Qualitative ordinal scales: the concept of ordinal range

Many practical problems of quality control involve the use of ordinal scales. Questionnaires planned to collect judgments on qualitative or linguistic scales, whose levels are terms such as "good," "bad," "medium," etc., are extensively used both in evaluating service quality and in visual controls for manufacturing industry. In an ordinal environment, the concept of distance between two generic levels of the same scale is not defined. Therefore, a population (universe) of judgments cannot be described using "traditional" statistical distributions since they are based on the notion of distance. The concept of "distribution shape" cannot be defined as well. In this article, we introduce a new statistical entity, the so-called ordinal distribution, to describe a population of judgments expressed on an ordinal scale. We also discuss which of the traditional location and dispersion measures can be used in this context and we briefly analyze some of their properties. A new dispersion measure, the ordinal range, as an extension of the cardinal range to ordinal scales, is then proposed. A practical application in the field of quality is developed throughout the articl

Exploiting Data Reliability and Fuzzy Clustering for Journal Ranking

This is the author accepted manuscript. The final version is available from IEEE Computational Intelligence Society via http://dx.doi.org/10.1109/TFUZZ.2016.2612265Journal impact indicators are widely accepted as possible measurements of academic journal quality. However, much debate has recently surrounded their use, and alternative journal impact evaluation techniques are desirable. Aggregation of multiple indicators offers a promising method to produce a more robust ranking result, avoiding the possible bias caused by the use of a single impact indicator. In this paper, fuzzy aggregation and fuzzy clustering, especially the Ordered Weighted Averaging (OWA) operators are exploited to aggregate the quality scores of academic journals that are obtained from different impact indicators. Also, a novel method for linguistic term-based fuzzy cluster grouping is proposed to rank academic journals. The work allows for the construction of distinctive fuzzy clusters of academic journals on the basis of their performance with respect to different journal impact indicators, which may be subsequently combined via the use of the OWA operators. Journals are ranked in relation to their memberships in the resulting combined fuzzy clusters. In particular, the nearest-neighbour guided aggregation operators are adopted to characterise the reliability of the indicators, and the fuzzy clustering mechanism is utilised to enhance the interpretability of the underlying ranking procedure. The ranking results of academic journals from six subjects are systematically compared with the outlet ranking used by the Excellence in Research for Australia (ERA), demonstrating the significant potential of the proposed approach.publishersversionPeer reviewe

Using OWA fuzzy operator to merge retrieval system results

With rapid growth of information sources, it is essential to develop methods that retrieve most relevant information according to the user requirements. One way of improving the quality of retrieval is to use more than one retrieval engine and then merge the retrieved results and show a single ranked list to the user. There are studies that suggest combining the results of multiple search engines will improve ranking when these engine are treated as independent experts. In this study, we investigated performance of Persian retrieval by merging four different language modeling methods and two vector space models with Lnu.ltu and Lnc.btc weighting schemes. The experiments were conducted on a large Persian collection of news archives called Hamshari Collection. Different variations of the Ordered Weighted Average (OWA) fuzzy operators method, called a quantifier based OWA operator and a degree-of-importance based OWA operator method have been tested for merging the results. Our experimental results show that the OWA operators produce better precision and ranking in comparison with weaker retrieval methods. But in comparison with stronger retrieval models they only produce minimal improvements

OWA-Based Multi-Criteria Decision Making based on Fuzzy Methods

One of the most important challenges in Multi-Attribute Decision Making (MADM) problem is "How can the optimal weights of the criteria be determined properly by the decision maker?". In the relevant research literature, various methods based on the requirements and assumptions of the problem were introduced to determine the weights of the criteria. In this regard, in particular, the Yager's OWA operator is one of the most significant and widely used approaches to evaluate the weight of criteria. But there is a drawback, which is that the results of Yager's OWA operator depend only on the level and size of decision-maker's risk and the dimension of the criteria. Therefore, in this paper, using a multi-objective decision making approach, we try to express this MADM challenge in the form of a generalization of the Yager's OWA operators and Ahn's method. One of the advantages of this generalization is that the proposed method uses all the information in the decision matrix compared to the methods proposed by Yager's OWA operators and the Ahn's method. The proposed approach is also able to enter the types of preferences considered by the decision maker for the criteria calculations as crisp or fuzzy quantities. Numerical examples and real dataset analysis based on a survey of students' opinions on teaching activities are provided

OWA-FRPS: A Prototype Selection method based on Ordered Weighted Average Fuzzy Rough Set Theory

The Nearest Neighbor (NN) algorithm is a well-known and effective classification algorithm. Prototype Selection (PS), which provides NN with a good training set to pick its neighbors from, is an important topic as NN is highly susceptible to noisy data. Accurate state-of-the-art PS methods are generally slow, which motivates us to propose a new PS method, called OWA-FRPS. Based on the Ordered Weighted Average (OWA) fuzzy rough set model, we express the quality of instances, and use a wrapper approach to decide which instances to select. An experimental evaluation shows that OWA-FRPS is significantly more accurate than state-of-the-art PS methods without requiring a high computational cost.Spanish Government TIN2011-2848

Ordered samples control charts for ordinal variables

The paper presents a new method for statistical process control when ordinal variables are involved. This is the case of a quality characteristic evaluated by an ordinal scale. The method allows a statistical analysis without exploiting an arbitrary numerical conversion of scale levels and without using the traditional sample synthesis operators (sample mean and variance). It consists of a different approach based on the use of a new sample scale obtained by ordering the original variable sample space according to some specific ‘dominance criteria' fixed on the basis of the monitored process haracteristics. Samples are directly reported on the chart and no distributional shape is assumed for the population (universe) of evaluations. Finally, a practical application of the method in the health sector is provided