FUZZY TRANSLATIONS OF A FUZZY SET IN UP-ALGEBRAS

Aiyared Iampan


Abstract


In this paper, we apply the concept of fuzzy translations of a fuzzy set to UP-algebras.For any fuzzy set $\mu$ in a UP-algebra,the concepts of fuzzy $\alpha$-translations of $\mu$ of type \textrm{I} and of fuzzy $\beta$-translations of $\mu$ of type \textrm{II} are introduced, their basic properties are investigated and some useful examples are discussed.The concepts of prime fuzzy sets and of weakly prime fuzzy sets in UP-algebras are also studied.Moreover, we discuss the concepts of extensions and of intensions of a fuzzy set in UP-algebras.

Keywords


UP-algebra, fuzzy set, fuzzy translation, extension, intension

References


bibitem{Akram2005}

Akram, M. and Dar, K.~H., {$t$-fuzzy ideals in {BCI}-algebras}, {em Internat. J.

Math. & Math. Sci.}, textbf{18} (2005), 1899-1907.

bibitem{Akram2007}

Akram, M. and Dar, K.~H., {Fuzzy ideals of {K}-algebras}, {em An. Univ. Craiova Ser. Mat.

Inform.}, textbf{34} (2007), 11-20.

bibitem{Ansari2014pp657}

Ansari, M.~A.~A. and Chandramouleeswaran, M., {Fuzzy translations of fuzzy

$beta$-ideals of $beta$-algebras}, {em Int. J. Pure Appl. Math.}, textbf{92}

(2014), no.~5, 657-667.

bibitem{Barbhuiya2016pp23}

Barbhuiya, S.~R., {Fuzzy translations and fuzzy multiplications of

interval-valued doubt fuzzy ideals of {BF}-algebras}, {em J. Inf. Optim. Sci.},

textbf{37} (2016,), no.~1, 23-36.

bibitem{Bhowmik2015pp1}

Bhowmik, M. and Senapati, T., {Fuzzy translations of fuzzy subalgebras in

{BG}-algebras}, {em J. Math. Informatics}, textbf{4} (2015,), 1-8.

bibitem{Chandramouleeswaran2013pp5216}

Chandramouleeswaran, M., Muralikrishna, P. and Srinivasan, S., {Fuzzy

translation and fuzzy multiplication in {BF/BG}-algebras}, {em Indian J. Sci.

Technol.}, textbf{6} (2013), no.~9, 5216-5219.

bibitem{Gerla1998pp49}

Gerla, G. and Scarpati, L., {Extension principles for fuzzy set theory},

{em Inf. Sci.}, textbf{106} (1998), 49-69.

bibitem{Hashemi2016pp1}

Hashemin, M.~A., {Fuzzy translations of fuzzy associative ideals in

${BCI}$-algebras}, {em Br. J. Math. Comput. Sci.}, textbf{16} (2016), no.~1, 1-9.

bibitem{Hu1983}

Hu, Q.~P. and Li, X., {On {BCH}-algebras}, {em Math. Semin. Notes, Kobe Univ.},

textbf{11} (1983), 313-320.

bibitem{Iampan2014}

Iampan, A., {A new branch of the logical algebra: {UP}-algebras},

Manuscript submitted for publication, April 2016.

bibitem{Imai1966}

Imai, Y. and Is'{e}ki, K., {On axiom system of propositional calculi,

{XIV}}, {em Proc. Japan Acad.}, textbf{42} (1966), no.~1, 19-22.

bibitem{Iseki1966}

Is'{e}ki, K., {An algebra related with a propositional calculus}, {em Proc.

Japan Acad.}, textbf{42} (1966), no.~1, 26-29.

bibitem{Jun2001v2}

Jun, Y.~B., {$q$-fuzzy subalgebras of {BCK/BCI}-algebras}, {em Sci. Math. Jpn.

Online}, textbf{4} (2001), 197-202.

bibitem{Jun2004}

Jun, Y.~B., {On $(alpha,beta)$-fuzzy ideals of {BCK/BCI}-algebras}, {em Sci.

Math. Jpn. Online}, textbf{7} (2004), 101-105.

bibitem{Jun2011pp349}

Jun, Y.~B., {Translations of fuzzy ideals in {BCK/BCI}-algebras}, {em Hacet. J.

Math. Stat.}, textbf{40} (2011), no.~3, 349-358.

bibitem{Jun2009pp399}

Jun, Y.~B., Kim, H.~S. and Lee, K.~J., {Bipolar fuzzy translations in

{BCK/BCI}-algebras}, {em J. Chungcheong Math. Soc.}, textbf{22} (2009,), no.~3,

-408.

bibitem{Jun2002}

Jun, Y.~B., Roh, E.~H. and Kim, H.~S., {On fuzzy {B}-algebras}, {em Czechoslovak

Math. J.}, textbf{52} (2002), no.~127, 375-384.

bibitem{Jun2005}

Jun, Y.~B. and Song, S., {Intuitionistic fuzzy semi-preopen sets and

intuitionistic fuzzy semi-precontinuous mappings}, {em J. Appl. Math. Comput.},

textbf{19} (2005), 467-474.

bibitem{Keawrahun2011}

Keawrahun, S. and Leerawat, U., {On isomorphisms of {SU}-algebras}, {em Sci.

Magna}, textbf{7} (2011), no.~2, 39-44.

bibitem{Lee2009pp353}

Lee, K.~J., Jun, Y.~B. and Doh, M.~I., {Fuzzy translations and fuzzy

multiplications of ${BCK/BCI}$-algebras}, {em Commun. Korean Math. Soc.},

textbf{24} (2009), no.~3, 353-360.

bibitem{Lele2001}

Lele, C., Wu, C., Weke, P., Mamadou, T. and Njock, G.~E., {Fuzzy ideals and

weak ideals in {BCK}-algebras}, {em Sci. Math. Jpn. Online}, textbf{4} (2001),

-612.

bibitem{Mostafa2011}

Mostafa, S.~M., Abdel Naby, M.~A. and Elgendy, O.~R., {Intuitionistic

fuzzy {KU}-ideals in {KU}-algebras}, {em Int. J. Math. Sci. Appl.}, textbf{1}

(2011), no.~3, 1379-1384.

bibitem{Mostafa2015}

Mostafa, S.~M., Naby, M.~A.~A. and Elkabany, A.~E.~I., {$alpha$-anti fuzzy

new ideal of {PU}-algebra}, {em Int. J. Fuzzy Log. Syst.}, textbf{5} (2015),

no.~2/3, 1-13.

bibitem{Prabpayak2009}

Prabpayak, C. and Leerawat, U., {On ideals and congruences in

{KU}-algebras}, {em Sci. Magna}, textbf{5} (2009), no.~1, 54-57.

bibitem{Priya2014pp93}

Priya, T. and Ramachandran, T., {Homomorphism and cartesian product on fuzzy

translation and fuzzy multiplication of {PS}-algebras}, {em Int. J. Pure Appl.

Math.}, textbf{8} (2014), no.~1, 93-104.

bibitem{Saeid2008}

Saeid, A.~B. and Jun, Y.~B., {Redefined fuzzy subalgebras of

{BCK/BCI}-algebras}, {em Iran. J. Fuzzy Syst.}, textbf{5} (1994), no.~2, 63-70.

bibitem{Senapati2015pp45}

Senapati, T., Bhowmik, M., Pal, M. and Davvaz, B., {Fuzzy translations of

fuzzy ${H}$-ideals in {BCK/BCI}-algebras}, {em J. Indones. Math. Soc.}, textbf{21}

(2015), no.~1, 45-58.

bibitem{Sitharselvam2012}

Sitharselvam, P.~M., Priya, T. and Ramachandran, T., {Anti {Q}-fuzzy

{KU}-ideals in {KU}-algebras and its lower level cuts}, {em Int. J. Eng. Res.

Appl.}, textbf{2} (2012), no.~4, 1286-1289.

bibitem{Somjanta2014}

Somjanta, J., Thuekaew, N., Kumpeangkeaw, P. and Iampan, A., {Fuzzy sets in

{UP}-algebras}, Manuscript accepted for publication, February 2015.

bibitem{Song2010}

Song, S.~Z., Jun, Y.~B. and Lee, K.~J., {Fuzzy ideals in {BE}-algebras},

{em Bull. Malays. Math. Sci. Soc. (2)}, textbf{33} (2010), no.~1, 147-153.

bibitem{Yamini2014}

Yamini, C. and Kailasavalli, S., {Fuzzy {B}-ideals on {B}-algebras}, {em Int. J.

Math. Arch.}, textbf{5} (2014), no.~2, 227-233.

bibitem{Zadeh}

Zadeh, L.~A., {Fuzzy sets}, {em Inf. Cont.}, textbf{8} (1965), 338-353.


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