Journal of Mahani Mathematical Research
Volume:11 Issue: 3, Summer and Autumn 2022

The aim of this article is to apply a $(3,2)$-fuzzy set to the UP-subalgebras and UP-filters of UP-algebras. The concepts of $(3,2)$-fuzzy UP-subalgebra, $(3,2)$ -fuzzy near UP-filter and $(3,2)$ -fuzzy UP-filter in UP-algebras are introduced and  several properties, including their relations, are investigated. The conditions under which the $(3,2)$-fuzzy UP-subalgebra $($resp., $(3,2)$ -fuzzy near UP-filter$)$ can be the $(3,2)$-fuzzy near UP-filter $($resp., $(3,2)$-fuzzy UP-filter$)$ are searched. The characterizations of $(3,2)$-fuzzy UP-filter is provided and the relationship between intuitionistic fuzzy UP-subalgebra and $(3,2)$-fuzzy UP-subalgebra is discussed. We use fuzzy UP-subalgebra $($resp., fuzzy near UP-filter, fuzzy UP-filter$)$ to create a $(3,2)$-fuzzy UP-subalgebra $($resp., $(3,2)$-fuzzy near UP-filter, $(3,2)$-fuzzy UP-filter$)$.

In this article we introduce wavelet sets and consider a special wavelet set in R. We build a basis associated to this type wavelet sets and use operational matrix of this basis to solve nonlinear Riccati differential equations and Riemann-Liouville fractional integral equations of order $\alpha >0$, numerically. Convergence analysis of this basis is investigated. Also, we give examples that show the accuracy of the new method by comparing it with previous methods.

In this paper first, we introduce and analyze the strongly regular relations $\lambda^*_{e}$ and $\Lambda^*_{e}$ on a hyperring such that the derived quotient ring is unitary and unitary commutative, respectively. Next, we define and study the notion of $\lambda_e$-parts in a hyperring and  characterize the $\lambda_e$-parts in a $\lambda_e$-strong hyperring $R$. Finally, we introduce the notion of $\lambda_e$-closed hyperideal in a hyperring and study some of its fundamental properties in Krasner hyperrings.

In mobile ad hoc networks (MANETs), innumerable intermediate nodes interchange information without the need for infrastructure. In these networks, nodes depend upon each other for routing and forwarding packets, and communication among them is very important. Forwarding packets consumes network bandwidth, local CPU time, memory, and energy. Therefore, some nodes might intend not to forward packets to save resources for their use that called selfish nodes. The destruction of basic action of the network can occur due to this selfish behavior of the node. So, in this paper, we focused on dropper misbehavior for data packets and route request packets. For detecting this kind of nodes in this paper, we improved the ad hoc on-demand distance vector (AODV) routing protocol and proposed a new routing protocol for detecting selfish nodes. The performance analysis shows that the DSNAODV (Detecting Selfish Node based on Ad hoc On-demand Distance Vector routing protocol) protocol can improve the packet delivery ratio and use less energy compared to AODV and EBTS protocols.

In BCK-algebra, the concept of  a positive implicative $T\&F$-ideal is introduced, and further several properties are  investigated. The relationship between  $T\&F$-ideals and  positive implicative $T\&F$-ideals is established, and an example is given to reveal that  a $T\&F$-ideal is not a positive implicative $T\&F$-ideal. Various conditions under which  a $T\&F$-ideal can be a positive implicative $T\&F$-ideal are explored and various characterizations of a positive  implicative $T\&F$-ideal are studied. The extended property of a positive implicative $T\&F$-ideal is constructed.

Using the kronecker product definition of two simple graphs, the kronecker product of two RL-graphs was defined and is defined and it is further shown to be an RL-graph. Consequently, it is demonstrated that the kronecker product of two RL-graphs is commutative properties (i.e G⨂H = H⨂G). It is also stated that the kronecker product of two strong RL- graphs is a strong RL-graph but not necessarily vice-versa. It is bounded α and β of the kronecker product of two RL-graphs by α and β of its constituent graphs, respectively. Moreover, if H is an RL-graph, and G and G' are two isomorphic RL-graphs, then the kronecker product of G and H and the kronecker product of G' and H are isomorphic RLgraphs.In addition, some notions such as regular RL-graphs, α-regular RL-graphs, and totally regular RL-graphs are proposed and explicated. One application of this operation, which has determined and estimated the group, having the maximum efficiency work among its members, is also suggested. Finally, it is brought one application of this operation that is  determined and estimated the group that has the maximum interact among its members. Ultimately, in light of the  above, some related theorems are proved and several examples are provided to illustrate these new notions.

This paper is concerned with the blow-up and global existence of solutions for Higher-Order Kirchhoff-Type Equations with variable exponents. Under suitable assumptions, we prove some finite time blow-up results for certain solutions with positive initial energy by using a concavity-type method. This work improves and generalizes several interesting recent blow-up results on wave equations in particular on Kichhoff-type equations. We also show the global existence of solutions under appropriate conditions.

We know that $\Gamma-$ring, $\Gamma-$incline, $\Gamma-$semiring, $\Gamma-$semigroup are generalizations ofring, incline, semiring and semigroup respectively. In this paper, we introduce the concept of $\Gamma-$BCK-algebras as a generalization of BCK-algebras and study $\Gamma-$BCK-algebras. We also introduce subalgebra, ideal, closed ideal, normal subalgebra, normal ideal and construct quotient of $\Gamma-$BCK-algebras. We prove that if $f: M\to L$ be a normal homomorphism of $\Gamma-$BCK-algebras $M$ and $N,$ then $\Gamma-$BCK-algebra $M/N$ is isomorphic to $Im (f)$ where $N =Ker (f).$

Software Development Effort Estimation (SDEE) can be interpreted as a set of efforts to produce a new software system. To increase the estimation accuracy, the researchers tried to provide various machine learning regressors for SDEE. Kernel Ridge Regression (KRR) has demonstrated good potentials to solve regression problems as a powerful machine learning technique. Gravitational Search Algorithm (GSA) is a metaheuristic method that seeks to find the optimal solution in complex optimization problems among a population of solutions. In this article, a hybrid GSA algorithm is presented that combines Binary-valued GSA (BGSA) and the real-valued GSA (RGSA) in order to optimize the KRR parameters and select the appropriate subset of features to enhance the estimation accuracy of SDEE. Two benchmark datasets are considered in the software projects domain for assessing the performance of the proposed method and similar methods in the literature. The experimental results on Desharnais and Albrecht datasets have confirmed that the proposed method significantly increases the accuracy of the estimation comparing some recently published methods in the literature of SDEE.

‎In probability and statistics‎‎ the earliest concept related to independence is the uncorrelatedness. ‎It is well known that a pair of independent random variables are uncorrelated‎, ‎but uncorrelated random variables may or may not be independent‎.‎The aim of this paper is to provide some new models for the joint distribution of the uncorrelated random variables that are not independent. ‎The proposed models include a bivariate mixture structure, a transformation method, and copula method. Several examples illustrating the results are included.

In an earlier paper by Seliga, Siran and the second author (J. Mahani Math. Res. Center 8 (2019) 37–51) on lifting continuity properties of aggregation functions to their super- and sub-additive transformations it was shown that uniform continuity is preserved by super-additive transformations in dimension 1. We give a shorter and more direct proof of this result and of a related linear bound on uniformly continuous aggregation functions.

In this paper, a new algorithm is proposed for solving a multicriteria optimization problem where the feasible set is an $m-$dimensional cube. In fact, the idea of the multicriteria big cube small cube method is employed to develop the new algorithm. It is proved that, for a given epsilon vector, the output of the suggested algorithm involves all epsilon efficient solutions as well as all efficient solutions. Furthermore, the algorithm is applied to a multicriteria location problem. The results show that the recommended algorithm can obtain more epsilon efficient solutions in comparison with the main multicriteria big cube small cube method.