For the theory of fuzzy group, the classification, most especially the finite p-groups cannot be ... more For the theory of fuzzy group, the classification, most especially the finite p-groups cannot be overlooked. The aspect of pure mathematics has undergone a lot of dynamic developments over the years. For instance, many researchers have treated cases of finite abelian groups. Since inception, the study has been extended to some other important classes of finite abelian and nonabelian groups such as the dihedral, quaternion, semidihedral, and hamiltonian groups. Other different approaches have been so far, applied for the classification. The fuzzy sets were introduced by Zadeh [15]. Even though, the story of fuzzy logic started much more earlier, it was specially designed mathematically to represent uncertainty and vagueness. It was also, to provide formalized tools for dealing with the imprecision intrinsic to many problems. The term fuzzy logic is generic as it can be used to describe the likes of fuzzy arithmetic, fuzzy mathematical programming, fuzzy topology, fuzzy graph theory ad fuzzy data analysis which are customarily called fuzzy set theory. This theory of fuzzy sets has a wide range of applications, one of which is that of fuzzy groups developed by Rosenfield [16]. This by far, plays a pioneering role for the study of fuzzy algebraic structures. Other notions have been developed based on this theory. These, amongst others, include the notion of level subgroups by P.S. Das used to characterize fuzzy subgroups of finite groups and that of equivalence of fuzzy subgroups introduced by Murali and Makamba which we use in this work [1]-[9].
For the theory of fuzzy group, the classification, most especially the finite p-groups cannot be ... more For the theory of fuzzy group, the classification, most especially the finite p-groups cannot be overlooked. The aspect of pure mathematics has undergone a lot of dynamic developments over the years. For instance, many researchers have treated cases of finite abelian groups. Since inception, the study has been extended to some other important classes of finite abelian and nonabelian groups such as the dihedral, quaternion, semidihedral, and hamiltonian groups. Other different approaches have been so far, applied for the classification. The fuzzy sets were introduced by Zadeh [15]. Even though, the story of fuzzy logic started much more earlier, it was specially designed mathematically to represent uncertainty and vagueness. It was also, to provide formalized tools for dealing with the imprecision intrinsic to many problems. The term fuzzy logic is generic as it can be used to describe the likes of fuzzy arithmetic, fuzzy mathematical programming, fuzzy topology, fuzzy graph theory ad fuzzy data analysis which are customarily called fuzzy set theory. This theory of fuzzy sets has a wide range of applications, one of which is that of fuzzy groups developed by Rosenfield [16]. This by far, plays a pioneering role for the study of fuzzy algebraic structures. Other notions have been developed based on this theory. These, amongst others, include the notion of level subgroups by P.S. Das used to characterize fuzzy subgroups of finite groups and that of equivalence of fuzzy subgroups introduced by Murali and Makamba which we use in this work [1]-[9].
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