Abstract
The **ordered** **weighted** **averaging** **objective** (OWA) is an aggregate func- tion over multiple optimization criteria which received increasing attention by the research community over the last decade. Different to the **ordered** **weighted** sum, weights are attached to **ordered** **objective** functions (i.e., a weight for the largest value, a weight for the second-largest value and so on). As this contains max-min or worst-case optimization as a special case, OWA can also be considered as an **alternative** approach to robust optimization.

Figure 2 shows the sequence of actions in classic spatial decision making and in GIS-based spatial decision making. Although the **alternative**-focused approach is mentioned in connection with the generation of alternatives, values are in general more fundamental than alternatives with respect to a decision problem. In other words, alternatives are the means to achieving the more fundamental values. Once the decision problem is defined, the spatial multi-criteria analysis focuses on evaluation criteria, which means specifying a comprehensive set of objectives that reflects all concerns relevant to the decision problem, and measures for achieving those objectives. Such measures are called attributes. A measurement scale must be established for each attribute. The degree, to which the objectives are met, as determined by the attributes, is the basis for comparing alternatives. The evaluation criteria are associated with geographical entities and relationships between entities and therefore can be represented in the forms of maps (a raster or a vector model). GIS data- handling and analysis capabilities are used to generate inputs to spatial multi-criteria decision analysis [21].

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The analysis of indirect citations in patent citation networks adds to our understanding of citation network dynamics by considering the role of the indirect ties among nodes, a somewhat overlooked issue in the literature. This thesis applies the OWA (originally developed in the context of web search engines) as an **alternative** method to analyse networks of knowledge flows, and to assess the role of indirect ties and reduce complexity for decision makers and analysts. This study provides evidence on the use of the OWA in decision making analysis in the complex context of large citation networks. More specifically, the thesis shows that the OWA operator provides measures of the cumulative inventive process by accounting for the diffusion of knowledge along several stages of the knowledge creation process. The measures provided explain how indirect citations to previous inventions reflect awareness of that knowledge in the specific knowledge context. For example, if an invention is not cited immediately, but does not disappear, it can take some time for subsequent inventors to acknowledge it. Within this perspective, investigating long citation chains using OWA will uncover more historical citations information.

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exhibit the characteristics of affirmation, negation, and hesitation. In such cases, the data or preferences given by the experts may be appropriately expressed in IFNs. For example, in multi-criteria decision-making problems, such as personnel evaluations, medical diagnosis, project investment analysis, etc., each IFN provided by the expert can be used to express both the degree that an **alternative** should satisfy a criterion and the degree that the **alternative** should not satisfy the criterion. The IFN is highly useful in depicting uncertainty and vagueness of an object, and thus can be used as a powerful tool to express data information under various different fuzzy environments which has attracted great attentions [29-39].

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Spatial MCA focuses on geographically defined decision alternatives which are evaluated by a set of criteria (Carver, 1991; Jankowski, 1995; Malczewski, 1999). The kernel of spatial MCA is the integration of MCA and GIS methods. Conventional MCA can be used to deal with the complexity of the real world problems that may involve a large number of alternatives and multiple and conflicting evaluation criteria. Nevertheless, to solve spatial decision problems, MCA also requires spatial analytical functions and the capacity of processing geographic data. This calls for the integration MCA and GIS. In spatial multicriteria analysis or GIS-MCA, attributes, represented as map layers, are the properties of geographical entities; hence attributes can be interpreted as criteria (criterion maps). The weight associated with a criterion map represents the preference of decision makers (or experts). It indicates the relative importance of criteria. The spatial units (locations or areas) represent the decision (or evaluation) alternatives. In the raster data, each raster cell or a combination of cells is considered as an **alternative**. In the vector data, alternatives are represented by points, lines, polygons or a combination of these three spatial objects.

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Data mining, also known as knowledge discovery in databases, provides efficient automated techniques for discovering potentially useful, hidden knowledge or relations among data from large databases (Han & Kamber, 2006). Data mining functions include classification, clustering, prediction, regression, and link analysis (associations), etc. Data analysts are primarily concerned with discerning trends in the data and thus a system that provides approximate answers in a timely fashion would suit their requirements better. Mining association rules represent an unsupervised data mining method that allows identifying interesting associations, correlations between items, and frequent patterns from large transactional databases and this problem was first introduced by Agrawal et al.,(1993). Haleh et al., (2012) have applied data mining techniques in MCDM problems involving educational databases to evaluate question weights in scientific examinations. Kweku-Muata & Osei-Bryson, (2004) worked on the evaluation of decision trees through MCDM approaches. Kaplan, (2006) proposed a solid waste management system model and optimization using MCDM applications and data mining techniques. The case study provided by Peng et al., (2011) demonstrated that combining data mining and MCDM methods provided **objective** and comprehensive assessments of huge data sets. Khan et al., (2008) provide various means where data mining techniques enhances the Decision Support Systems.

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Distortion risk measures, OWA and WOWA operators can be analyzed using the theory of measure. Classical measure functions are additive, and linked to the Lebesgue integral. When the additivity is relaxed, **alternative** measure functions and, hence, associated integrals are derived. This is the case of non-additive measure functions 2 , often called capacities as it was the name coined by Choquet (1954). We show that the link between distortion risk measures and OWA and WOWA operators is derived by means of the integral linked to capacities, i.e. the Choquet integral. We present the concept of degree of orness for distortion risk measures and illustrate its usefulness.

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1. Lan R.X., “The Developing Status and Trends of GIS”, Geospacial Information Journal, 2 (1), pp.9-12, 2004.
2. Zhang W.H., Chen S.F., “Research on hybrid index hierarchy fuzzy decision making method”, Journal of Management Sciences in China, 8(1),pp.7-11, 2005.
3. Jacek. Malczewski. **Ordered** **weighted** **averaging** with fuzzy quantifiers: GIS-based multicriteria evaluation for land-use suitability analysis [J]. International Journal of Applied Earth Observation and Geoinformation, 8(4): 270-277, 2006.

Although there are a variety of solution procedures for multi-**objective** or multi-criteria linear programming (MOLP or MCLP), only goal programming had been suggested for optimizing all objectives simultaneously. The difficulty of a multi-**objective** problem is not just in finding an optimal solution for each **objective** function but to find an optimal solution that simultaneously optimizes all objectives. In most cases, no single optimal solution would satisfy all the conditions simultaneously, thus requiring a set of efficient or non-dominated solutions. Further details on MOLP problem can be found in (Cohon, 1987; Dimitris P, 2003).

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Eq. (7) shows Greene 13 ’s version of the Bayesian Information Criteria (BIC). The BIC is inappropriate to form model **averaging** weights for the AIE models because the BIC definition of complexity is inapplicable as the number of free parameters in the AIE model is constant but the complexity of the model varies greatly by altering two parameters: (1) the probability of a link being rewired and (2) the number of links in a network. Together, they provide for 121 levels of complexity or network structures. The 121 structures are the product of the 11 settings for the number of links in the network and 11 settings for the probability of a link being rewired. Levin 14 ’s Kt complexity provides a more suitable and **alternative** complexity measure. Levin complexity makes the assumption that Universal Turing machines are able to simulate each other in linear time to retain invariance with Kolmogorov complexity (Ref. 15). The time for an AIE model to run becomes a proxy for complexity. Each of the 121 network structures require different running times; generally the more links in the network the longer the running time; intuitively more complex. The probability of a link being rewired has the general effect of making the running time longer; again intuitively more complex. Eq. (8) shows the complexity component of the BIC formula in Eq. (7) replaced with the Levin 14 ’s Kt complexity; t is the model runtime and the constant K renamed c is determined by experiment. This constant c will vary according to the speed of the computer running the AIE model, using the same computer to measure the runtime for all the versions of the AIE model would prevent this problem. Alternatively each computer could be benchmarked using the runtime of the least complex AIE model. This runtime on each computer becomes the unit time for each computer, allowing for a quasi universal constant c.

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sure, which has been used in previous studies on fuzzy rough classifiers as well. Alternatives exist, but we do not expect that our observations and conclusions in Sections 4.3-4.4 will greatly change when a different (sensible) relation is used. When an **alternative** similarity measure is more suitable for a particular dataset, the performance of the classifier will improve, but we believe that the relative

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A marked **ordered** labeled tree (Kazama and Tori- sawa, 2005) is an **ordered** labeled tree in which each node can have a mark in addition to a label. We can encode a k-node relation by using k distinct marks. In this study, we determine an argument node with- out considering other arguments of the same pred- icate, i.e., we represent an argument relation as a two-node relation using two marks. For example, the relation (a) in Figure 1 can be represented as the marked **ordered** labeled tree (a’). 1

As mentioned earlier, the motivation for developing a column generation approach for the production planning problem with **alternative** machine types was that only a small proportion of all the possible columns would actually be assigned non-zero production. Since the Path-Based model generates all the possible columns in the beginning and uses the variables for all possible (path, period) pairs in the mathematical model, it might be more time- efficient to use the Column Generation approach instead of solving the Path-Based model. Experimentation is performed to see how solve times differ for CG and PB approaches, and the results can be observed in Figure 4.6 and Figure 4.7. As it can be seen, PB approach performs better than CG in the problems solved within the scope of this research for comparison purposes. CG approach results in solve times much higher than the PB approach. Here, we must take into consideration the following facts:

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users of VP indicated that they would prefer a formulation that is easier to swallow, even if it needed to be taken twice per day. This study provides preliminary data upon which further investigation should be based. Additional research is needed to clarify issues of patient medication preferences and to better quantify the impact of oral **formulations** that are easy to swallow and smaller in size on patient adherence with therapy.

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Because the most widely available type of hu- man judgments are relative ranking (RR) judg- ments, the main machine learning method used for training the metrics were based on the learning- to-rank framework (Li, 2011). While the effec- tiveness of this framework for training evaluation metrics has been confirmed many times, e.g., (Ye et al., 2007; Duh, 2008; Stanojevi´c and Sima’an, 2014; Ma et al., 2016), so far there is no prior work exploring **alternative** **objective** functions for train- ing learning-to-rank models. Without exception, all existing learning-to-rank models are trained to rank sentences while completely ignoring the cor- pora judgments, likely because human judgments come in the form of sentence rankings.

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The region and the data are presented in Section 2, while the **alternative** model **formulations** and estimation results are briefly reviewed in Section 3. Section 4 starts by defining a standard house, before predicted and observed prices are compared at **alternative** locations. In this section we also predictability from a comparison between zonal average observed and zonal average predicted prices for all houses that were traded, and the prediction accuracy is illustrated by 95% prediction intervals. We also consider the predictability of MF2 in a case where data on the spatial distribution of job opportunities. Section 5 deals with predicting effects on house prices of hypothetical changes in the spatial distribution of employment. We are concerned both with the performance of **alternative** model **formulations** and with forecasting the redistribution of assets through capitalization of property values. This also applies for Section 6, which focuses on predicting how house prices are affected by changes in the road transportation network. We introduce the hypothesis that a relative measure of labor market accessibility is appropriate for studying the impact of changes in the road transportation network. Finally, we offer some concluding remarks in Section 7.

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The same framework can be utilized for multilingual DNN training. To this end, we use the language-based distributed learning algorithm in which each GPU uses the full data from one language and trains the normal DNN model. For the sake of eﬃciency, we consider the same number of samples, which is 400000, to be processed for each language before **averaging** the parameters. This reduces the waiting time before **averaging**, but we need to consider di ﬀerent epochs for languages depending on the amount of available training data for each language. Moreover, we only average the parameters of input and hidden layers across languages and keep the output layers language dependent. Although the initialization of the multilingual DNN can be done in the greedy layerwise manner, in this work, we simply borrow the hidden layers from an already trained DNN and only randomly initialize the softmax layer.

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This work compares two already proposed integer-linear **formulations** of the SPPTWCC with a new one; all of them are solved by branch-and-bound. The purpose is to select the most efficient one for embedding it into column generation algorithms tailored to solve routing problem variations. Numerical examples for testing alterna- tive **formulations** are solved with such aims.

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Abstract In Wireless Sensor Networks (WSNs), the network’s performance is usually influenced by energy constraint. Through a well-designed clustering algorithm, WSN’s energy consumption can be decreased evidently. In this paper, an Improved Multi-**Objective** **Weighted** Clustering Algo- rithm (IMOWCA) is proposed using additional constraints to select cluster heads in WSN. IMOWCA aims at handling a WSN in some critical circumstances where each sensor satisfies its own mission depending on its location. In addition to fulfill its mission, the sensor tries to improve the quality of communication with its neighboring nodes. Our proposed algorithm divides the net- work into different clusters and selects the best performing sensors based on residual energy to com- municate with the Base Station (BS). IMOWCA uses four critical parameters: EC i : Energetic

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Keywords: triangular cubic hesitant fuzzy set (TCFS); Einstein t-norm; arithmetic **averaging** operator; multi-attribute decision making (MADM)
1. Introduction
Multicriteria decision-making (MCDM) problems seek great attention to practical fields, whose target is to find the best **alternative**(s) among the feasible options. In primitive times, decisions were framed without handling the uncertainties in the data, which may lead to inadequate results toward the real-life operating situations. Since all these facilitate the uncertainties to a great extent, they cannot withstand situations where the decision the maker has to consider the falsity corresponding to the truth a value ranging over an interval. IFSs have the advantage that permits the user to model some uncertainty on the membership function of the elements. That is, fuzzy sets require a membership degree for each element in the reference set, whereas an IFS permits us to

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