A study on multiplication operation on triangular fuzzy numbers

The arithmetic operations on fuzzy number are basic content in fuzzy mathematics. But still the operations of fuzzy arithmetic operations are not established. There are some arithmetic operations for computing fuzzy number. Certain are analytical methods and further are approximation methods. In this paper we, compare the multiplication operation on triangular fuzzy number between α-cut method and standard approximation method and give some examples.

A new method for dividing flood period in the variable-parameter Muskingum models

The Muskingum routing model is favored by water engineers owing to its simplicity and accuracy. A large amount of research is done to improve the accuracy of the model. One way to do so is to consider variable hydrological parameters during the flood routing period. In this study, the random selection (RS) method was proposed to divide the flood period of the nonlinear Muskingum model into three sub-periods. The proposed method was based on RS of members in each sub-region. It was applied to rout three flood hydrographs, and the objective function was the sum of squared errors. Comparing the results from the three variable-parameter nonlinear Muskingum model with those from the variable-parameter nonlinear Muskingum models in previous studies, the proposed model optimized the objective function in these hydrographs up to 61%. The uncertainty analysis of Muskingum parameters for Wilson's hydrograph was performed by the fuzzy alpha cut method, and it was found that the uncertainty of the parameter x is greater than the uncertainty of the parameters k and m.

A Short-Cut Data Mining Method for the Mass Spectrometric Characterization of Block Copolymers

A new data mining approach as a short cut method is given for the determination of the copolymer composition from mass spectra. Our method simplifies the copolymer mass spectra by reduction of the number of mass peaks. The proposed procedure, namely the selection of the mass peaks, which is based on the most abundant peak of the mass spectrum, can be performed manually or more efficiently using our recently invented Mass-remainder analysis (MARA). The considerable reduction of the MS spectra also simplifies the calculation of the copolymer quantities for instance the number- and weight-average molecular weights (Mn and Mw, respectively), polydispersity index (Đ = Mw/Mn), average molar fraction (cA) and weight fraction (wA) of the comonomer A and so on. These copolymer properties are in line with those calculated by a reference method taking into account all the mass peaks of the copolymer distribution. We also suggest a highly efficient method and template for the determination of the composition drift by processing the reduced mass spectra.

An Interpretation of Non-Preemptive Priority Fuzzy Queuing Model with Asymmetrical Service Rates

This paper presents Non-Preemptive priority fuzzy queuing model with asymmetrical service rates. Arrival rate and service rate are taken to be hexagonal, heptagonal, and octagonal fuzzy numbers. Here an interpretation is given to determine the performance measures by applying a new ranking technique through which the fuzzy values are reduced to the crisp values. This ranking technique has the benefit of being precise and relevant compared to other methods such as alpha-cut method and LR method. The main intention is to evaluate the fuzziness before the performance measures are processed by utilizing the regular queueing hypothesis. Three numerical examples are exhibited to show the validity implementation of the methodology.

Application of the Jaya algorithm to solve the optimal reliability allocation for reduction oxygen supply system of a spacecraft

In this paper the reliability of reduction oxygen supply system (ROSS) of a spacecraft which was calculated as a complex system using minimal cut method. The reliability of each component of system was calculated as well as the reliability importance of the system. The cost of each component of the system was possible approaches of the allocation values of reliability based the minimization of the overall cost in this system. The advantage of this algorithm can be used to allocate the optimization of reliability for simple or complex system. This optimization is achieved using the Jaya algorithm. The proposed technique is based on the notion that a conclusion reached on a particular problem should pass near the best results and avoid the worst outcomes. The original findings of this paper are: i) the system used in this paper is a spacecraft’s reduced oxygen supply system with the logarithmic cost function; and ii) the results obtained were by using the Jaya algorithm to solve specific system reliability optimization problems.

Analytic tadpole coefficients of one-loop integrals

One remaining problem of unitarity cut method for one-loop integral reduction is that tadpole coefficients can not be straightforward obtained through this way. In this paper, we reconsider the problem by applying differential operators over an auxiliary vector R. Using differential operators, we establish the corresponding differential equations for tadpole coefficients at the first step. Then using the tensor structure of tadpole coefficients, we transform the differential equations to the recurrence relations for undetermined tensor coefficients. These recurrence relations can be solved easily by iteration and we can obtain analytic expressions of tadpole coefficients for arbitrary one-loop integrals.

A Special Case of the Multiple Traveling Salesmen Problem in End-of-Aisle Picking Systems

This study focuses on the problem of sequencing requests for an end-of-aisle automated storage and retrieval system in which each retrieved load must be returned to its earlier storage location after a worker has picked some products from the load. At the picking station, a buffer is maintained to absorb any fluctuations in speed between the worker and the storage/retrieval machine. We show that, under conditions, the problem of optimally sequencing the requests in this system with a buffer size of m loads forms a special case of the multiple traveling salesmen problem in which each salesman visits the same number of cities. Several interesting structural properties for the problem are mathematically shown. In addition, a branch-and-cut method and heuristics are proposed. Experimental results show that the proposed simulated annealing-based heuristic performs well in all circumstances and significantly outperforms benchmark heuristics. For instances with negligible picking times for the worker, we show that this heuristic provides solutions that are, on average, within 1.8% from the optimal value.