Fuzzy Parameterized Fuzzy Soft Measure Spaces

Deniz Fidan; Serdar Enginoğlu

doi:10.32323/ujma.1970388

Fuzzy Parameterized Fuzzy Soft Measure Spaces

Abstract

This study first defines some families of fuzzy parameterized fuzzy soft sets (fpfs-sets) such as fpfs-rings, fpfs-$\sigma$-rings, fpfs-algebras, fpfs-$\sigma$-algebras, fpfs-$\pi$-systems, and fpfs-$\lambda$-systems. It also investigates some fundamental properties of these fpfs-set families and analyzes their relations with each other. Then, this study proposes the concept of fpfs-pre-measures based on fpfs-$\sigma$-rings and exemplifies them. Subsequently, it defines fpfs-measures based on fpfs-$\sigma$-algebras, illustrates them by examples, and studies some of their basic properties. Moreover, this article propounds several types of functions, defined from an fpfs-$\sigma$-algebra to the extended real numbers and referred to as additive, finitely additive, null additive, subadditive, subtractive, and so on, and investigates some of their basic properties. Afterward, it suggests fpfs-outer measures, exemplifies them, and explores some of their essential properties. Furthermore, this article offers $m^*$-fpfs-measability and analyzes some of its key properties. Finally, it addresses whether further research into these aspects is warranted.

Keywords

fpfs-sets, fpfs-$\sigma$-algebras, fpfs-measures, fpfs-outer measures, $m^*$-fpfs-measurable sets

Supporting Institution

Çanakkale Onsekiz Mart University

Project Number

FYL-2023-4546

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Deniz Fidan
0000-0002-5020-1682
Türkiye

Serdar Enginoğlu ^*
0000-0002-7188-9893
Türkiye

Early Pub Date

September 12, 2026

Publication Date

September 13, 2026

Submission Date

June 13, 2026

Acceptance Date

September 9, 2026

Published in Issue

Year 2026 Volume: 9 Number: 3

DOI

https://doi.org/10.32323/ujma.1970388

IZ

https://izlik.org/JA62MB74FU

APA

Fidan, D., & Enginoğlu, S. (2026). Fuzzy Parameterized Fuzzy Soft Measure Spaces. Universal Journal of Mathematics and Applications, 9(3), 203-231. https://doi.org/10.32323/ujma.1970388

AMA

1.Fidan D, Enginoğlu S. Fuzzy Parameterized Fuzzy Soft Measure Spaces. Univ. J. Math. Appl. 2026;9(3):203-231. doi:10.32323/ujma.1970388

Chicago

Fidan, Deniz, and Serdar Enginoğlu. 2026. “Fuzzy Parameterized Fuzzy Soft Measure Spaces”. Universal Journal of Mathematics and Applications 9 (3): 203-31. https://doi.org/10.32323/ujma.1970388.

EndNote

Fidan D, Enginoğlu S (September 1, 2026) Fuzzy Parameterized Fuzzy Soft Measure Spaces. Universal Journal of Mathematics and Applications 9 3 203–231.

IEEE

[1]D. Fidan and S. Enginoğlu, “Fuzzy Parameterized Fuzzy Soft Measure Spaces”, Univ. J. Math. Appl., vol. 9, no. 3, pp. 203–231, Sept. 2026, doi: 10.32323/ujma.1970388.

ISNAD

Fidan, Deniz - Enginoğlu, Serdar. “Fuzzy Parameterized Fuzzy Soft Measure Spaces”. Universal Journal of Mathematics and Applications 9/3 (September 1, 2026): 203-231. https://doi.org/10.32323/ujma.1970388.

JAMA

1.Fidan D, Enginoğlu S. Fuzzy Parameterized Fuzzy Soft Measure Spaces. Univ. J. Math. Appl. 2026;9:203–231.

MLA

Fidan, Deniz, and Serdar Enginoğlu. “Fuzzy Parameterized Fuzzy Soft Measure Spaces”. Universal Journal of Mathematics and Applications, vol. 9, no. 3, Sept. 2026, pp. 203-31, doi:10.32323/ujma.1970388.

Vancouver

1.Deniz Fidan, Serdar Enginoğlu. Fuzzy Parameterized Fuzzy Soft Measure Spaces. Univ. J. Math. Appl. 2026 Sep. 1;9(3):203-31. doi:10.32323/ujma.1970388

Universal Journal of Mathematics and Applications

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Fuzzy Parameterized Fuzzy Soft Measure Spaces

Abstract

Keywords

Supporting Institution

Project Number

References

Details

Primary Language

Subjects

Journal Section

Authors

Early Pub Date

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

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