A Multi-MOORA decision making method based on muirhead mean operators and complex spherical fuzzy uncertain linguistic setting

The Muirhead mean (MM) operators offer a flexible arrangement with its modifiable factors because of Muirhead’s general structure. On the other hand, MM aggregation operators perform a significant role in conveying the magnitude level of options and characteristics. In this manuscript, the complex spherical fuzzy uncertain linguistic set (CSFULS), covering the grade of truth, abstinence, falsity, and their uncertain linguistic terms is proposed to accomplish with awkward and intricate data in actual life dilemmas. Furthermore, by using the MM aggregation operators with the CSFULS, the complex spherical fuzzy uncertain linguistic MM (CSFULMM), complex spherical fuzzy uncertain linguistic weighted MM (CSFULWMM), complex spherical fuzzy uncertain linguistic dual MM (CSFULDMM), complex spherical fuzzy uncertain linguistic dual weighted MM (CSFULDWMM) operators, and their important results are also elaborated with the help of some remarkable cases. Additionally, multi-attribute decision-making (MADM) based on the Multi-MOORA (Multi-Objective Optimization Based on a Ratio Analysis plus full multiplicative form), and proposed operators are developed. To determine the rationality and reliability of the elaborated approach, some numerical examples are illustrated. Finally, the supremacy and comparative analysis of the elaborated approaches with the help of graphical expressions are also developed.

Selection of third party reverses logistic providers: an approach of BCF-CRITIC-MULTIMOORA using Archimedean power aggregation operators

One of the most powerful tools to operate imprecision is bipolar complex fuzzy sets (BCFSs), which is an enlargement of bipolar fuzzy sets (BFSs) as well as complex fuzzy sets (CFSs). This paper deals with an integrated MULTIMOORA (multi-objective optimization on the basis of ratio analysis plus full multiplicative form) framework as a generalization of fuzzy MULTIMOORA procedure to assess the multi-criteria decision-making (MCDM) problems with BCFSs. We develop BCF-Archimedean power weighted (ordered weighted) arithmetic and geometric aggregation operators (AOs) and discuss their properties from this point of view. The proposed Archimedean power-weighted AOs can eliminate the influence of extreme evaluating criteria values from some biased experts with different preference attitudes under the BCF setting. Afterward, we put forward an integrated MULTIMOORA algorithm based on the proposed AOs, where criteria weights are estimated using the CRITIC (criteria importance through inter-criteria correlation) method, which is a well-known objective weighting method based on aggregated score values of options, intensity contrast of every criteria and conflict among attributes. In the proposed methodology, criteria values are aggregated based on the MULTIMOORA method that involves three sub-methods: the ‘ratio system’, the ‘reference point’ and the ‘full multiplicative form’ and thus takes less computational time, minimum mathematical evaluations and bears good stability. In the following, third-party reverse logistics providers' (3PRLP) selection problem is brought into consideration to manifest the sufficiency of the developed methodology. At the end of this study, we draw attention to a comparison between the proposed decision-making approach with the corresponding BCF-CRITIC-TOPSIS and BCF-CRITIC-WASPAS methods.

Utilisation of Holt-Winters Forecasting Model in Lembaga Zakat Selangor (LZS) For Zakat Collection

Predicting the collection of zakat in Malaysian zakat institutions is crucial for effective zakat distribution. The surplus problems in zakat funds motivated this study to use more precise statistical methods to predict the future trend of zakat collection. The main objective of this paper is to forecast monthly zakat collection for 12 months ahead of the Lembaga Zakat Selangor (LZS). This research used the Seasonal Exponential Smoothing (Holt-Winters) model to predict zakat collection in LZS. The study utilised monthly zakat collection time series data from 2010 to 2018. The analysis was carried out using Excel Solver. The findings show that the Holt-Winters model is suitable to forecast the monthly zakat collection of LZS as it accounts for seasonal variation. The finding of this study indicates that the Holt-Winters Multiplicative (HWM) model best fits the monthly zakat collection time series data. The multiplicative form of Holt-Winters model yields 24.51% lower error compared to the additive one using the Mean Absolute Percentage Error (MAPE). The findings of this study will help zakat institutions to accurately predict future zakat collection which may consequently improve the management of zakat distribution without leaving a significant amount of zakat surplus. The forecast results can also be used to create a strategy to handle zakat funds based on the amount of registered asnaf. In addition, the study can serve as a basis for the development of a framework to forecast future zakat collections.

Assessment of the application feasibility of the genetic algorithm for airports operations optimization based on the collaborative decision-making principles

The article proposes a formalization methodology of the basic characteristics of the production processes of the aviation industry major components, such as airlines, airports and air traffic control authorities. This technique is not exhaustive, but it is quite suitable as the basis for the formation of the initial data for decision-making optimization under the conditions of airport operations performance and air traffic management, based on the principles of work coordination of the airports operational units. It is proposed to use a genetic algorithm as a tool for optimizing collaborative decision-making, which allows for a smaller number of iterations in real time to obtain a suboptimal solution that meets the requirements of the process participants. The mathematical model in multiplicative form is presented in making an assessment of the application feasibility of the genetic algorithm, taking into account the interests of three stakeholders. Planning the use of aircraft for the airport flight schedule based on the formalized data of the airline fleet, the capabilities of the base airport apron, as well as the restrictions of permanent and temporary nature is accepted as the original product. The article demonstrates the potential advantage of the genetic algorithm, the point of which is that within each step of a suboptimal choice of priorities instead of brute-force options limited but effective direct search of a reduced number of those options that have been chosen as the "elite" by using multiplicative form is carried out.

Asymptotic Expansion in Multiplicative Form in the Central Limit Theorem in the Case of Gamma Distribution

Study of estimation of accuracy of approximations in the Central limit theorem (CLT) is one of the known problems in probability theory. The main result here is the estimate of the theorem of Berry — Esseen. Its low accuracy is well known. So this theorem guarantees accuracy of approximation 103 in the CLT only if the number of summands in the normed sum is greater than 160 000. Therefore, increasing the accuracy of the approximations in the CLT is an actual task. In particular, for this purpose are used asymptotic expansions in the Central limit theorem. As a rule, asymptotic expansions have additive form. Although it is possible to construct expansions in the multiplicative form. So V.M. Kalinin in [3] received the multiplicative form of the asymptotic expansions. However, he constructed asymptotic expansions for probability distributions (multinomial, Poisson, Student’s t-distribution). So very naturally the question arises: how to build multiplicative expansions in CLT? Secondly, what are the forms of decompositions in CLT in terms of accuracy approximations are better: additive or multiplicative? This paper proposes new asymptotic expansions in the central limit theorem which permit us to approximate distributions of normalized sums of independent gamma random variables with explicit estimates of the approximation accuracy and comparing them with expansions in terms of Chebyshev — Hermite polynomials. New asymptotic expansions is presented in the following theorem. Comparing multiplicative asymptotic expansion from theorem 1 with the additive asymptotic expansion from [5], we obtain that multiplicative asymptotic expansion of the density of normalized the sums in the case of gamma distribution give a much greater accuracy numerical calculations are compared with asymptotic additive expansion provided a much smaller number of calculations. The author would like to thank Vladimir Senatov for setting the task and paying attention to this work.

Rényi Entropy Power Inequalities via Normal Transport and Rotation

Following a recent proof of Shannon’s entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Rényi entropy is presented that uses transport arguments from normal densities and a change of variable by rotation. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.

Rényi Entropy Power Inequalities via Normal Transport and Rotation

Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Rényi entropy is presented that uses transport arguments from normal densities and a change of variable by rotation. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.