Hesitant fuzzy semigroups with a frontier

Article type: Research Article

Authors: Jun, Young Bae^a | Song, Seok-Zun^{b; *} | Muhiuddin, G.^c

Affiliations: [a] Department of Mathematics Education, Gyeongsang National University, Jinju, Korea | [b] Department of Mathematics, Jeju National University, Jeju, Korea | [c] Department of Mathematics, University of Tabuk, Tabuk, Saudi Arabia

Correspondence: [*] Corresponding author. Seok-Zun Song, Department of Mathematics, Jeju National University, Jeju 690-756, Korea. Tel.: +82 64 754 3562; Fax: +82 64 725 2573; E-mail: szsong@jejunu.ac.kr.

Abstract: The notion of a hesitant fuzzy semigroup with a frontier is introduced, and several properties are investigated. Characterizations of a hesitant fuzzy semigroup with a frontier are considered, and a condition for a special set to be a subsemigroup is provided. The hesitant union and hesitant intersection of two hesitant fuzzy semigroups with a frontier are dealt with, and the hesitant fuzzy pre-image and hesitant fuzzy image of a hesitant fuzzy semigroup with a frontier under the homomorphism are discussed.

Keywords: Hesitant fuzzy semigroup (with a frontier), hesitant fuzzy pre-image, hesitant fuzzy image

DOI: 10.3233/IFS-151869

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 3, pp. 1613-1618, 2016