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http://hdl.handle.net/10603/323727
Title: | Fuzzy Structures on Z Algebras |
Researcher: | Sowmiya S |
Guide(s): | Jeyalakshmi P |
Keywords: | Physical Sciences Mathematics |
University: | Avinashilingam Deemed University For Women |
Completed Date: | 2020 |
Abstract: | In 1966, Imai and Iseki [25,26] introduced two new classes of abstract algebras: BCK-algebras and BCI-algebras. These algebras have been extensively studied since their introduction. In 2017, Chandramouleeswaran et al.[18] introduced the concept of Z-algebras as a new structure of algebra based on propositional calculus. The Z-algebra is not a generalization of BCK/BCI-algebras. In 1965, Zadeh[73] introduced the fundamental concept of a fuzzy set which is a generalization of an ordinary set. The fuzzy set theories developed by Zadeh and others are found many applications in the domain of mathematics and elsewhere. In 1971, Rosenfeld [65] introduced the notion of fuzzy groups. In 1991, following the idea of fuzzy groups, Xi[71] introduced the notion of fuzzy BCK-algebras. In 1994, Jun and Meng [32] introduced the notion of fuzzy p-ideals and in 1999, Khalid and Ahmad [40] introduced the concept of fuzzy H-ideals in BCI-algebras and studied their properties. In 1997, Meng et al. [49] and Mostafa [50] fuzzified the concept of implicative ideals in BCK-algebras, independently. In the year 2009, fuzzy translations and fuzzy multiplications in BCK/BCI-algebras have been discussed by Lee et al.[44]. newlineIn 1986, the idea of intuitionistic fuzzy set was first published by Atanassov [8], as a generalization of the notion of fuzzy set. In 1984, intuitionistic L-fuzzy set was introduced by Atanassov and Stoeva [11] as a generalization of L-fuzzy set. In 1975, Zadeh [74] introduced the notion of interval-valued fuzzy sets as an extension of fuzzy sets [73]. In 1989, K. T. Atanassov and G. Gargov [10] proposed interval-valued intuitionistic fuzzy set based on the comparative analysis of interval-valued fuzzy sets and intuitionistic fuzzy sets. Intuitively, the extension of intuitionistic fuzzy sets to interval-valued intuitionistic fuzzy sets furnishes additional capability to handle the vague information. In 2012, Jun et al. [36] have introduced a remarkable theory, namely, the theory of cubic sets. This structure is comprised |
Pagination: | 217 p. |
URI: | http://hdl.handle.net/10603/323727 |
Appears in Departments: | Department of Mathematics |
Files in This Item:
File | Description | Size | Format | |
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01_title.pdf | Attached File | 3.8 kB | Adobe PDF | View/Open |
02_certificate.pdf | 340.59 kB | Adobe PDF | View/Open | |
03_acknowledgement.pdf | 8.11 kB | Adobe PDF | View/Open | |
04_contents.pdf | 27.31 kB | Adobe PDF | View/Open | |
05_chapter 1.pdf | 942.29 kB | Adobe PDF | View/Open | |
06_chapter 2.pdf | 1.29 MB | Adobe PDF | View/Open | |
07_chapter 3.pdf | 968.09 kB | Adobe PDF | View/Open | |
08_chapter 4.pdf | 838.92 kB | Adobe PDF | View/Open | |
09_chapter 5.pdf | 1.25 MB | Adobe PDF | View/Open | |
10_chapter 6.pdf | 952.47 kB | Adobe PDF | View/Open | |
11_chapter 7.pdf | 950.45 kB | Adobe PDF | View/Open | |
12_chapter 8.pdf | 726.21 kB | Adobe PDF | View/Open | |
13_chapter 9.pdf | 791.49 kB | Adobe PDF | View/Open | |
14_chapter 10.pdf | 962.13 kB | Adobe PDF | View/Open | |
15_chapter 11.pdf | 842.68 kB | Adobe PDF | View/Open | |
16_chapter 12.pdf | 724.64 kB | Adobe PDF | View/Open | |
17_bibliography.pdf | 764.88 kB | Adobe PDF | View/Open | |
80_recommendation.pdf | 3.73 kB | Adobe PDF | View/Open |
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