Öz
Bulanık mantık, hem uygulama hem de cebirsel alanlarda klasik yapılara alternatif olarak kullanılan bir teoridir. Sabit nokta teoremi, matematikte özellikle metrik uzaylarda ve kısmi metrik uzaylarda yaygın olarak kullanılan bir teoremdir. Sabit nokta teoremi klasik metrik yapılar üzerinde kullanılmakla birlikte, bulanık metrik uzaylar, bulanık kısmi metrik uzaylar ve sezgisel bulanık metrik uzaylar üzerinde de yaygın olarak kullanılmaktadır. Bu çalışmada, sezgisel bulanık kısmi metrik uzaylar tanımlanmış, temel özellikleri ve örnekleri elde edilmiştir. Bunun için açık küre, yakınsak dizi ve Cauchy dizisi tanımlanmış ve temel özellikleri tanıtılmıştır. Ayrıca, sezgisel bulanık kısmi metrik uzaylar, klasik metrik uzaylar, bulanık metrik uzaylar, bulanık kısmi metrik uzaylar ve sezgisel bulanık metrik uzaylar arasındaki ilişkiler incelenmiştir. Bu inceleme sonucunda, her bir klasik metrik, klasik kısmi metrik ve sezgisel bulanık metrikten bir sezgisel bulanık kısmi metrik elde edilebileceği gösterilmiştir. Ayrıca, bir sezgisel bulanık metriğin aynı zamanda bir sezgisel bulanık kısmi metrik uzay olduğu elde edilmiştir. Böylece kısmi metrik yapısı sezgisel bulanık metrik uzaylara aktarılarak yeni bir yapı verilmiştir.
Anahtar Kelimeler
Kısmi Metrik Uzaylar Bulanık Metrik Uzaylar Bulanık Kısmi Metrik Uzaylar Sezgisel Bulanık Metrik Uzaylar Sezgisel Bulanık Kısmi Metrik Uzaylar
Kaynakça
- Matthews, S.G., Partial metric topology, Annals of the New York Academy of Sciences, 728(1), 183–197, 1994.
- Zadeh, L.A., Fuzzy sets, Information and Control, 8(3), 338–353, 1965.
- Emniyet, A., & Şahin, M., Fuzzy normed rings, Symmetry, 10(10), 515, 2018.
- Kum, G., Sönmez, M.E., & Kargın, A., An Alternative Process for Determining Erosion Risk: The Fuzzy Method, Coğrafya Dergisi, 44, 219–229, 2022.
- Wang, D., Yuan, Y., Liu, Z., Zhu, S., & Sun, Z., Novel Distance Measures of q-Rung Orthopair Fuzzy Sets and Their Applications, Symmetry, 16(5), 574, 2024.
- Xu, K., & Wang, Y., A Novel Fuzzy Bi-Clustering Algorithm with Axiomatic Fuzzy Set for Identification of Co-Regulated Genes, Mathematics, 12(11), 1659, 2024.
- Plebankiewicz, E., & Karcińska, P., Model for supporting construction workforce planning based on the theory of fuzzy sets, Applied Sciences, 14(4), 1655, 2024.
- Kramosil, I., & Michálek, J., Fuzzy metrics and statistical metric spaces, Kybernetika, 11(5), 336–344, 1975.
- Grabiec, M., Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems. 27, 385–389, 1989.
- Shukla, S., Dubey, N., & Miñana, J.J., Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems, Axioms, 13(4), 252, 2024.
- Gregori, V., Miñana, J.J., Roig, B., & Sapena, A., On Completeness and Fixed Point Theorems in Fuzzy Metric Spaces, Mathematics, 12(2), 287, 2024.
- Huang, H., Properties of several metric spaces of fuzzy sets. Fuzzy Sets and Systems. 475, 108745, 2024.
- Olgun, N., Şahin, M., Kargın, A., and Uluçay, V., “Fuzzy generalized Meir-Keeler-type contraction on fuzzy partial metric space”, in Proceedings of the Eighth International Conference on Soft Computing, Computing with Words and Perceptions in System Analysis, Decision and Control, 2015.
- Gregori, V., Minana, J.J., Miravet, D. Fuzzy partial metric spaces, International Journal of General Systems, 48, 260–279, 2019.
- Amer, F. J., “Fuzzy partial metric spaces”, in Proceedings of the Computational Analysis:AMAT, Selected Contributions, Springer International Publishing, 185–191, 2016.
- Aygün, H., Güner, E., Miñana, J.J., & Valero, O., Fuzzy partial metric spaces and fixed point theorems, Mathematics, 10(17), 3092, 2022.
- Gregori, V., Miñana, J.J., & Miravet, D., A duality relationship between fuzzy partial metrics and fuzzy quasi-metrics, Mathematics, 8(9), 1575, 2020.
- Atanassov, T.K., Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20, 87–96, 1986.
- Ngan, S.C., An extension framework for creating operators and functions for intuitionistic fuzzy sets, Information Sciences, 666, 120336, 2024.
- Gerogiannis, V. C., Tzimos, D., Kakarontzas, G., Tsoni, E., Iatrellis, O., Son, L.H., et al., An Approach Based on Intuitionistic Fuzzy Sets for Considering Stakeholders’ Satisfaction, Dissatisfaction, and Hesitation in Software Features Prioritization, Mathematics, 12(5), 680, 2024.
- Rajafillah, C., El Moutaouakil, K., Patriciu, A.M., Yahyaouy, A., & Riffi, J., INT-FUP: Intuitionistic Fuzzy Pooling, Mathematics, 12(11), 1740, 2024.
- Park, J.H., Intuitionistic fuzzy metric spaces, Chaos, Solitons Fractals, 22(5), 1039–1046, 2004.
- Alaca, C., Turkoglu, D., & Yildiz, C., Fixed points in intuitionistic fuzzy metric spaces, Chaos, Solitons Fractals, 29(5), 1073–1078, 2006.
- Gregori, V., Romaguera, S., & Veeramani, P., A note on intuitionistic fuzzy metric spaces, Chaos, Solitons Fractals, 28(4), 902–905, 2006.
- Rahmat, R.S., & Noorani, S.M., Fixed point theorem on intuitionistic fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 3(1), 23–29, 2006.
- Saadati, R., Sedghi, S., & Shobe, N., Modified intuitionistic fuzzy metric spaces and some fixed point theorems, Chaos, Solitons Fractals, 38(1), 36–47, 2008.
- Wong, K. S., Salleh, Z., & Akhadkulov, H., Exploring Fixed Points and Common Fixed Points of Contractive Mappings in Complex-Valued Intuitionistic Fuzzy Metric Spaces, International Journal of Analysis and Applications, 22, 91–91, 2024.
- Singh, R.M., Singh, D., & Gourh, R., Approach to fuzzy differential equations in Intuitionistic fuzzy metric spaces using generalized contraction theorems, Journal of Hyperstructures, 13(1), 109-123, 2024.
- Schweizer B, Sklar A., Statistical metric spaces, Pacific Journal of Mathematics, 10, 314–340, 1960.
Öz
Fuzzy logic is a theory that is used as an alternative to classical structures in both application and algebraic fields. The fixed point theorem is a theorem widely used in mathematics, especially in metric spaces and partial metric spaces. The fixed point theorem is used on classical metric structures, but it is also widely used on fuzzy metric spaces, fuzzy partial metric spaces and intuitionistic fuzzy metric spaces. In this paper, intuitionistic fuzzy partial metric spaces are defined, their basic properties and examples are obtained. For it, open ball, convergent sequence, and Cauchy sequence are defined and their basic properties are introduced. Furthermore, the relations between intuitionistic fuzzy partial metric spaces, classical metric spaces, fuzzy metric spaces, fuzzy partial metric spaces, and intuitionistic fuzzy metric spaces are analyzed. As a result of this investigation, it is shown that from each classical metric, classical partial metric, and intuitionistic fuzzy metric, an intuitionistic fuzzy partial metric can be obtained. Moreover, it is achieved that an intuitionistic fuzzy metric is also an intuitionistic fuzzy partial metric space. Thus, a new structure is given by transferring the partial metric structure to intuitionistic fuzzy metric spaces.
Anahtar Kelimeler
Metric Spaces Partial Metric Spaces Fuzzy Metric Spaces Fuzzy Partial Metric Spaces Intuitionistic Fuzzy Metric Spaces Intuitionistic Fuzzy Partial Metric Spaces.
Kaynakça
- Matthews, S.G., Partial metric topology, Annals of the New York Academy of Sciences, 728(1), 183–197, 1994.
- Zadeh, L.A., Fuzzy sets, Information and Control, 8(3), 338–353, 1965.
- Emniyet, A., & Şahin, M., Fuzzy normed rings, Symmetry, 10(10), 515, 2018.
- Kum, G., Sönmez, M.E., & Kargın, A., An Alternative Process for Determining Erosion Risk: The Fuzzy Method, Coğrafya Dergisi, 44, 219–229, 2022.
- Wang, D., Yuan, Y., Liu, Z., Zhu, S., & Sun, Z., Novel Distance Measures of q-Rung Orthopair Fuzzy Sets and Their Applications, Symmetry, 16(5), 574, 2024.
- Xu, K., & Wang, Y., A Novel Fuzzy Bi-Clustering Algorithm with Axiomatic Fuzzy Set for Identification of Co-Regulated Genes, Mathematics, 12(11), 1659, 2024.
- Plebankiewicz, E., & Karcińska, P., Model for supporting construction workforce planning based on the theory of fuzzy sets, Applied Sciences, 14(4), 1655, 2024.
- Kramosil, I., & Michálek, J., Fuzzy metrics and statistical metric spaces, Kybernetika, 11(5), 336–344, 1975.
- Grabiec, M., Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems. 27, 385–389, 1989.
- Shukla, S., Dubey, N., & Miñana, J.J., Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems, Axioms, 13(4), 252, 2024.
- Gregori, V., Miñana, J.J., Roig, B., & Sapena, A., On Completeness and Fixed Point Theorems in Fuzzy Metric Spaces, Mathematics, 12(2), 287, 2024.
- Huang, H., Properties of several metric spaces of fuzzy sets. Fuzzy Sets and Systems. 475, 108745, 2024.
- Olgun, N., Şahin, M., Kargın, A., and Uluçay, V., “Fuzzy generalized Meir-Keeler-type contraction on fuzzy partial metric space”, in Proceedings of the Eighth International Conference on Soft Computing, Computing with Words and Perceptions in System Analysis, Decision and Control, 2015.
- Gregori, V., Minana, J.J., Miravet, D. Fuzzy partial metric spaces, International Journal of General Systems, 48, 260–279, 2019.
- Amer, F. J., “Fuzzy partial metric spaces”, in Proceedings of the Computational Analysis:AMAT, Selected Contributions, Springer International Publishing, 185–191, 2016.
- Aygün, H., Güner, E., Miñana, J.J., & Valero, O., Fuzzy partial metric spaces and fixed point theorems, Mathematics, 10(17), 3092, 2022.
- Gregori, V., Miñana, J.J., & Miravet, D., A duality relationship between fuzzy partial metrics and fuzzy quasi-metrics, Mathematics, 8(9), 1575, 2020.
- Atanassov, T.K., Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20, 87–96, 1986.
- Ngan, S.C., An extension framework for creating operators and functions for intuitionistic fuzzy sets, Information Sciences, 666, 120336, 2024.
- Gerogiannis, V. C., Tzimos, D., Kakarontzas, G., Tsoni, E., Iatrellis, O., Son, L.H., et al., An Approach Based on Intuitionistic Fuzzy Sets for Considering Stakeholders’ Satisfaction, Dissatisfaction, and Hesitation in Software Features Prioritization, Mathematics, 12(5), 680, 2024.
- Rajafillah, C., El Moutaouakil, K., Patriciu, A.M., Yahyaouy, A., & Riffi, J., INT-FUP: Intuitionistic Fuzzy Pooling, Mathematics, 12(11), 1740, 2024.
- Park, J.H., Intuitionistic fuzzy metric spaces, Chaos, Solitons Fractals, 22(5), 1039–1046, 2004.
- Alaca, C., Turkoglu, D., & Yildiz, C., Fixed points in intuitionistic fuzzy metric spaces, Chaos, Solitons Fractals, 29(5), 1073–1078, 2006.
- Gregori, V., Romaguera, S., & Veeramani, P., A note on intuitionistic fuzzy metric spaces, Chaos, Solitons Fractals, 28(4), 902–905, 2006.
- Rahmat, R.S., & Noorani, S.M., Fixed point theorem on intuitionistic fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 3(1), 23–29, 2006.
- Saadati, R., Sedghi, S., & Shobe, N., Modified intuitionistic fuzzy metric spaces and some fixed point theorems, Chaos, Solitons Fractals, 38(1), 36–47, 2008.
- Wong, K. S., Salleh, Z., & Akhadkulov, H., Exploring Fixed Points and Common Fixed Points of Contractive Mappings in Complex-Valued Intuitionistic Fuzzy Metric Spaces, International Journal of Analysis and Applications, 22, 91–91, 2024.
- Singh, R.M., Singh, D., & Gourh, R., Approach to fuzzy differential equations in Intuitionistic fuzzy metric spaces using generalized contraction theorems, Journal of Hyperstructures, 13(1), 109-123, 2024.
- Schweizer B, Sklar A., Statistical metric spaces, Pacific Journal of Mathematics, 10, 314–340, 1960.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematiksel Mantık, Kümeler Teorisi, Kafesler ve Evrensel Cebir, Topoloji |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Temmuz 2025 |
| Gönderilme Tarihi | 7 Şubat 2025 |
| Kabul Tarihi | 20 Nisan 2025 |
| Yayımlandığı Sayı | Yıl 2025 Cilt: 15 Sayı: 1 |
Kaynak Göster
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