A comprehensive study of implicator-conjunctor based and noise-tolerant fuzzy rough sets: definitions, properties and robustness analysis

© 2014 Elsevier B.V. Both rough and fuzzy set theories offer interesting tools for dealing with imperfect data: while the former allows us to work with uncertain and incomplete information, the latter provides a formal setting for vague concepts. The two theories are highly compatible, and since the late 1980s many researchers have studied their hybridization. In this paper, we critically evaluate most relevant fuzzy rough set models proposed in the literature. To this end, we establish a formally correct and unified mathematical framework for them. Both implicator-conjunctor-based definitions and noise-tolerant models are studied. We evaluate these models on two different fronts: firstly, we discuss which properties of the original rough set model can be maintained and secondly, we examine how robust they are against both class and attribute noise. By highlighting the benefits and drawbacks of the different fuzzy rough set models, this study appears a necessary first step to propose and develop new models in future research.Lynn D’eer has been supported by the Ghent University Special Research Fund, Chris Cornelis was partially supported by the Spanish Ministry of Science and Technology under the project TIN2011-28488 and the Andalusian Research Plans P11-TIC-7765 and P10-TIC-6858, and by project PYR-2014-8 of the Genil Program of CEI BioTic GRANADA and Lluis Godo has been partially supported by the Spanish MINECO project EdeTRI TIN2012-39348-C02-01Peer Reviewe

GIS-Based Local Ordered Weighted Averaging: A Case Study in London, Ontario

GIS-based multicriteria analysis is a procedure for combining a set of criterion maps and associated criterion weights to obtain overall value for each spatial unit (location) in the study area. Ordered Weighted Averaging (OWA) is a generic algorithm of the multicriteria analysis. It has been integrated into GIS and applied for tackling a wide range of spatial problems. However, the conventional OWA method is based on an assumption of spatial homogeneity of its parameters. Therefore, it is referred to as a global model. This thesis proposes a local form OWA. The local model is based on the range sensitivity principle. A case study of examining spatial patterns of socioeconomic status in London, Ontario is presented. The results show that there are substantial differences between the spatial patterns generated by the global and local OWA methods

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

Managing Interacting Criteria: Application to Environmental Evaluation Practices

The need for organizations to evaluate their environmental practices has been recently increasing. This fact has led to the development of many approaches to appraise such practices. In this paper, a novel decision model to evaluate company’s environmental practices is proposed to improve traditional evaluation process in different facets. Firstly, different reviewers’ collectives related to the company’s activity are taken into account in the process to increase company internal efficiency and external legitimacy. Secondly, following the standard ISO 14031, two general categories of environmental performance indicators, management and operational, are considered. Thirdly, since the assumption of independence among environmental indicators is rarely verified in environmental context, an aggregation operator to bear in mind the relationship among such indicators in the evaluation results is proposed. Finally, this new model integrates quantitative and qualitative information with different scales using a multi-granular linguistic model that allows to adapt diverse evaluation scales according to appraisers’ knowledge

Land Use Compatibility Assessment Using a Mdified Topsis Model: a Case Study of Elementary Schools in Tehran

Being one of the most controversial issues in urban planning, land use planning has always been in the focus of researches. Land use planning is a subdivision of urban planning which tends to arrange land uses in order to avoid conflicts among them. In order to achieve a transparent and effective urban planning, land uses should be located and allocated in an ideal situation so that avoid negative impacts from neighbouring parcels and land uses. Neighbouring land uses can produce externalities and negative impacts on other land uses because of inter-land use interaction. These externalities may be undesirable effects such as noise, air and visual pollution or may be caused by hazardous facilities. The main objective of this research is to propose a new multi-criteria evaluation model for land use compatibility assessment. Considering the fact that a considerable number of factors affect the compatibility degree of neighbouring land uses, a multi-criteria evaluation approach is employed to address the aforementioned problem. This research employs the integration of Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Ordered Weighted Averaging (OWA) methods to facilitate land use compatibility evaluation with respect to optimism degree. The applicability of the proposed model is illustrated by the problem of land use compatibility assessment for elementary schools in Tehran. The results indicate that most of the current schools are situated in a location which is incompatible for the land use type of elementary school especially in the southern and central parts of the city

Saw-Dmss Model For Intuitionistic Fuzzy Multi Attribute Decision Making Problems

This work introduces a new SAW-DMSS (Simple Additive Weighting-Decision Making Support System) technique for decision-makers to choose the most ideal alternative that has been provided. This also deals with the problem based on SAW algorithm which is a multiple criteria decision making approach with weight determining methods which gives the weights to indicators which is partially or completely unknown or not presented by the decision makers. The SAW algorithm deals with the conflicts between indicators based on certain way to sort the scheme and choose the best scheme. A numerical example is proposed to illustrate the effectiveness of this algorithm. However, comparison of two weight determining methods based on Gaussian distribution and Linguistic quantifier guided aggregation is performed to make the result of evaluations more objective and accurate

Pension service institution selection by a personalized quantifier-based MACONT method

With the emergence of a variety of pension service institutions, how to choose a suitable institution has become a strategic decision-making problem faced by pension service demanders. To solve this problem, this study identifies key evaluation criteria of pension service institutions through the analysis of the relevant literature. Then, this study proposes a mixed aggregation by comprehensive normalization technique (MACONT) with a personalized quantifier to select pension service institutions, where the personalized qualifier with cubic spline interpolation is used to derive the position weights of criteria, and the MACONT is improved to determine the ranking of alternatives. A case study about the selection of pension service institutions is provided to verify the feasibility of the proposed model. It is found that the proposed method is effective in dealing with heterogeneous evaluation information, and the personalized quantifiers can be combined with MACONT methods to obtain an optimal solution associated with the attitude of pension service demanders. The identified key evaluation criteria are not only significant for pension service demanders, but also conducive to the further improvement of property management related to pension services

OWA operators in regression problems

We consider an application of fuzzy logic connectives to statistical regression. We replace the standard least squares, least absolute deviation, and maximum likelihood criteria with an ordered weighted averaging (OWA) function of the residuals. Depending on the choice of the weights, we obtain the standard regression problems, high-breakdown robust methods (least median, least trimmed squares, and trimmed likelihood methods), as well as new formulations. We present various approaches to numerical solution of such regression problems. OWA-based regression is particularly useful in the presence of outliers, and we illustrate the performance of the new methods on several instances of linear regression problems with multiple outliers.<br /