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The main aim to perform the mouse cursor operations and scrolling function and also move the cursor. A professional webcam, novel process of managing mouse click was developed. The integration of different efforts would include changing keypad elements, integrating more keys, or shifting the monitoring ball's placement. However, they recommend that the hardware design be altered. The proposed approach solves present inadequacies as well as utilized of a hardware mouse, but also numerous motions cause injury in the palms. It should be predicated on a visualization impact of motion, accompanied by artificial intelligence technology, image classification, and motion tracking, to regulate mouse tasks (left and right-clicking, double- clicking, and scrolling), as well as Machine Cognitive approach to obtain a greater virtual touchpad to the current systems. A camera should be used to capture palm motions.

In this article, We introduced intuitionistic fuzzy translation and intuitionistic fuzzy multiplication on INK-algebras and derived some results to get the structure of intuitionistic fuzzy INK-subalgebra.

In this paper, first we define the notation of INK-algebra-ideal, fuzzy set, intuitionistic fuzzy K-ideals and intuitionistic fuzzy closed K-ideals ,direct product of intuitionistic fuzzy K-ideals in INK-algebras .Using the concept of level subset, we prove some theorems which show that there are some relationships between these notation. Finally we define the homomorphism of INK-algebra and then we give related theorem about the relationship between their images and direct product of intuitionistic fuzzy K-ideals.

A batch arrival retrial queueing model with k optional stages of service, extended Bernoulli vacation and stand-by is studied. After completion of the ith stage of service, the customer may have the option to choose (i + 1)th stage of service with probability θi or may leave the system with probability qi = 1 − θi, I = 1, 2, …, k − 1 and qk = 1. After service completion of each customer, the server may take a vacation with probability v1 and extend a vacation with probability v2 or rejoin the system after the first vacation with probability 1 − v2. Busy server may get to breakdown and the stand-by server provides service only during the repair times. At the completion of service, vacation or repair, the server searches for the customer in the orbit (if any) with probability α or remains idle with probability 1 − α. By using the supplementary variable method, steady state probability generating function for system size, some system performance measures like Lq, Ls, Wq and Ws are discussed. Simulation results are given using MATLAB.

The objective of the paper is to analyse two-level control policy of an MX∕G(a, b)∕1 queueing system with fast and slow vacation rates and vacation disruption. In the service completion epoch, if the queue length is less than ‘a’, then the server leaves for a vacation. In this model depending upon the queue length, the server is allowed to take two types of vacation called fast vacation and slow vacation. Addressing this in the service completion epoch, if the queue length ψ(say) is less than β where β ζ, where a − 1 ≥ ζ > β during service completion, then the server leaves for fast vacation. During slow vacation if the queue length reaches the value ζ, then the server breaks the slow vacation and switches over to fast vacation. Also if the queue length attains the threshold value ‘a’ during fast vacation, then the server breaks the fast vacation too and moves to tune-up process to start the service. After tune-up process service will be initiated only if ψ ≥ N(N > b). For the designed queueing system probability, generating function of the queue size at an arbitrary time epoch is obtained by using supplementary variable technique. Various performance characteristics will also be derived with suitable numerical illustrations. Cost-effective analysis is also carried out in the paper.

This paper concentrates on single server bulk arrival queue system with batch size dependent service and working vacation. The server provides service in two service modes depending upon the queue length. The server provides single service if the queue length is at least ‘a’. On the other hand the server provides fixed batch service if the queue length is at least ‘k’ (k > a). Batch service is provided with some fixed batch size ‘k’. After completion of service if the queue length is less than ‘a’ then the server leaves for working vacation. During working vacation customers are served with lower service rate than the regular service rate. Service during working vacation also contains two service modes. For the proposed model probability generating function of the queue length at an arbitrary time will be obtained by using supplementary variable technique. Some performance measures will also be presented with suitable numerical illustrations.This paper concentrates on single server bulk arrival queue system with batch size dependent service and working vacation. The server provides service in two service modes depending upon the queue length. The server provides single service if the queue length is at least ‘a’. On the other hand the server provides fixed batch service if the queue length is at least ‘k’ (k > a). Batch service is provided with some fixed batch size ‘k’. After completion of service if the queue length is less than ‘a’ then the server leaves for working vacation. During working vacation customers are served with lower service rate than the regular service rate. Service during working vacation also contains two service modes. For the proposed model probability generating function of the queue length at an arbitrary time will be obtained by using supplementary variable technique. Some performance measures will also be presented with suitable numerical illustrations.

In this paper we examine IVF INK-ideal in INK-algebras by giving a couple of definitions and relative hypotheses. The image and preimage of IVF INK-ideal become i-v fuzzy INK-ideals in INK-algebras.

Every year countless hours are lost in traffic jams. When the density of traffic is sufficiently high small disturbances in vehicle’s accelerations can cause phantom traffic jams. We can relate the traffic flow to mathematics and physics like that of liquids and gases. This paper presents mathematical model for phantom jams and Gauss Jordan elimination for traffic flow.

An idempotent of a semigroup T is an element e in T such that In many semigroups, idempotents can be recognized easily. Thus it plays an important role in the structure of semigroups especially on regular semigroups. This article reviews about some research work done about the structure of regular semigroups with a special emphasis on its idempotents.

Unreliable vacation retrial queue and multi stages of service delay in repair is studied. After completion of the i th (i=1,2,...k) stage of service, the unit may have the option to choose (i+1)th stage of service with probability θi , or with pi may join into orbit to give feedback or may leave the station with probability qi = 1 – pi – θi , (i = 1,2,...k –1) and qi = 1 – pi , (i = k). After service completion if the orbit has no units, server takes avacation. During repair, the unit waiting in the system to complete the remaining service (delay time) is discussed. We analyzed the system using the method of supplementary variable. Simulation results are given using MATLAB.

In this paper, we have considered an MX / (a,b) / 1 queueing system with server breakdown without interruption, multiple vacations, setup times and N-policy. After a batch of service, if the size of the queue is ξ (< a), then the server immediately takes a vacation. Upon returns from a vacation, if the queue is less than N, then the server takes another vacation. This process continues until the server finds atleast N customers in the queue. After a vacation, if the server finds at least N customers waiting for service, then the server needs a setup time to start the service. After a batch of service, if the amount of waiting customers in the queue is ξ (≥ a) then the server serves a batch of min(ξ,b) customers, where b ≥ a. We derived the probability generating function of queue length at arbitrary time epoch. Further, we obtained some important performance measures.

In this paper, server provides service in two service modes, as single or in bulk according to the queue length. The server provides single service, if the queue length reaches value 'a' and batch service, if the queue length reaches the value 'c' (c > a). After completing the service if the queue length is less than 'a' then the server leaves for vacation. During secondary job (vacation) if the queue length attains the value 'a' then the server breaks the vacation and provides primary service. In the service completion epoch if the server is not reliable then the server has undergone renovation of service station. For the proposed model probability generating function of queue size at an arbitrary time epoch is obtained. Various performance measures are derived with suitable numerical illustration. A cost model is also presented for the proposed model.

In this paper, we have investigated bulk retrial queueing system with Bernoulli vacation schedule and variable server capacity. According to the variable server capacity bulk service rule, the server can serve a minimum of one customer and a maximum of B customers in a batch. After completion of a batch of service, if the orbit is empty, then the server will go for a vacation. After completion of each batch of service, if the orbit is non-empty, then the server either go for a vacation with probability p or resumes its service with probability p. If arriving customers finds the server is busy with service or on vacation, they are grouped and it termed as unsatisfied customers or orbit. Unsatisfied customers will retry its appeal for service after some time. We have presented steady state system equations for the proposed model. Also, we have obtained some important performance measures for this system. Further, we have given numerical justification for this queueing system.

This paper deals with the steady state analysis of unreliable batch arrival feedback retrial queue with k stages of service and Bernoulli vacation policy, where the busy server is subjected to breakdown due to the arrival of negative customers. After completion of the ith, (i = 1, 2, ..., k) stage of service, the customer may have the option to choose (i + 1)th stage with probability θi, with probability pi may join into orbit as feedback customer or may leave the system with probability 1 – θi – pi = qi, if the service is successful. The server takes Bernoulli vacation after the service completion. Arriving positive customers may balk (or renege) the system at particular times. After completion of the service, vacation or repair, the server searches for the customer in the orbit or remains idle. The system is solved by using the supplementary variable method and numerical illustrations are discussed.

The concept of T-normed fuzzy TM-subalgebras is introduced by applying the notion of t-norm to fuzzy TM-algebra and its properties are investigated. The ideas based on minimum t-norm are generalized to all widely accepted t-norms in a fuzzy TM-subalgebra.The characteristics of an idempotent T-normed fuzzy TM-subalgebra are studied. The properties of image and the inverse image of a T-normed fuzzy TM-subalgebra under homomorphism is discussed. The T-direct product and T-product of T-normed fuzzy TM-subalgebras are also considered.