Some harmonic aggregation operators for N-valued neutrosophic trapezoidal numbers and their application to multi-criteria decision-making
As an extension of the both trapezoidal fuzzy numbers and neutrosophic trapezoidal numbers, the N-valued neutrosophic trapezoidal numbers, which are special neutrosophic multi-sets on subset of real numbers. Harmonic mean is a conservative average, which is widely used to aggregate central tendency...
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| Format: | Article |
| Language: | English |
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University of New Mexico
2025-04-01
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| Series: | Neutrosophic Sets and Systems |
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| Online Access: | https://fs.unm.edu/NSS/20HarmonicAggregation.pdf |
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| author | İrfan DELİ Vakkas ULUÇAY |
| author_facet | İrfan DELİ Vakkas ULUÇAY |
| author_sort | İrfan DELİ |
| collection | DOAJ |
| description | As an extension of the both trapezoidal fuzzy numbers and neutrosophic trapezoidal numbers, the N-valued neutrosophic trapezoidal numbers, which are special neutrosophic multi-sets on subset of real numbers. Harmonic mean is a conservative average, which is widely used to aggregate central tendency data. In the existing literature, the harmonic mean is generally considered as a fusion technique of numerical data information. In this paper, we investigate a method for the situations in which the input data are expressed in neutrosophic values. Therefore, we propose two aggregations are called harmonic aggregation operators and weighted harmonic mean operators on N-valued neutrosophic trapezoidal numbers. We also proved some desired properties such as idempotency, monotoniticy, commutativity and boundedness of the developed operators. Moreover, we developed an algorithm by defining a score function under N-valued neutrosophic trapezoidal numbers to compare the N-valued neutrosophic trapezoidal numbers. Finally, we gave an illustrative example, using the proposed aggregation operators to rank the alternatives with N-valued neutrosophic trapezoidal numbers. |
| format | Article |
| id | doaj-art-e7d48db4466f4dbd8e75f1c47f870935 |
| institution | Kabale University |
| issn | 2331-6055 2331-608X |
| language | English |
| publishDate | 2025-04-01 |
| publisher | University of New Mexico |
| record_format | Article |
| series | Neutrosophic Sets and Systems |
| spelling | doaj-art-e7d48db4466f4dbd8e75f1c47f8709352025-08-20T03:47:17ZengUniversity of New MexicoNeutrosophic Sets and Systems2331-60552331-608X2025-04-017935537510.5281/zenodo.14538076Some harmonic aggregation operators for N-valued neutrosophic trapezoidal numbers and their application to multi-criteria decision-makingİrfan DELİ Vakkas ULUÇAYAs an extension of the both trapezoidal fuzzy numbers and neutrosophic trapezoidal numbers, the N-valued neutrosophic trapezoidal numbers, which are special neutrosophic multi-sets on subset of real numbers. Harmonic mean is a conservative average, which is widely used to aggregate central tendency data. In the existing literature, the harmonic mean is generally considered as a fusion technique of numerical data information. In this paper, we investigate a method for the situations in which the input data are expressed in neutrosophic values. Therefore, we propose two aggregations are called harmonic aggregation operators and weighted harmonic mean operators on N-valued neutrosophic trapezoidal numbers. We also proved some desired properties such as idempotency, monotoniticy, commutativity and boundedness of the developed operators. Moreover, we developed an algorithm by defining a score function under N-valued neutrosophic trapezoidal numbers to compare the N-valued neutrosophic trapezoidal numbers. Finally, we gave an illustrative example, using the proposed aggregation operators to rank the alternatives with N-valued neutrosophic trapezoidal numbers.https://fs.unm.edu/NSS/20HarmonicAggregation.pdfneutrosophic setsneutrosophic multi-setsn-valued neutrosophic trapezoidal numbersscore degreesaccuracy degreesmulti-criteria decision-making |
| spellingShingle | İrfan DELİ Vakkas ULUÇAY Some harmonic aggregation operators for N-valued neutrosophic trapezoidal numbers and their application to multi-criteria decision-making Neutrosophic Sets and Systems neutrosophic sets neutrosophic multi-sets n-valued neutrosophic trapezoidal numbers score degrees accuracy degrees multi-criteria decision-making |
| title | Some harmonic aggregation operators for N-valued neutrosophic trapezoidal numbers and their application to multi-criteria decision-making |
| title_full | Some harmonic aggregation operators for N-valued neutrosophic trapezoidal numbers and their application to multi-criteria decision-making |
| title_fullStr | Some harmonic aggregation operators for N-valued neutrosophic trapezoidal numbers and their application to multi-criteria decision-making |
| title_full_unstemmed | Some harmonic aggregation operators for N-valued neutrosophic trapezoidal numbers and their application to multi-criteria decision-making |
| title_short | Some harmonic aggregation operators for N-valued neutrosophic trapezoidal numbers and their application to multi-criteria decision-making |
| title_sort | some harmonic aggregation operators for n valued neutrosophic trapezoidal numbers and their application to multi criteria decision making |
| topic | neutrosophic sets neutrosophic multi-sets n-valued neutrosophic trapezoidal numbers score degrees accuracy degrees multi-criteria decision-making |
| url | https://fs.unm.edu/NSS/20HarmonicAggregation.pdf |
| work_keys_str_mv | AT irfandeli someharmonicaggregationoperatorsfornvaluedneutrosophictrapezoidalnumbersandtheirapplicationtomulticriteriadecisionmaking AT vakkasulucay someharmonicaggregationoperatorsfornvaluedneutrosophictrapezoidalnumbersandtheirapplicationtomulticriteriadecisionmaking |