Search results for: implicative pseudo-ideal

Authors: Alireza Gilani

Abstract:

In this paper, we consider the fuzzification of implicative pseudo-ideal in a pseudo-BCK algebra, and then we investigate some of their properties. We prove that the family of fuzzy implicative pseudo-ideal is completely distributive lattice.

Keywords: BCK-algebra, pseudo-BCK algebra, pseudo-ideal, implicative pseudo-ideal

Procedia PDF Downloads 339

Authors: Tumadhir Fahim M Alsulami

Abstract:

The concept of this paper builds on connecting between two important notions, fuzzy ideals of BCK-algebras and derivation of BCI-algebras. The result we got is a new concept called derivation fuzzy ideals of BCI-algebras. Followed by various results and important theorems on different types of ideals. In chapter 1: We presented the basic and fundamental concepts of BCK\ BCI- algebras as follows: BCK/BCI-algebras, BCK sub-algebras, bounded BCK-algebras, positive implicative BCK-algebras, commutative BCK-algebras, implicative BCK- algebras. Moreover, we discussed ideals of BCK-algebras, positive implicative ideals, implicative ideals and commutative ideals. In the last section of chapter 1 we proposed the notion of derivation of BCI-algebras, regular derivation of BCI-algebras and basic definitions and properties. In chapter 2: It includes 3 sections as follows: Section 1 contains elementary concepts of fuzzy sets and fuzzy set operations. Section 2 shows O. G. Xi idea, where he applies fuzzy sets concept to BCK-algebras and we studied fuzzy sub-algebras as well. Section 3 contains fuzzy ideals of BCK-algebras basic definitions, closed fuzzy ideals, fuzzy commutative ideals, fuzzy positive implicative ideals, fuzzy implicative ideals, fuzzy H-ideals and fuzzy p-ideals. Moreover, we investigated their concepts in diverse theorems and propositions. In chapter 3: The main concept of our thesis on derivation fuzzy ideals of BCI- algebras is introduced. Chapter 3 splits into 4 sections. We start with General definitions and important theorems on derivation fuzzy ideal theory in section 1. Section 2 and 3 contain derivations fuzzy p-ideals and derivations fuzzy H-ideals of BCI- algebras, several important theorems and propositions were introduced. The last section studied derivations fuzzy implicative ideals of BCI-algebras and it includes new theorems and results. Furthermore, we presented a new theorem that associate derivations fuzzy implicative ideals, derivations fuzzy positive implicative ideals and derivations fuzzy commutative ideals. These concepts and the new results were obtained and introduced in chapter 3 were submitted in two separated articles and accepted for publication.

Keywords: BCK, BCI, algebras, derivation

Procedia PDF Downloads 95

Authors: Stephen Osakue Amiandamhen, Schwaller Andreas, Martina Meincken, Luvuyo Tyhoda

Abstract:

Invasive alien tree species are currently being cleared in South Africa as a result of the forest and water imbalances. These species grow wildly constituting about 40% of total forest area. They compete with the ecosystem for natural resources and are considered as ecosystem engineers by rapidly changing disturbance regimes. As such, they are harvested for commercial uses but much of it is wasted because of their form and structure. The waste is being sold to local communities as fuel wood. These species can be considered as potential feedstock for the production of phosphate bonded composites. The presence of bark in wood-based composites leads to undesirable properties, and debarking as an option can be cost implicative. This study investigates the potentials of these invasive species processed without debarking on some fundamental properties of wood-based panels. Some invasive alien tree species were collected from EC Biomass, Port Elizabeth, South Africa. They include Acacia mearnsii (Black wattle), A. longifolia (Long-leaved wattle), A. cyclops (Red-eyed wattle), A. saligna (Golden-wreath wattle) and Eucalyptus globulus (Blue gum). The logs were chipped as received. The chips were hammer-milled and screened through a 1 mm sieve. The wood particles were conditioned and the quantity of bark in the wood was determined. The binding matrix was prepared using a reactive magnesia, phosphoric acid and class S fly ash. The materials were mixed and poured into a metallic mould. The composite within the mould was compressed at room temperature at a pressure of 200 KPa. After initial setting which took about 5 minutes, the composite board was demoulded and air-cured for 72 h. The cured product was thereafter conditioned at 20°C and 70% relative humidity for 48 h. Test of physical and strength properties were conducted on the composite boards. The effect of binder formulation and fly ash content on the properties of the boards was studied using fitted response surface technology, according to a central composite experimental design (CCD) at a fixed wood loading of 75% (w/w) of total inorganic contents. The results showed that phosphate/magnesia ratio of 3:1 and fly ash content of 10% was required to obtain a product of good properties and sufficient strength for intended applications. The proposed products can be used for ceilings, partitioning and insulating wall panels.

Keywords: invasive alien tree species, phosphate bonded composites, physical properties, strength

Procedia PDF Downloads 262