The identity and religion of Ikhwan-al Safa, which was a secret organization in the Islamic Middle Ages, is the subject of study by a large number of current scholars. Regarding the religion of Ikhwan-al-Safa, there are differences among scholars that have inevitably led them to different theories in explaining their religion. This article tries to evaluate the scientific validity of each prominent theories expressed in the explanation of the religion by descriptive-analytical method. In this article, while dealing with the identity of Ikhwan Al-Safa, the prominent theories that have been proposed by current scholars in explaining this religion, have been examined and criticized. Among the two theories of atheism and faith, the theory of atheism, was rejected and among the theories on their faith, the theories: Mu'tazilites, Ismailis, Imamis, Zaidis and Sufis were recognized as weak. However, the integrated theory, which seemed more appropriate, was recognized as an almost correct theory.

Let G = (V; E) be a simple connected graph of order p and size q. A decomposition of a graph G is a collection  of edge-disjoint subgraphs G1; G2; : : :; Gn of G such that every edge of G belongs to exactly one Gi; (1  i  n). The decomposition  = fG1; G2; : : :; Gng of a connected graph G is said to be a distinct edge geodetic decomposition if g1(Gi) 6= g1(Gj ); (1  i 6= j  n). The maximum cardinality of  is called the distinct edge geodetic decomposition number of G and is denoted by  dg1 (G), where g1(G) is the edge geodetic number of G. Some general properties sat-is ed by this concept are studied. Connected graphs of  dg1 (G)  2 are characterized and connected graphs of order p with  dg1 (G) = p 2 are characterized.

In this paper we classify fuzzy subgroups of the dihedral group Dpqrs for distinct primes p, q, r and s. This follows similar work we have done on distinct fuzzy subgroups of some dihedral groups. We present formulae for the number of (i) distinct maximal chains of subgroups, (ii) distinct fuzzy subgroups and (iii) non-isomorphic classes of fuzzy subgroups under our chosen equivalence and isomorphism. Some results presented here hold for any dihedral group of order 2n where n is a product of any number of distinct primes.

One of the most perplexing issues in Arabic Logic is the particular quantifier for conditionals. Before discussing particular quantifier at cogent conditionals, Ibn-Sina deals with particular quantifier at categorical propositions and its divisions. But, as we shall see, his explanation at categorical propositions is inconsistent with his discussion at conditionals; and his analogy between the two realms is more confusing than explaining! Despite this, in this paper, I’ ll show that by using some branches in Modern Logic, such as second-order logic, modal logic and temporal logic, many of the ambiguities and the objections can be replied. Also, I’ ll glance at the reflection of the discussion in some of Ibn-Sina’ s great followers: Fakhr Al-Din Al-Razi, Afdal Al-Din Al-Khunaji, Athir Al-Din Al-Abhari, Khaje Nasir Al-Tusi, Shams Al-Din Al-Samaqandi and Qutb Al-Din Al-Razi. I shall show haw far they are from Ibn-Sina. Besides, it will be clear that their distinctions between contingent conditional and particular cogent conditional are very weak and, indeed, cannot help any way to understand the distinction.