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Title: A study on doubt fuzzy BCK/BCI-algebras and other algebraic structures
Authors: Bej, Tripti
Pal, Madhumangal
Keywords: Doubt intuitionistic fuzzy ideal
Doubt interval-valued fuzzy ideal
Doubt intuitionistic fuzzy hyper filter
Hyper BE-algebra
Issue Date: 8-Jan-2020
Publisher: Department of Applied Mathematics with Oceanology and computer Programming , Vidyasagar University , Midnapore , West Bengal , India
Abstract: Fuzzy set theories provide strict mathematical frameworks using vague phenomena and can be precisely and rigorously studied. The core theories in mathematics such as algebra, topology, lattices and analysis are subject to fuzzi cation. Many researchers have dealt with subalgebras, ideals, subimplicative ideals, P-ideals, H-ideals, implica- tive ideals, hyper structure etc. and their fuzzi cation. This study attempts to introduce a new class of algebraic structures in intuitionis- tic fuzzy set and interval-valued fuzzy set. The concepts of doubt intuitionistic fuzzy subalgebra/ideals, doubt intuitionistic fuzzy H-ideals, doubt intuitionistic fuzzy sub- implicative ideals, doubt intuitionistic fuzzy P-ideals and doubt intuitionistic fuzzy translations of doubt intuitionistic fuzzy sub-implicative ideals are introduced for BCK/BCI-algebra and their properties are duly characterized. The notion of direct product of two doubt intuitionistic fuzzy subalgebras and two doubt intuitionistic fuzzy H-ideals of two BCK/BCI-algebras has also been discussed and some related properties have investigated. We have also found that the direct product of two intuitionistic fuzzy sets becomes doubt intuitionistic fuzzy H-ideals and doubt intuitionistic fuzzy subalgebras if and only if for any t; s 2 [0; 1], upper and lower level sets are H-ideals or subalgebras of BCK/BCI algebra X Y . Results of doubt interval-valued fuzzy subalgebras and doubt interval-valued fuzzy ideals in BCK-algebras and BF-algebras are also provided. Cartesian product of two interval-valued fuzzy sets is de ned and its properties are established. The relation between doubt intuitionistic fuzzy ideals and an upper level and lower level cuts of BCK/BCI-algebra have also been explored. Besides doubt intuitionistic fuzzy hyper lters in hyper BE-algebras have also been established in the present work.
Appears in Collections:Applied Mathematics with Oceanology and Computer Programming - Ph.D

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01_Title.pdf75.37 kBAdobe PDFView/Open
02_declaration.pdf190.12 kBAdobe PDFView/Open
03_certificate.pdf58.6 kBAdobe PDFView/Open
04_Acknowledgement.pdf113.16 kBAdobe PDFView/Open
05_Content.pdf97.69 kBAdobe PDFView/Open
06_Chapter1.pdf268.09 kBAdobe PDFView/Open
07_Chapter2.pdf336.51 kBAdobe PDFView/Open
08_Chapter3.pdf362.81 kBAdobe PDFView/Open
09_Chapter4.pdf338.47 kBAdobe PDFView/Open
10_Chapter5.pdf274.48 kBAdobe PDFView/Open
11_Chapter6.pdf319 kBAdobe PDFView/Open
12_Chapter7.pdf302.64 kBAdobe PDFView/Open
13_Chapter8.pdf275.58 kBAdobe PDFView/Open
14_Conclusion.pdf126.96 kBAdobe PDFView/Open
15_Bibliography.pdf146.2 kBAdobe PDFView/Open

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