The notion of a G-semigroup was introduced by Sen [8] in 1981. We can see that any semigroup can be considered as a G-semigroup. The aim of this article is to study the concept of (0-)minimal and max- imal ordered bi-ideals in ordered G-semigroups, and give some charac- terizations of (0-)minimal and maximal ordered bi-ideals in ordered G- semigroups analogous to the characterizations of (0-) minimal and maxi- mal ordered bi-ideals in ordered semigroups considered by Iampan [5].

In this paper, we introduce the concept of Krasner hyperring (R,+,.) together with a suitable partial order relation £. Also, we con-sider some Krasner hyperrings and dene a binary relation on them which become ordered Krasner hyperrings. By using the notion of pseudoorder on an ordered Krasner hyperring (R,+,.,£), we obtain an ordered ring. Moreover, we give some results on ordered Krasner hyperrings.

Let S be an ordered semi group. A fuzzy subset of S is an arbitrary mapping from S into [0,1], where [0,1] is the usual interval of real numbers. In this paper, the concept of fuzzy generalized bi-ideals of an ordered semi group S is introduced. Regular ordered semi groups are characterized by means of fuzzy left ideals, fuzzy right ideals and fuzzy (generalized) bi-ideals. Finally, two main theorems which characterize regular ordered semi groups and intraregular ordered semi groups in terms of fuzzy left ideals, fuzzy right ideals, fuzzy bi-ideals or fuzzy quasi-ideals are given. The paper shows that one can pass from results in terms of fuzzy subsets in semi groups to ordered semi groups. The corresponding results of unordered semi groups are also obtained.

Based on a complete Heyting algebra, we modify the definition of lattice-valued fuzzifying convergence space using fuzzy inclusion order and construct in this way a Cartesian-closed category, called the category of L-ordered fuzzifying convergence spaces, in which the category of L-fuzzifying topological spaces can be embedded. In addition, two new categories are introduced, which are called the category of principal L-ordered fuzzifying convergence spaces and that of topological L-ordered fuzzifying convergence spaces, and it is shown that they are isomorphic to the category of L-fuzzifying neighborhood spaces and that of L-fuzzifying topological spaces respectively.

Developing mixed matrix membranes (MMMs) is a way to fabricate high permeation-performance membranes. The arrangement of the fillers, especially the specific-shaped ones, in the membranes has a non-negotiable influence on the gas-transport performance. With the assistance of a magnetic field, the Fe3O4 decorated attapulgite (ATP) is orderly arranged into the polymer of intrinsic microporosity (PIM-1) to form ATP/PIM-1 MMMs. Moreover, Fe3O4 decorated ATPs were coated with polydimethylsiloxane to avoid the polymeric matrix filling the cavity of ATPs. Chemical compositions of modified ATPs were determined by Fourier transform infrared spectroscopy. Morphologies of modified ATPs were observed via transmission electron microscopy and wide-angle X-ray diffraction. Morphologies of ATP/PIM-1 MMMs investigated by field-emission scanning electron microscopy. The effects of the vertically-arranged, parallelly-arranged, and disorderly-arranged ATPs on gas permeation-separation performances of ATP/PIM-1 MMMs were also reported. The parallelly-arranged ATP/PIM-1 MMMs display the best gas permeability compared with vertically-arranged and disorderly-arranged ATP/PIM-1 MMMs. And introducing the parallelly-arranged ATP brings about higher gas permeability and selectivity. Compared with the original PIM-1 membrane, the parallelly-arranged ATP/PIM-1 MMM with 5 wt.% ATP loading shows CO2 permeability of ~4018 Barrer coupled with CO2/N2 selectivity of ~19, and O2 permeability of ~672 Barrer coupled with O2/N2 selectivity of ~3. The CO2 permeability and O2 permeability increases to ~2.7 times.

A generalization of bipolar OWA operators, bipolar ordered weighted quasi-averages, based on the bipolar Choquet g-integrals, so called g-BIOWA operators are introduced and investigated. A generalization of induced OWA operators considering non-negative inputs and order-inducing variables, induced bipolar ordered weighted averages are introduced considering real inputs and order-inducing vectors. Their main properties are considered and some illustrative examples are presented.