zhang JQ. 2024. On modularity property for uninorms with continuous underlying functions. Iranian Journal of Fuzzy Systems 21(2), 105–116.
  • [29] Yang E. 2021. Micanorm aggregation operators: basic logico-algebraic properties. Soft Computing 25, 13167–13180.
  • [30] Yang B., Lı W., Liu YH., Xu J. 2023. The distributiv-ity of extended semi-t-operators over extended S-uninorms on fuzzy truth values. Soft Computing 28(4), 2823–2841.
  • [31] Zhang HP., Ouyang Y., De Baets B. 2021. Construc-tions of uni-nullnorms and null-uninorms on a bounded lattice. Fuzzy Sets and Systems 403, 78–87.
  • [32] Zong WW., Su Y., Liu HW. 2024. Conditionally distributive uninorms locally internal on the boundary. Semigroup Forum 1–9.

Unibelirleyici

Yıl 2025, Cilt: 29 Sayı: 1, 220 - 227, 25.04.2025

Selim Çetin

https://doi.org/10.19113/sdufenbed.1666339

Öz

Bu çalışmada, hem t-belirleyici (t-definer) hem de t-eşbelirleyici (t-codefiner) yapılarını kapsayan birleşik bir çerçeve sağlayan ve [0,∞]aralığında tanımlanan unibelirleyici (unidefiner) kavramını incelemekteyiz. [0,1]aralığında tanımlanan uninormlara benzer bir yaklaşımla, unibelirleyici, [0,∞] üzerinde tanımlı, değişmeli (komütatif), birleşmeli (assosiatif) ve monoton olan bir ikili işlemdir ve e∈[0,∞] olmak üzere birim (nötr) elemana sahiptir. Buna bağlı olarak, e=0 durumunda bir t-belirleyici, e=∞ durumunda ise bir t-eşbelirleyici elde edilir. Bu çalışma, unibelirleyicilerin teorik özelliklerini ele almakta ve t-belirleyici ile t-eşbelirleyici yapılarla olan ilişkilerini incelemektedir. Sonuç olarak, unibelirleyicilerin, [0,∞] aralığında uygun bir birim değeri (e ≠ 0,e ≠ ∞) seçildiğinde, uninormlara benzer şekilde "genelleştirilmiş bir bağlayıcı" olarak işlev görebileceği vurgulanmaktadır.

Anahtar Kelimeler

Unibelirleyici t-belirleyici t-eşbelirleyici birim eleman monoid

Kaynakça

  • [1] Aşıcı E., Mesiar R. 2021. On the direct product of uninorms on bounded lattices. Kybernetika 57(6), 989–1004
  • [2] Aşıcı E., Mesiar R. 2024. Some investigations on the U-partial order induced by uninorms. Aequa-tiones mathematicae 1-14.
  • [3] Cao M., Du WS. 2023. On residual implications derived from 2-uninorms. International Journal of Approximate Reasoning 159, 108926.
  • [4] Çaylı GD. 2023. An alternative construction of uninorms on bounded lattices. International Journal of General Systems 52(5), 574–596.
  • [5] Çaylı GD. 2024. Constructing uninorms on bounded lattices through closure and interior op-erators. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 32(1), 109–129.
  • [6] Çaylı GD., Ertuğrul U., Karaçal F. 2023. Some fur-ther construction methods for uninorms on bounded lattices. International Journal of General Systems 52(4), 414–442.
  • [7] Csiszar O, Pusztahazi LS., Denes-Fazakas L., Gashler MS., Kreinovich V, Csisz´ar G. 2023. Un-inorm-like parametric activation functions for human-understandable neural models. Knowledge-Based Systems 260, 110095.
  • [8] Dan Y. 2023. A unified way to studies of t-seminorms, t-semiconorms and semi-uninorms on a complete lattice in terms of behaviour oper-ations. International Journal of Approximate Rea-soning 156, 61–76.
  • [9] Dan Y., Hu BQ., De Baets B. 2022. Nullnorms on bounded lattices constructed by means of closure and interior operators. Fuzzy Sets and Systems 439, 142–156.
  • [10] De Campos Souza PV., Lughofer E. 2022. An ad-vanced interpretable fuzzy neural network model based on uni-nullneuron constructed from n-uninorms. Fuzzy Sets and Systems 426, 1–26.
  • [11] Dvorak A., Holcapek M., Paseka J. 2022. On ordi-nal sums of partially ordered monoids: A unified approach to ordinal sum constructions of t-norms, t-conorms and uninorms. Fuzzy Sets and Systems 446, 4–25.
  • [12] Fodor J., De Baets B. 2007. Uninorm basics. In Fuzzy Logic: A Spectrum of Theoretical & Practical Issues 49–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 15s.
  • [13] Fodor JC., Yager RR., Rybalov A. 1997. Structure of uninorms. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 5(4), 411–427.
  • [14] Gürdal U., Oğur O., Çetin S. Unima on [0,1]. Manu-script submitted for publication.
  • [15] He SY., Xie LH., Yan PF. 2022. On ⋆-metric spaces. Filomat 36(18), 6173–6185.
  • [16] Hlinena D., Kalina M. 2011. Characterization of uninorms on bounded lattices and pre-order they induce. International Journal of Computational In-telligence Systems 14(1), 148–158.
  • [17] İnce MA., Karaçal F. 2023. Determination of the smallest-greatest uni-nullnorms and null-uninorms on an arbitrary bounded lattice L. Inter-national Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 31(1), 103–119.
  • [18] Jiang DX., Liu HW. 2024. Migrativity of uninorms not internal on the boundary over continuous t-(co)norms. Iranian Journal of Fuzzy Systems 21(3), 103–121.
  • [19] ] Jocic D., Stajner-Papuga I. 2023. Distributivity of a uni-nullnorm with continuous and Archimedean underlying T-norms and T-conorms over an arbi-trary uninorm. Mathematica Slovaca 73(6), 1527–1544.
  • [20] Karaçal F., Ertuğrul U., Arpacı S., Kesicioğlu MN. 2023. Congruence relations and direct decomposi-tion of uninorms on bounded lattices. Interna-tional Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 31(6), 1033–1059.
  • [21] Karaçal F., Ertuğrul U., Kesicioğlu M. 2021. Gener-ating methods for principal topologies on bound-ed lattices. Kybernetika 57(4), 714-736.
  • [22] Karaçal F., Köroğlu T. 2022. A principal topology obtained from uninorms. Kybernetika 58(6), 863–882.
  • [23] Khatami SMA., Mirzavaziri M. 2020. Yet another generalization of the notion of a metric space. arXiv preprint. arXiv:2009.00943
  • [24] Mesiarova-Zemankova A., Mesiar R., Su Y., Wang ZD. 2024. Idempotent uninorms on bounded lat-tices with at most single point incomparable with the neutral element: Part I. International Journal of General Systems 1-34.
  • [25] Ouyang Y., Zhang HP., De Baets B. 2024. Decom-position and construction of uninorms on the unit interval. Fuzzy Sets and Systems 493–494, 109083.
  • [26] Wang SM. 2019. The logic of pseudo-uninorms and their residua, Symmetry 11(3), 368-380.
  • [27] Wen H., Wu X., Çaylı GD. 2023. Characterizing some types of uninorms on bounded lattices. In-ternational Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 31(4), 533–549.
  • [28] Xie A., Zhang JQ. 2024. On modularity property for uninorms with continuous underlying functions. Iranian Journal of Fuzzy Systems 21(2), 105–116.
  • [29] Yang E. 2021. Micanorm aggregation operators: basic logico-algebraic properties. Soft Computing 25, 13167–13180.
  • [30] Yang B., Lı W., Liu YH., Xu J. 2023. The distributiv-ity of extended semi-t-operators over extended S-uninorms on fuzzy truth values. Soft Computing 28(4), 2823–2841.
  • [31] Zhang HP., Ouyang Y., De Baets B. 2021. Construc-tions of uni-nullnorms and null-uninorms on a bounded lattice. Fuzzy Sets and Systems 403, 78–87.
  • [32] Zong WW., Su Y., Liu HW. 2024. Conditionally distributive uninorms locally internal on the boundary. Semigroup Forum 1–9.
Toplam 32 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Sayısal Analiz, Matematiksel Mantık, Kümeler Teorisi, Kafesler ve Evrensel Cebir, Uygulamalı Matematik (Diğer)
Bölüm Makaleler
Yazarlar

Selim Çetin 0000-0002-9017-1465

Yayımlanma Tarihi 25 Nisan 2025
Gönderilme Tarihi 26 Mart 2025
Kabul Tarihi 12 Nisan 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 29 Sayı: 1

Kaynak Göster

APA Çetin, S. (2025). Unidefiners. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 29(1), 220-227. https://doi.org/10.19113/sdufenbed.1666339
AMA Çetin S. Unidefiners. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. Nisan 2025;29(1):220-227. doi:10.19113/sdufenbed.1666339
Chicago Çetin, Selim. “Unidefiners”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 29, sy. 1 (Nisan 2025): 220-27. https://doi.org/10.19113/sdufenbed.1666339.
EndNote Çetin S (01 Nisan 2025) Unidefiners. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 29 1 220–227.
IEEE S. Çetin, “Unidefiners”, Süleyman Demirel Üniv. Fen Bilim. Enst. Derg., c. 29, sy. 1, ss. 220–227, 2025, doi: 10.19113/sdufenbed.1666339.
ISNAD Çetin, Selim. “Unidefiners”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 29/1 (Nisan 2025), 220-227. https://doi.org/10.19113/sdufenbed.1666339.
JAMA Çetin S. Unidefiners. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2025;29:220–227.
MLA Çetin, Selim. “Unidefiners”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 29, sy. 1, 2025, ss. 220-7, doi:10.19113/sdufenbed.1666339.
Vancouver Çetin S. Unidefiners. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2025;29(1):220-7.
 Kapak Resmi İndir

e-ISSN :1308-6529
Linking ISSN (ISSN-L): 1300-7688

Dergide yayımlanan tüm makalelere ücretiz olarak erişilebilinir ve Creative Commons CC BY-NC Atıf-GayriTicari lisansı ile açık erişime sunulur. Tüm yazarlar ve diğer dergi kullanıcıları bu durumu kabul etmiş sayılırlar. CC BY-NC lisansı hakkında detaylı bilgiye erişmek için tıklayınız.