Annals of Communications in Mathematics

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.

G. MUHIUDDIN
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF TABUK, TABUK 71491, SAUDI ARABIA.
Email: chishtygm@gmail.com

 The notion of hybrid structures is introduced, and several properties are investigated. Applications in BCK/BCI-algebras and linear spaces are discussed. Hybrid subalgebra, hybrid field and hybrid linear space are introduced, and related properties are investigated.

YOUNG BAE JUN
DEPARTMENT OF MATHEMATICS EDUCATION, GYEONGSANG NATIONAL UNIVERSITY, JINJU 660-701,
KOREA
Email: skywine@gmail.com

SEOK ZUN SONG
DEPARTMENT OF MATHEMATICS,, JEJU NATIONAL UNIVERSITY, JEJU 690-756, KOREA
Email: szsong@jejunu.ac.kr

G. MUHIUDDIN
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF TABUK, TABUK 71491, SAUDI ARABIA
Email: chishtygm@gmail.com

Characterizations of neutrosophic quadruple BCI-algebra are considered. Conditions for the neutrosophic quadruple BCI-set to be a p-semisimple BCI-algebra are provided. A condition for a subalgebra to be an ideal in neutrosophic quadruple BCIalgebra is given. Conditions for the set NQ(A, B) to be a neutrosophic quadruple closed ideal and neutrosophic quadruple p-ideal are discussed. Characterizations of neutrosophic quadruple p-ideal are considered.

G. MUHIUDDIN
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF TABUK, TABUK 71491, SAUDI ARABIA
Email: chishtygm@gmail.com

YOUNG BAE JUN
DEPARTMENT OF MATHEMATICS EDUCATION, GYEONGSANG NATIONAL UNIVERSITY, JINJU 660-701,
KOREA
Email: skywine@gmail.com

The theory of intuitionistic fuzzy sets (IFS) is a viable tool in decision science, robotics and control, medical imaging, among others. From the applications of IFS, it is proven that the concept of IFS is useful in providing a reliable and efficient framework or model to tackle uncertainty and vagueness embedded in decision making. In this paper, we explore the resourcefulness of IFS in competency based test evaluation (CBTE) for course selection into higher institution. We employ distance and similarity measures for IFS to achieve the test through a BESPOKE program developed using an object oriented programming language, JAVA to be specific. Using the output of the program in terms of distance and similarity between applicants and courses in intuitionistic fuzzy sense, we determine applicants suitable courses.

P. A. EJEGWA
DEPARTMENT OF MATHEMATICS/STATISTICS/COMPUTER SCIENCE, UNIVERSITY OF AGRICULTURE, P.M.B. 2373, MAKURDI, NIGERIA
Email: ejegwa.augustine@uam.edu.ng  ocholohi@gmail.com

I. C. ONYEKE
DEPARTMENT OF MATHEMATICS/STATISTICS/COMPUTER SCIENCE, UNIVERSITY OF AGRICULTURE, P.M.B. 2373, MAKURDI, NIGERIA
Email: onyeke.idoko@gmail.com

In this paper, a new approach is introduced to find the shortest path between two given vertices on interval-valued fuzzy hypergraphs. When only crisp numbers are not sufficient to measure a real world parameter, fuzzy numbers are considered. But, there are many types of fuzzy numbers available in literature. Most useful fuzzy number is trapezoidal fuzzy numbers. Throughout this paper the interval-valued trapezoidal fuzzy number is used as the arc length of the interval-valued fuzzy hypergraph. We have measured similarity between two interval-valued fuzzy numbers to find the shortest path. An algorithm is also designed to find all possible hyperpaths in a hypergraph and calculated its time complexity

TARASANKAR PRAMANIK
DEPARTMENT OF MATHEMATICS, KHANPUR GANGCHE HIGH SCHOOL, PASCHIM MEDINIPUR, 721201, INDIA
Email: tarasankar.math07@gmail.com

MADHUMANGAL PAL
DEPARTMENT OF APPLIED MATHEMATICS WITH OCEANOLOGY AND COMPUTER PROGRAMMING, VIDYASAGAR UNIVERSITY, MIDNAPORE, 721102, INDIA
Email: mmpalvu@gmail.com

 In this paper, the notion of cubic subalgebras of BCH-algebras are introduced. Some characterization of cubic subalgebras of BCH-algebras are given. The homomorphic image and inverse image of cubic subalgebras are studied and investigated some related properties

TAPAN SENAPATI
DEPARTMENT OF APPLIED MATHEMATICS WITH OCEANOLOGY AND COMPUTER PROGRAMMING, VIDYASAGAR UNIVERSITY, MIDNAPORE 721102, INDIA.
Email: math.tapan@gmail.com

K. P. SHUM
INSTITUTE OF MATHEMATICS, YUNNAN UNIVERSITY, KUNMING 650091, PEOPLE’S REPUBLIC OF CHINA
Email: kpshum@ynu.edu.cn

 In this article, the notion of a new kind of derivation is introduced for a lattice L called symmetric bi-(T, F)-derivations on L as a generalization of derivation of lattices and characterized some of its related properties. Some equivalent conditions provided for a lattice L with greatest element 1 by the notion of isotone symmetric bi- (T, F)-derivation on L. By using the concept of isotone derivation, we characterized the modular and distributive lattices by the notion of isotone symmetric bi-(T, F)-derivation

CHIRANJIBE JANA
DEPARTMENT OF APPLIED MATHEMATICS WITH OCEANOLOGY AND COMPUTER PROGRAMMING, VIDYASAGAR UNIVERSITY, MIDNAPORE 721102, INDIA
Email: jana.chiranjibe7@gmail.com

MADHUMANGAL PAL 
DEPARTMENT OF APPLIED MATHEMATICS WITH OCEANOLOGY AND COMPUTER PROGRAMMING, VIDYASAGAR UNIVERSITY, MIDNAPORE 721102, INDIA
Email: mmpalvu@gmail.com