New Generalizations of Hesitant and Interval-Valued Fuzzy Ideals of Semigroups

Abstract

In this paper, we introduce the notion of $\sup$-hesitant fuzzy ideals of semigroups, which is the general notion of hesitant fuzzy ideals and interval-valued fuzzy ideals. In addition, $\sup$-hesitant fuzzy ideals are characterized in terms of sets, fuzzy sets, hesitant fuzzy sets and interval-valued fuzzy sets. Finally, $\sup$-hesitant fuzzy translations and $\sup$-hesitant fuzzy extensions of $\sup$-hesitant fuzzy ideals of semigoups are discussed, and their relations are investigated.

(inf , sup)-Hesitant Fuzzy Subalgebras of BCK/BCI-Algebras

“…For each element Θ ∈ ℘([0, 1]) and HFS κ on U, define the elements SUP Θ [14,20] and INF Θ [15, 16] of [0, 1] and the subset [U, κ, Θ] of U as follows:…”

New Generalizations of sup-Hesitant Fuzzy Ideals of Semigroups

“…(1) the element SUP [12,35] of [0, 1] by Let SC( ε) be the set of all supremum complements of ε. Then, we obtain that…”

“…Jittburus and Julatha [12] introduced a sup-hesitant fuzzy ideal, which is a generalization of the concepts of an IvFI and a HFI, of a semigroup and studied its properties via sets, FSs, HFSs and IvFSs in the following.…”

“…Jun et al [21] and Talee et al [39] studied hesitant fuzzy sets in semigroup. Studying hesitant fuzzy sets, in the meaning of the supremum of their images, on semigroups, Jittburus and Julatha [12] introduced sup-hesitant fuzzy ideals of semigroups and investigated properties via sets, fuzzy sets, interval-valued fuzzy sets and hesitant fuzzy sets. Phummee et al [35] introduced sup-hesitant fuzzy interior ideals of semigroups and studied its properties by sets, fuzzy sets, interval-valued fuzzy sets and hesitant fuzzy sets.…”

(inf, sup)-Hesitant Fuzzy Ideals of BCK/BCI-Algebras

“…Muhiuddin and Jun [34] Muhiuddin et al [35] Muhiuddin et al [38], Harizavi and Jun [37], Jun and Song [39] and Takallo et al [36] used hesitant fuzzy sets related to the infimum or supremum of their images in study of BCK/BCI-algebras. Jittburus and Julatha [24,25], Phummee et al [28], and Jittburus et al [27] used hesitant fuzzy sets related to the infimum or the supremum of their images in study of semigroups. [21][22][23]26] used hesitant fuzzy sets related to the infimum or the supremum of their images in study of ternary semigroups and Γ-semigroups.…”