A study on fuzzy tm algebra

Abstract

Fuzzy set theoriesprovide strict mathematical frameworks using newlinevague phenomena and can be precisely and rigorously studied The core newlinetheories in mathematics such as algebra topology and analysis are subject to newlinefuzzification Many researchers have dealt with subalgebras ideals newlineimplicative ideals hyper structure homomorphism and relations etc and newlinetheirfuzzification This study attempts to introduce a new class of algebra: newlineTMalgebra generalized with some results of BCH BCIBCKQalgebras newlinewith illustrationsThe concepts of psemisimple ideal closed ideal and newlinesubalgebra in TMalgebra have been introduced and it is proved that every newlineclosed ideal of a TMalgebra is a TMsubalgebra The concepts of newlinecongruence positive implicative weakly positive implicative and translations newlineare introduced for TMalgebra and their properties are duly characterized newlineResults of fuzzy subalgebras and fuzzy ideals in TMalgebras are also newlineprovidedCartesian product of two fuzzy sets is defined and its properties are newlineestablished The relation between intuitionistic fuzzy closed ideals and an newlineupper level and lower level cuts of TMalgebra have also been explored newlineandthe image and preimage of an intuitionistic fuzzy ideal of TMalgebras newlineunder homomorphism are analysed fuzzy subalgebras and ideals by newlineusing the relations belonging to and quasicoincidence with newline between fuzzy points and fuzzy sets have been introduced and some of newlinetheir properties are examined Besides fuzzy hyper TM subalgebra of type newline have also been established in the present work newline newline