Soft Neutrosophic Modules

In this study, for the first time, we study some basic definitions of soft neutrosophic modules in algebra being generalized and its several related properties, structural characteristics are investigated with suitable examples. In this paper, we utilized neutrosophic soft sets and neutrosophic modules. As a result, we defined soft neutrosophic modules. After weak soft neutrosophic modules and strong soft neutrosophic modules are described and illustrated by examples. Finally soft neutrosophic module homomorphism is defined and soft neutrosophic module isomorphism is explained.

[1]  Naim Çagman,et al.  Soft sets and soft groups , 2007, Inf. Sci..

[2]  Generalized Fuzzy σ - Algebra and Generalized Fuzzy Measure on Soft Sets , 2016 .

[3]  Shabir Muhammad,et al.  Soft Neutrosophic Group , 2013 .

[4]  Bekir Tanay,et al.  Computers and Mathematics with Applications , 2022 .

[5]  F. Smarandache,et al.  Generalization of Soft Neutrosophic Rings and Soft Neutrosophic Fields , 2014 .

[6]  Nasruddin Hassan,et al.  Generalized Neutrosophic Soft Expert Set for Multiple-Criteria Decision-Making , 2018, Symmetry.

[7]  F. Smarandache,et al.  Neutrosophic Triplet G-Module , 2018 .

[8]  Mehmet Sahin,et al.  Similarity measures of bipolar neutrosophic sets and their application to multiple criteria decision making , 2018, Neural Computing and Applications.

[9]  Mehmet Sahin,et al.  Isomorphism theorems for soft G-modules , 2018, Afrika Matematika.

[10]  A. Kılıçman,et al.  On neutrosophic soft lattices , 2017 .

[11]  F. Smarandache,et al.  Neutrosophic Rings , 2006, math/0607765.

[12]  Jing Liu,et al.  Soft Sets and Soft Modules , 2008, RSKT.

[13]  A. R. Roy,et al.  Soft set theory , 2003 .

[14]  F. Smarandache,et al.  Soft Nuetrosophic Ring and Soft Neutrosophic Field , 2014 .

[15]  Mehmet Sahin,et al.  Normed quotient rings , 2018 .

[16]  D. Molodtsov Soft set theory—First results , 1999 .

[17]  N. K. Mahapatra,et al.  On Neutrosophic Soft Linear Spaces , 2017 .

[18]  Mehmet Şahin,et al.  Soft normed rings , 2016, SpringerPlus.

[19]  J. Baylis Steps in commutative algebra (2nd edn), by R. Y. Sharp. LMS Student Texts 51. Pp. 355. £17.95. 2000. ISBN 0 521 64623 5 (Cambridge University Press). , 2002, Mathematical Gazette.

[20]  Necati Olgun,et al.  A New Type Fuzzy Module over Fuzzy Rings , 2014, TheScientificWorldJournal.

[21]  Mehmet Sahin,et al.  Q-Neutrosophic Soft Expert Set and its Application in Decision Making , 2018, Int. J. Fuzzy Syst. Appl..