Approach to obtaining weights of uncertain ordered weighted geometric averaging operator

The ordered weighted geometric averaging（OWGA） operator is extended to accommodate uncertain conditions where all input arguments take the forms of interval numbers. First, a possibility degree formula for the comparison between interval numbers is introduced. It is proved that the introduced formula is equivalent to the existing formulae, and also some desired properties of the possibility degree is presented. Secondly, the uncertain OWGA operator is investigated in which the associated weighting parameters cannot be specified, but value ranges can be obtained and the associated aggregated values of an uncertain OWGA operator are known. A linear objective-programming model is established; by solving this model, the associated weights vector of an uncertain OWGA operator can be determined, and also the estimated aggregated values of the alternatives can be obtained. Then the alternatives can be ranked by the comparison of the estimated aggregated values using the possibility degree formula. Finally, a numerical example is given to show the feasibility and effectiveness of the developed method.

Generalized ordered weighted averaging operators based methods for MADM in intuitionistic fuzzy set setting

Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and the relative degrees of non-membership are formulated as IF sets, the weights and values of alternatives on both qualitative and quantitative attributes may be expressed as IF sets in a unified way.Then a MADM method based on generalized ordered weighted averaging operators is proposed.The proposed method is illustrated with a numerical example.

Linear goal programming approach to obtaining the weights of intuitionistic fuzzy ordered weighted averaging operator

The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.

An anomaly detection method for spacecraft solar arrays based on the ILS-SVM model

Solar arrays are important and indispensable parts of spacecraft and provide energy support for spacecraft to operate in orbit and complete on-orbit missions.When a spacecraft is in orbit,because the solar array is exposed to the harsh space environment,with increasing working time,the performance of its internal electronic components gradually degrade until abnormal damage occurs.This damage makes solar array power generation unable to fully meet the energy demand of a spacecraft.Therefore,timely and accurate detection of solar array anomalies is of great significance for the on-orbit operation and maintenance management of spacecraft.In this paper,we propose an anomaly detection method for spacecraft solar arrays based on the integrated least squares support vector machine(ILS-SVM)model:it selects correlated telemetry data from spacecraft solar arrays to form a training set and extracts n groups of training subsets from this set,then gets n corresponding least squares support vector machine(LS-SVM)submodels by training on these training subsets,respectively;after that,the ILS-SVM model is obtained by integrating these submodels through a weighting operation to increase the prediction accuracy and so on;finally,based on the obtained ILS-SVM model,a parameterfree and unsupervised anomaly determination method is proposed to detect the health status of solar arrays.We use the telemetry data set from a satellite in orbit to carry out experimental verification and find that the proposed method can diagnose solar array anomalies in time and can capture the signs before a solar array anomaly occurs,which reflects the applicability of the method.

Three methods for generating monotonic OWA operator weights with given orness level

Based on the properties of ordered weighted averaging (OWA) operator and regular increasing monotone (RIM) quantifier, three methods for generating monotonic OWA operator weights are proposed. They are geometric OWA operator weights, equidifferent OWA operator weights and the modified RIM quantifier OWA weights. Compared with most of the common OWA methods for generating weights, the methods proposed in this paper are more intuitive and efficient in computation. And as there are more than one solution in most cases, the decision maker can set some initial condition and chooses the appropriate solution in the real decision process, which increases the flexibility of decision making to some extent. All these three OWA methods for generating weights are illustrated by numerical examples.

Preservation of the NBUCA Class of Life Distributions

The purpose of this paper is to discuss the closure properties of increasing convex average order and NBUCA life distributions. Under the assumption that the units are only independent, characterizations of NBUCA class of life distributions are given. It is shown that NBUCA class is closed under the random maxima and the formation of parallel systems of independent units. As an application of the main results, the behavior of this class is developed in terms of the monotonicity of the residual life of k-out-of n systems given the time at which the （n -k ）-th failure has occurred.

Some OWA operator weights determination methods with RIM quantifier

Based on the quantifier guided method,an ordered weighted averaging(OWA)weights generating method under given orness level with regular increasing monotone(RIM)quantifiers is proposed.Then the RIM quantifier based OWA weights generating method is modified to make the generated weights be monotonic,which can be used to express the decision maker's consistent preference information.Finally,both of these weights generating methods are extended to their generic forms,so that they can generate the OWA weights for any ordinary elements set with any given aggregated value.

Interval-valued intuitionistic fuzzy aggregation operators

The notion of the interval-valued intuitionistic fuzzy set （IVIFS） is a generalization of that of the Atanassov＇s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVlFSs. These operators are not monotone with respect to the total order of IVIFS, which is undesirable. This paper shows how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. Moreover, two new aggregation operators based on the t.ukasiewicz triangular norm are proposed, which are monotone with respect to the total order of IVIFS. Finally, an application of the interval-valued intuitionistic fuzzy weighted averaging operator is given to multiple criteria decision making.

Land use suitability analysis for town development planning in Nanjing hilly areas: A case study of Tangshan new town, China

Land use suitability analysis plays an important role in sustainable land use and solving environmental problems caused by rapid urban development.A land use suitability mapping approach for town development planning in hilly areas was constructed based on two multi-criteria evaluation methods:Weighted Linear Combination(WLC)and Ordered Weighted Averaging(OWA),to comparatively evaluate and map land use suitability of Tangshan new town in Nanjing,China.Fourteen evaluation factors related to topographic,environmental,socio-economics and historical sites data were used as suitability criteria.The analytic hierarchy process(AHP)method and GIS techniques were integrated into the evaluation models to create the land use suitability map for town development planning.The results of WLC approach showed that 11.4%of the total area is highly suitable while the 48.6%is unsuitable.The results of WLC and OWA approach showed the distribution of degree of land use suitability is almost the same.The areas located at the southern and eastern flat regions are highly suitable for land use,whereas the areas close to the mountain forests,steep slopes,waters,and hot springs,have lower suitability for land use.Sensitivity analysis indicated that the suitability results of the two proposed methods are robust.Indirect validation was achieved by mutual comparison of suitability maps derived from the WLC and OWA methods.It demonstrated that the overall agreement is 90.81%and kappa coefficient is 0.81,indicating that both methods provide very similar spatial suitability distributions.By overlaying the resultant map with the previous master plan map of Tangshan new town,the overlay map once again indicated a satisfactory ecological fit between the two maps.At last,several recommendations are proposed aiming at improving the long-term town development plan for Tangshan new town.

Impact of Sophisticated Stationary Forecast Techniques on the Bullwhip Effect in a Supply Chain

The bullwhip effect in a multistage supply chain was analyzed using sophisticated stationary forecasts (third order moving average and third order exponential smoothing forecasts). The third order exponential smoothing and third order moving average forecasts sometimes have a variance reducing effect on the supply chain.In a supply chain with positively correlated or independent and identically distributed (i.i.d) demands, the order variance based on simple moving average forecast (or simple exponential smoothing forecast) is larger than the order variance based on second order moving average forecast (or second order exponential smoothing forecast),and the order variance based on second order moving average forecast( or second order exponential smoothing forecast) is larger than the order variance based on third order moving average forecast( or third order exponential smoothing forecast). In addition, for i.i.d demands, third order exponential smoothing forecast leads to a larger variation than third order moving average forecast.

Data envelopment analysis procedure with two non-homogeneous DMU groups

The classic data envelopment analysis（DEA） model is used to evaluate decision-making units＇（DMUs） efficiency under the assumption that all DMUs are evaluated with the same criteria setting. Recently, new researches begin to focus on the efficiency analysis of non-homogeneous DMU arose by real practices such as the evaluation of departments in a university, where departments argue for the adoption of different criteria based on their disciplinary characteristics. A DEA procedure is proposed in this paper to address the efficiency analysis of two non-homogeneous DMU groups. Firstly, an analytical framework is established to compromise diversified input and output（IO） criteria from two nonhomogenous groups. Then, a criteria fusion operation is designed to obtain different DEA analysis strategies. Meanwhile, Friedman test is introduced to analyze the consistency of all efficiency results produced by different strategies. Next, ordered weighted averaging（OWA） operators are applied to integrate different information to reach final conclusions. Finally, a numerical example is used to illustrate the proposed method. The result indicates that the proposed method relaxes the restriction of the classical DEA model,and can provide more analytical flexibility to address different decision analysis scenarios arose from practical applications.

Applied Machine Learning Methods for Detecting Fractured Zones by Using Petrophysical Logs

In the last decade, a few valuable types of research have been conducted to discriminate fractured zones from non-fractured ones. In this paper, petrophysical and image logs of eight wells were utilized to detect fractured zones. Decision tree, random forest, support vector machine, and deep learning were four classifiers applied over petrophysical logs and image logs for both training and testing. The output of classifiers was fused by ordered weighted averaging data fusion to achieve more reliable, accurate, and general results. Accuracy of close to 99% has been achieved. This study reports a significant improvement compared to the existing work that has an accuracy of close to 80%.

A Scalable Synthesis of Multiple Models of Geo Big Data Interpretation

The paper proposes a scalable fuzzy approach for mapping the status of the environment integrating several distinct models exploiting geo big data. The process is structured into two phases: the first one can exploit products yielded by distinct models of remote sensing image interpretation defined in the scientific literature, and knowledge of domain experts, possibly ill-defined, for computing partial evidence of a phenomenon. The second phase integrates the partial evidence maps through a learning mechanism exploiting ground truth to compute a synthetic Environmental Status Indicator (ESI) map. The proposal resembles an ensemble approach with the difference that the aggregation is not necessarily consensual but can model a distinct decision attitude in between pessimistic and optimistic. It is scalable and can be implemented in a distributed processing framework, so as to make feasible ESI mapping in near real time to support land monitoring. It is exemplified to map the presence of standing water areas, indicator of water resources, agro-practices or natural hazard from remote sensing by considering different models.

Two upper bounds for the Erdos-Hooley Delta-function

For integer n≥1 and real u,let Δ(n,u):=|{d:d] n,e^(u)<d≤e^(u+1)}|.The Erdos-Hooley Deltafunction is then defined by Δ(n):=Max_(u∈R)Δ(n,u).We improve the current upper bounds for the average and normal orders of this arithmetic function.

基于适宜性评价的国土空间分区及其生态效应研究——以鄂州市为例

Exploring the spatial zoning of urban territories and their ecological effects under different decision preferences is an important approach to promote the sustainable utilization of regional resources.This paper constructs an index system for evaluating the suitability of territorial space development from the perspectives of urban development,agricultural production,and ecological conservation.It predicts and simulates the trade-offs between territorial space development and protection in Ezhou under different decision preferences using the Analytic Hierarchy Process(AHP) and Ordered Weighted Averaging(OWA) method.The modified equivalent factor method is used to analyze the ecosystem service values of different functional areas.The results indicate the following:(1) the preferences of decision-makers considerably influence the level of territorial space suitability.Higher(lower)levels of concern for risk result in more optimistic(pessimistic) evaluators,and this affects the priority given to ecological protection(development and utilization).(2) Under the ecological priority scenario,the status quo scenario and development priority scenario,there are significant differences in regional suitability levels.The ecological priority scenario gives high importance to ecological protection,resulting in the absolute protection of the Liangzi lake area,with 42.59% of Liangzihu district considered unsuitable for development.In contrast,the development orientation scenario designates Echeng district,an economic and political center,as highly suitable for development,with over 60% of the area available for development.(3) The total value of ecosystem services in Ezhou city was 213.355 billion yuan in 2018.Ecosystem service values were mainly provided by the water area in the permanently unsuitable development zone,leading to a mismatch between the supply and demand of ecosystem services under different scenarios.

A Novel Dependent Aggregation Approach for Intuitionistic Uncertain Linguistic Multiple Attribute Group Decision Making

The multiple attribute group decision making problem in which the input arguments take the form of intuitionistic uncertain linguistic information is studied in the paper.Based on the operational principles of intuitionistic uncertain linguistic variables and the concept of the expected value and accuracy function,some new dependent aggregation operators with intuitionistic uncertain linguistic information including the dependent intuitionistic uncertain linguistic ordered weighted average(DIULOWA)operator,the dependent intuitionistic uncertain linguistic ordered weighted geometric(DIULOWG)operator,the generalized dependent intuitionistic uncertain linguistic ordered weighted aggregation(GDIULOWA)operator and so on are developed,in which the associated weights only depend on the aggregated arguments.Also,we study some desirable properties of the aggregation operators.Moreover,the approach of multiple attribute group decision making with intuitionistic uncertain linguistic information based on the developed operators is proposed.Finally,an illustrative numerical example is given to show the practicality and effectiveness of the proposed approaches.

Development of a mathematical model to evaluate the rate of aggregate risk of invasive alien plant species： Fuzzy risk assessment approach

This study presents a novel approach to evaluate the rate of aggregate risk of Invasive Alien Plant Species. Using risk values and grade of importance of weights of risk factors which may reflect invasiveness of plant species are considered. We use Linguistic Ordered Weighted Averaging operator to evaluate the grade of important of weights. Since the risk values and important weights are identified from two different linguistic term sets, fuzzy set theory techniques were used to combine the two sets. The rates obtained from the model were compared with NRA risk levels and the model was validated with data from known and non-invasive species. The model is improved by weighting the risk values of risk factors. The improved model produced significant results and resulted a better tracking system for identifying potential invaders than the conventional risk assessment.