رحمۃ للعالمينﷺ کے غیر مسلموں سے معاملات قرآن و سیرت طیبہ کی روشنی میں

Dealings of the Holy Prophet (S.A.W) with non-Muslim show that Islam is the religion of peace, brotherhood, religious tolerance, independence and humanity. Before the spread of Islam the conversations and dealings of the Holy Prophet with non-Muslims forced them to call him Al-Sadiq and Al-Ameen. Sympathy and tolerance in clandestine and public preaching, the style of letters to non-Muslim empires, the dialogues with non-Muslim delegations in Madani era, the orders given for the safety of their wealth, belongings and their life, the tolerance, forgiveness and prayers for the enemies, the good behavior with the non-Muslim prisoners, even when Muslims got dominance over non-Muslims at the time of the conquest of Makkah, the common pardon given by Holy Prophet (S.A.W) are the true example that Islam preaches peace. The attitude of Sahaba-e-Karam (R.A) and the liberty of rights given to Non-Muslims by them- no religion and no community of the World can give this example. The people responsible for maintaining the peace of the world and brotherhood should see how Muslims are treated all over the world? Muslims had given to non-Muslim permission to practice their religious festivities freely and even to wear any type of clothes. The ban of Hijab in France, the punishment of innocent Dr. Afia Siddiqui, the Egyptian pregnant woman (Marwa Sharbeney) had been mercilessly assassinated and her husband injured by knives in the court of Germany because of Hijab, the discussions going on to restrict the domes of Mosques and Adhan (Call to prayer) in Switzerland, the insult of the Holy Quran by Pope Terry John, of Florida, the disrespect of Holy Prophet (S.A.W) etc are the questions awaiting answers from West and United Nation. Islam promotes of peace, equality and religious freedom. It also invites non-Muslims to come and sit on a platform and discuss these problems for the sake of worldly peace to end the religious hatred and to form true peace in the world.

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.