Dual hesitation fuzzy sets are applied to handle inaccurate, preliminary or incomplete information and knowledge situations in actual operational investigation situations. This work presents a new method called Russell's Approximation Method (RAM) to solve the dual hesitant fuzzy transport problem. This procedure is illustrated using a numerical example, and the results achieved by this procedure are compared to the result obtained from North West corner method.

Conceptualisation and characterization of fuzzy prime ideals in near-subtraction semigroups is already carried out. We, in our paper, introduce the concept of anti-fuzzy prime ideals in near-subtraction semigroups. Further, we explore some of its properties.

In this paper, the notions of alpha-multi fuzzy sub algebra, alpha-multi fuzzy normal sub algebra, alpha-multi anti fuzzy sub algebra and alpha-multi anti fuzzy normal sub algebra of BG-algebra are defined by combining the concepts of multi fuzzy sets and alpha-fuzzy sets. And also some of their related properties are investigated under cartesian product and homomorphism.

Cloud computing is a developing technology that enables on-demand network access to the users through a shared pool of cluster computing resources. However, maintaining the stability of processing several tasks in the cloud environment is a complex issue. Hence, it requires a load balancing technique that allocates the task to the Virtual Machines (VMs) without affecting the performance of the system. This paper presents a technique for load balancing, called fractional dragonfly based load balancing algorithm (FDLA), by proposing two selection probabilities and fractional dragonfly algorithm. The proposed load balancing model utilizes certain parameters of VMs and Physical Machines (PMs) to select the tasks to be reallocated in the VMs for load balancing. The selection is based on the probabilities, Task selection probability (TSP) and VM selection probability (VSP), which are newly designed. Further, the proposed fractional dragonfly algorithm that combines dragonfly algorithm (DA) with Fractional Calculus (FC) performs an optimal selection of VMs for the reallocation of the task using a newly designed fitness function. In the performance analysis of FDLA based on load and number of tasks reallocated, the proposed FDLA could achieve a minimum load of 0.2133 with 14 reallocated tasks, indicating its effectiveness in load balancing.

In this paper, the concept of normal multi-fuzzy BG-ideals of BG-algebra is introduced by combining the concepts of multi-fuzzy sets and BG-ideals and its related properties are established.Also the Cartesian product of multi-fuzzy BG-ideals of BG-algebra is defined and its properties are discussed.

In this paper we solve the Fuzzy Transportation problems by using a new algorithm namely EAVAM . We introduce an approach for solving a wide range of such problems by using a method which applies it for ranking of the fuzzy numbers. Some of the quantities in a fuzzy transportation problem may be fuzzy or crisp quantities. In many fuzzy decision problems, the quantities are represented in terms of fuzzy numbers. Fuzzy numbers may be normal or abnormal, triangular or trapezoidal or any LR fuzzy number. Thus, some fuzzy numbers are not directly comparable. First, we transform the fuzzy quantities as the cost, coefficients, supply and demands, into crisp quantities by using our method and then by using the EAVAM, we solve and obtain the solution of the problem. The new method is systematic procedure, easy to apply and can be utilized for all types of transportation problem whether maximize or minimize objective function. Finally we explain this method with a numerical example.