Cubic Interior Ideals in Semigroups

In this paper we apply the cubic set theory to interior ideals of a semigroup. The notion of cubic interior ideals is introduced, and related properties are investigated. Characterizations of (cubic) interior ideals are established, and conditions for a semigroup to be left (right) simple are provided

On t

We introduce the notion of t-derivation of a BCI-algebra and investigate related properties. Moreover, we study t-derivations in a p-semisimple BCI-algebra and establish some results on t-derivations in a p-semisimple BCI-algebra

Generalizations of Derivations in BCI-Algebras

In the present paper we introduced the notion of (q ,f )-derivations of a BCI-algebra X. Some interesting results on inside (or outside) (q ,f )-derivations in BCI-algebras are discussed. It is shown that for any commutative BCI-algebra X, every inside (q ,f )- derivation of X is isotone. Furthermore it is also proved that for any outside (q ,f )-derivation d(q ,f ) of a BCI-algebra X, d(q ,f )(x) = q (x)∧d(q ,f )(x) if and only if d(q ,f )(0) = 0 for all x ∈ X

Ideal Theory in BCK/BCI-algebras in the Frame Of Hesitant Fuzzy Set Theory

Several generalizations and extensions of fuzzy sets have been introduced in the literature, for example, Atanassov’s intuitionistic fuzzy sets, type 2 fuzzy sets and fuzzy multisets, etc. Using the Torra’s hesitant fuzzy sets, the notions of Sup-hesitant fuzzy ideals in BCK/BCI-algebras are introduced, and its properties are investigated. Relations between Sup-hesitant fuzzy subalgebras and Sup-hesitant fuzzy ideals are displayed, and characterizations of Sup-hesitant fuzzy ideals are discussed

History of Urdu language and literature down to 1720.

I. The available material dealing with this subject is very seanty, largely unscientific, and often based on second-hand information. Even the Catalogue have many mistakes in them. Therefore it was necessary to study the original Urdu and Persian manuscripts (both literary and historic) in the British Museum, India Office Library, Edinburgh University Library, and the Bibliotheque National, Paris.;II. New Discoveries. a. Nearly 70 poets hitherto unknown are here discussed, see list of Marsia-writers, p. 297. The others are: 1. Atishi 2. Muqimi 3. Khushnud 4. Amin 5. Nahmud 6. Feroz 7.Shaugi 8. Khisli 9. Ghulam'Ali b. The following Urdu works were also not known before: 1. Qutub Mushtari of Vajhi; 2. Padmavat of Ghulam 'Ali; 3. Jusuf Zalikha of Khushnud; 4. The Diwan of Rustumi (Not contained in any European Library).;III. Some misunderstandings about important writers have been corrected: 1. The author of Hasht Behisht is Khushnud, not Muhammad Shah (p. 121). 2. The author of Candar Badan-o-Mahyar is Muqimi, nor Aziz (p. 103). 3. The real author of Bahram-o-Banu Husn was Amin, not Daulat who only completed it (p. 107). 4. Information given about this Daulat, otherwise unknown (p. 123). 5. The name of Kamal kha was Rustumi, not Rasmi (p. 114); information given about his Khavar Nama (p.p. 114-117). 6. The name of Junaidi was not Shaikh Ahmad but 'Ali Akbar (p. 212). 7. Nusrati Guldasta-e-'Ishq not a masnavi but a collection of ghazals (p. 146). 8. Ibn-e-Nashati not translated a Tuti Nama (p. 216). 9. The Dah Majlis attributed to Vali Aurangabadi really by Vali of Vellore (p. 263). 10. Confusion about certain poets cleared up: (a) The 4 poets called Amin (pp. 106, 221 and 255). (b) " 4 " " Nuri (pp. 109 and 227). (c) " 3 " " Mirza (pp. 160 and 229). (d) Mashim and Hashimi (pp. 152 and 284).;IV. Much new information based on MS. Study about: 1. Vajhi (p. 189) 2. Rustumi (p. 114) 3. Nusrati (p. 126) 4. Ibn-e-Nashati (p. 213) 5. Hashim 'Ali (p. 284).;V. The writer has here presented some new views about the origin and development of Urdu. In this connection he has taken advantage of his belonging to the Dakhan in discussing the divergence between the northern and southern forms of Urdu

Concave Soft Sets, Critical Soft Points, and Union-Soft Ideals of Ordered Semigroups

The notions of union-soft semigroups, union-soft l-ideals, and union-soft r-ideals are introduced, and related properties are investigated. Characterizations of a union-soft semigroup, a union-soft l-ideal, and a union-soft r-ideal are provided. The concepts of union-soft products and union-soft semiprime soft sets are introduced, and their properties related to union-soft l-ideals and union-soft r-ideals are investigated. Using the notions of union-soft l-ideals and union-soft r-ideals, conditions for an ordered semigroup to be regular are considered. The concepts of concave soft sets and critical soft points are introduced, and their properties are discussed

Further results on -neutrosophic subalgebras and ideals in BCK/BCI-algebras

Characterizations of an (∈, ∈)-neutrosophic ideal are considered. Any ideal in a BCK/BCI-algebra will be realized as level neutrosophic ideals of some (∈, ∈)-neutrosophic ideal. The relation between (∈, ∈)-neutrosophic ideal and (∈, ∈)-neutrosophic subalgebra in a BCK-algebra is discussed. Conditions for an (∈, ∈)-neutrosophic subalgebra to be a (∈, ∈)-neutrosophic ideal are provided. Using a collection of ideals in a BCK/BCI-algebra, an (∈, ∈)-neutrosophic ideal is established. Equivalence relations on the family of all (∈, ∈)-neutrosophic ideals are introduced, and related properties are investigated

Neutrosophic subsemigroups

<p>In the present paper, we introduce the notion of (Φ, Ψ)-neutrosophic subsemigroups of a semigroup where Φ, Ψ ∈ {∈, q, ∈ ∨ q}, and related properties are investigated. We consider characterizations of an (∈, ∈)-neutrosophic subsemigroup and an (∈, ∈ ∨ q)-neutrosophic subsemigroup. Conditions for the neutrosophic ∈-subsets, neutrosophic q-subsets and neutrosophic ∈ ∨ q-subsets to be subsemigroups are discussed. Finally, we discuss conditions for a neutrosophic set to be a (q, ∈ ∨ q)-neutrosophic subsemigroup. </p&gt