یاجوج ماجوج: جدید تعبیرات اور معاصر اقوام پر اطلاق و انطباق: ایک تجزیاتی مطالعہ

Gog and Magog Interpretations by Modern Scholars and its Application on Contemporary Nations: An Analytical Study According to the Islamic point of view Gog and Magog (Ya’jūj Ma’jūj), are two such supernatural and aggressive powers that will reveal from some unknown place. According to Islamic sources the two disbelieving powers (tribes) are the children of Yāfith son of Noah. Humanity will affect badly at their severely harmful activities on the earth. In the beginning they were free into some unknown place. The famous king Dhulqarnayn imprisoned them behind an unknown thick wall in human history. There are many conjectures regarding the wall, and it is sometimes considered in any Norwegian country because of too long duration of sunrise in these countries. Their population will be 10 times more than the World’s populations. They will be so much trouble creating nation from the race of Noah (A.S) even Isa (Christ) will take refuge on the mountain of Toor and Muslims will pray Allah to get rid of them. Today some modern Islamic researchers have been claiming that they are in fact, Chines or Russians as we find their resemblance in prophet's traditions. In this article, an attempt has been made to unveil the disputed matter that either they exist in current age in form of living peoples or some hidden which will be revealed before the end of time. The purpose of this research is to revisit different speculations about Gog and Magog as we find them also into the Bible. Many Muslims research took effect from Bible’s concept ignoring the traditions of the prophet and find out many different solutions which, according to me are to be seen into the true and clear facts by Quran and Sunnah.

A Study of Fuzzy Ag-Subgroups

The idea of fuzzy sets has opened new door of research in the world of contemporary Mathematics. The concept of fuzzy sets provided a new approach to model imprecision and uncertainty present in phenomena without sharp boundaries. The fuzzi cation of algebraic structures, play a dynamic role in Mathematics with diverse applications in many other branches such as computer arithmetic''s, control engineering, error correcting codes and formal languages and many more. Moreover, during the course of the last decade, non-associative algebraic structures have gained popularity among the researchers. In this background, many researchers initiated the notion of AG-groupoids, its newly introduced subclasses and its fuzzi cation. The present research is among the very few where non-associative algebraic structures are investigated and fuzzi ed. In this thesis various constructions of AG-groups over theeld Zn are introduced, some related results and example of AG-groups are provided. Further, the structural properties of fuzzy AG-subgroup are introduced and various notions of fuzzy AG-subgroups are investigated, e.g. conjugate of a fuzzy AG-subgroup, fuzzy normal AG-subgroups, relations between fuzzy normal AG-subgroup and commutators in AG-groups and equal-height elements in fuzzy AG-subgroups. Moreover, the notion of fuzzy AG-subgroups is further extended and a fuzzy coset in AG-subgroups is introduced. It is worth mentioning that if A is any fuzzy AGsubgroup of G, thenA(xy) =A(yx) for all x; y 2 G, i.e. each fuzzy left coset is fuzzy right coset and vice versa. Also, fuzzy coset in AG-subgroup could be empty contrary to coset in group theory. However, order of the nonempty fuzzy coset is the same as the index number [G : A] where H is an AG-subgroup of an AG-group G. The notion of fuzzy quotient AG-subgroup, fuzzy AG-subgroup of the quotient (factor) AG-subgroup, fuzzy homomorphism of AG-group and fuzzy Lagrange''s Theorem ofnite AG-group is introduced. Finally, cubic AG-subgroups and its properties are explored.