The purpose of this thesis is to investigate some aspects of fuzzification of semigroups, partially ordered semigroups and gamma semigroups. In this thesis the concepts of fuzzy subsemigroups, fuzzy bi-ideals, fuzzy (1,2)-ideals, fuzzy quasi ideals, fuzzy ideals, fuzzy interior ideals, fuzzy prime and fuzzy semiprime ideals, cartesian product of fuzzy ideals, fuzzy prime ideals and fuzzy semiprime ideals, fuzzy ideal extensions in a gamma semigrouop have been introduced. These concepts are also studied via operator semigroups of a gamma semigroup. In this thesis some results of gamma semigroups have been rediscovered in terms of fuzzy subsets. Here some important characterization theorems in terms of fuzzy subsets have been obtained. It is important to note here that in the study of gamma semigroups in terms of fuzzy subsets operator semigroups play a crucial role.
The purpose of this thesis is to investigate some aspects of fuzzification of semigroups, partially ordered semigroups and gamma semigroups. In this thesis the concepts of fuzzy subsemigroups, fuzzy bi-ideals, fuzzy (1,2)-ideals, fuzzy quasi ideals, fuzzy ideals, fuzzy interior ideals, fuzzy prime and fuzzy semiprime ideals, cartesian product of fuzzy ideals, fuzzy prime ideals and fuzzy semiprime ideals, fuzzy ideal extensions in a gamma semigrouop have been introduced. These concepts are also studied via operator semigroups of a gamma semigroup. In this thesis some results of gamma semigroups have been rediscovered in terms of fuzzy subsets. Here some important characterization theorems in terms of fuzzy subsets have been obtained. It is important to note here that in the study of gamma semigroups in terms of fuzzy subsets operator semigroups play a crucial role.
During the springs of 2011 and 2012, the author was invited by Peking University to give an advanced undergraduate algebra course (once a week over two months each year). This book was written during...
The book contains elementary ideas of different Intuitionistic fuzzy algebraic structures viz. Intuitionistic fuzzy ideals and Intuitionistic fuzzy submodules. Some interesting relationships...
This book is intended as an introduction to fuzzy algebraic hyperstructures. As the first in its genre, it includes a number of topics, most of which reflect the authors' past research and thus...
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