Direct product of fuzzy multigroups under \(t\)-norms
ODAM-Vol. 3 (2020), Issue 1, pp. 75 – 85 Open Access Full-Text PDF
Rasul Rasuli
Abstract: This paper proposes the concept of direct product of fuzzy multigroups under \(t\)-norms and some of their basic properties are obtained. Next, we investigate and obtain some new results of strong upper alpha-cut, weak upper alpha-cut, strong lower alpha-cut and weak lower alpha-cut of them. Later, we prove conjugation and commutation between them. Finally, the notion of homomorphism in the context of fuzzy multigroups was defined and some homomorphic properties of fuzzy multigroups under \(t\)-norms in terms of homomorphic images and homomorphic preimages, respectively, were presented.
Reflection wave of a pulsed by a point source
OMS-Vol. 4 (2020), Issue 1, pp. 142 – 146 Open Access Full-Text PDF
Adel A. S. Abo Seliem
Abstract: We calculate the electromagnetic field contained by a pulsed above a planar interface by using the modified Cagniard technique. The power density of spectrum of the wave that is observed at the distance from its emptily science usually differs from that of the source excitation, the power spectrum depends strangles on the speed of the wave in two media and the position of the observation point with respect to the interface and the source, form results of the rendition form a past source a discretely layer medium.
Random attractors for semilinear reaction-diffusion equation with distribution derivatives and multiplicative noise on \(\mathbb{R}^{n}\)
OMS-Vol. 4 (2020), Issue 1, pp. 126 – 141 Open Access Full-Text PDF
Fadlallah Mustafa Mosa, Abdelmajid Ali Dafallah, Eshag Mohamed Ahmed, Mohamed Y. A. Bakhet, Qiaozhen Ma
Abstract: In this paper, we investigate the existence of random attractors for a semilinear reaction-diffusion equation with a nonlinearity having a polynomial growth of arbitrary order \(p-1(p\geq 2)\), and with distribution derivatives and multiplicative noise defined on unbounded domains. The random attractors are obtained in \(L^{2}(\mathbb{R}^{n})\) and \(L^{p}(\mathbb{R}^{n})\) respectively. The semilinear reaction-diffusion equation is recast as a continuous random dynamical system and asymptotic compactness for this demonstrated by using uniform a priori estimates for far-field values of solutions as well as the cut-off technique.
Pythagorean fuzzy multiset and its application to course placements
ODAM-Vol. 3 (2020), Issue 1, pp. 55 – 74 Open Access Full-Text PDF
Paul Augustine Ejegwa
Abstract: The concept of fuzzy set theory is of paramount relevance to tackling the issues of uncertainties in real-life problems. In a quest to having a reasonable means of curbing imprecision, the idea of fuzzy sets had been generalized to intuitionistic fuzzy sets, fuzzy multisets, Pythagorean fuzzy sets among others. The notion of intuitionistic fuzzy multisets (IFMS) came into the limelight naturally because there are instances when repetitions of both membership and non-membership degrees cannot be ignored like in the treatment of patients, where each consultations are key in diagnosis and therapy. In IFMS theory, the sum of the degrees of membership and non-membership is less than or equals one at each levels. Supposing the sum of the degrees of membership and non-membership is greater than or equal to one at any level, then the concept of Pythagorean fuzzy multisets (PFMS) is appropriate to handling such scenario. In this paper, the idea of PFMS is proposed as an extensional Pythagorean fuzzy sets proposed by R. R. Yager. In fact, PFMS is a Pythagorean fuzzy set in the framework of multiset. The main objectives of this paper are to expatiate the operations under PFMSs and discuss some of their algebraic properties with some related results. The concepts of level sets, cuts, accuracy and score functions, and modal operators are established in the setting of PFMSs with a number of results. Finally, to demonstrate the applicability of the proposed soft computing technique, a course placements scenario is discussed via PFMS framework using composite relation defined on PFMSs. This soft computing technique could find expression in other multi-criteria decision-making (MCDM) problems.
Capacitated vehicle routing problem with column generation and reinforcement learning techniques
ODAM-Vol. 3 (2020), Issue 1, pp. 41 – 54 Open Access Full-Text PDF
Abdullahi Ibrahim, Jeremiah Ishaya, Nassirou Lo, Rabiat Abdulaziz
Abstract: Capacitated vehicle routing problem is one of the variants of the vehicle routing problem which was studied in this research. In this research we applied a reinforcement learning algorithm to find set of routes from a depot to the set of customers while also considering the capacity of the vehicles, in order to reduce the cost of transportation of goods and services. Each vehicle originates from a depot, service the customers and return to the depot. We compare the reinforcement learning model with an exact method; column generation and Google’s OR-tool. Our objective is to solve a large-size of problem to near-optimality. We were able to use reinforcement learning to solve upto 101 nodes to near-optimality.
Optimal polynomial decay for a coupled system of wave with past history
OMA-Vol. 4 (2020), Issue 1, pp. 49 – 59 Open Access Full-Text PDF
S. M. S. Cordeiro, R. F. C. Lobato, C. A. Raposo
Abstract: This work deals with a coupled system of wave with past history effective just in one of the equations. We show that the dissipation given by the memory effect is not strong enough to produce exponential decay. On the other hand, we show that the solution of this system decays polynomially with rate \(t^{-\frac{1}{2}}\). Moreover by recent result due to A. Borichev and Y. Tomilov, we show that the rate is optimal. To the best of our knowledge, there is no result for optimal rate of polynomial decay for coupled wave systems with memory in the previous literature.
