Linguistic Quantifiers Research Articles

Linguistic rough sets

We introduce linguistic rough set (LRS) by integrating linguistic quantifiers in the rough set framework. The proposed LRS is inspired by the ways in which humans process imprecise information. It operates directly with the linguistic summaries and caters to imprecision implicit in the real world with partial knowledge. The measures of LRS are developed and its properties are investigated in detail. An approach is proposed for approximation of fuzzy concepts with the proposed LRS. This approach is applied in a real world case-study on the credit scoring analysis problem.

Numerical Methods to Calculate Fuzzy Boundaries for Brownfield Redevelopment Negotiations

A numerical method is proposed to represent the likelihood of contamination of a brownfield using fuzzy boundaries, and then to estimate the parameters in a fuzzy real options model for brownfield evaluation from different decision maker perspectives. These different values can be used to facilitate negotiations on redevelopment projects. Linguistic quantifiers and ordered weighted averaging (OWA) techniques are utilized to determine the pollution likelihood at sample locations based on multiple environmental indicators. Risk preferences of decision makers are expressed as different “orness” levels of OWA operators, which affect likelihood estimates. When the fuzzy boundary of a brownfield is generated by interpolation of sample points, the parameters of fuzzy real options, drift rate and volatility, can be calculated as fuzzy numbers. Hence, this proposed method can act as an intermediate between decision makers and the fuzzy real options models, making this model much easier to apply. A potential negotiation support system (NSS) implementing these numerical methods is discussed in the context of negotiating brownfield redevelopment projects. A public–private-partnership will be enhanced through information sharing, scenario generation, and conflict analysis provided by the NSS, encouraging more efficient brownfield redevelopment and leading to greater regional sustainability.

Multi-criteria multi-stakeholder decision analysis using a fuzzy-stochastic approach for hydrosystem management

Abstract. The conventional methods used to solve multi-criteria multi-stakeholder problems are less strongly formulated, as they normally incorporate only homogeneous information at a time and suggest aggregating objectives of different decision-makers avoiding water–society interactions. In this contribution, Multi-Criteria Group Decision Analysis (MCGDA) using a fuzzy-stochastic approach has been proposed to rank a set of alternatives in water management decisions incorporating heterogeneous information under uncertainty. The decision making framework takes hydrologically, environmentally, and socio-economically motivated conflicting objectives into consideration. The criteria related to the performance of the physical system are optimized using multi-criteria simulation-based optimization, and fuzzy linguistic quantifiers have been used to evaluate subjective criteria and to assess stakeholders' degree of optimism. The proposed methodology is applied to find effective and robust intervention strategies for the management of a coastal hydrosystem affected by saltwater intrusion due to excessive groundwater extraction for irrigated agriculture and municipal use. Preliminary results show that the MCGDA based on a fuzzy-stochastic approach gives useful support for robust decision-making and is sensitive to the decision makers' degree of optimism.

Efficient Multiple Attribute Group Decision Making Models with Correlation Coefficient of Vague Sets

A new approach for multiple attribute group decision making (MAGDM) problems where the attribute weights and the expert weights are real numbers and the attribute values take the form of vague values, is presented in this paper. Since families of ordered weighted averaging (OWA) operators are available in the literature, and only a few available for vague sets, the vague ordered weighted averaging (VOWA) operator and the induced vague ordered weighted averaging (IVOWA) operator are introduced in this paper and utilized for aggregating the vague information. The correlation coefficient for vague sets is used for ranking the alternatives and a new MAGDM model is developed based on the IVOWA operator and the vague weighted averaging (VWA) operator. In addition to the proposed model, two different models are proposed based on Linguistic Quantifiers for the situation when the expert weights are completely unknown. An illustrative example is given and a comparison is made between the models to demonstrate the applicability of the proposed approach of MAGDM.

An evaluation of retranslation methods in computing with words

To represent output fuzzy values of a computing with words (CW) system in natural language, a retranslation unit is required. In this work, retranslation methods applicable to a CW system are explored. Several methods that employ similarity measures of fuzzy sets, linguistic modifiers, or linguistic quantifiers have been applied to three real-world case studies. Performances of the applied methods have been evaluated through degree of validity, and comparison of characteristics of fuzzy sets such as fuzziness and specificity. Results show that invalid linguistic terms might be used in the retranslation process which also cause incomprehensible phrases in natural language.

APPLYING THE SUPERIOR IDENTIFICATION GROUP LINGUISTIC VARIABLE TO CONSTRUCT KANO MODEL ORIENTED QUALITY FUNCTION DEPLOYMENT

This study attempts to manipulate 2-tuple linguistic variables rather than pure linguistic variables in quality function deployment (QFD) in order to significantly improve the identification of the QFD model. The Kano model, a two-dimensional quality technique, is also integrated to recognize the degree of urgency in terms of enhancing and prioritizing quality-related requirements of customers via a fuzzy linguistic quantifier with a soft majority concept to fit the optimal aggregation weights. This study also retains the goodness on the usage of multi-granularity linguistic approach to facilitate the implementation of a group decision. Simultaneously, two-dimensional analysis is performed to explain the results synthetically between relationship matrix and correlation matrix from a management perspective, capable of providing comprehensive information for the decision process. Owing to the integration of several quality and management methods, results of this study demonstrate the capability of TRIZ.

First-order logic system $\mathbf{IMTL_{Q}^{*}}$ and triple I method in fuzzy reasoning with linguistic quantifiers

Based on first-order fuzzy logic system $\mathbf{K}^{*}$ and Ying's framework for linguistic quantifiers modeled by Sugeno integrals, a many-sorted first-order logic system $\mathbf{IMTL_{Q}^{*}}$ is constructed. Applying the triple I method, some fuzzy reasoning forms with linguistic quantifiers are investigated.

Exploring multi-criteria decision strategies in GIS with linguistic quantifiers: an extension of the analytical network process using ordered weighted averaging operators

Many real-world spatial planning and management problems give rise to a geographical information system (GIS)-based multi-criteria decision-making. Analytical network process (ANP) provides a comprehensive methodology for representing complex multi-criteria decision-making problems as a network of criteria and alternatives, where feedback and interdependence relationships may exist within and between all the criteria and alternatives. Experts’ experiences are used to estimate relative magnitudes of tangible and intangible factors through paired comparisons in order to make rational and consistent decisions. However, the GIS-based ANP, an adoption of weighted linear aggregation rule, typically employed a high trade-off decision strategy and neglected other decision strategies. This paper develops a novel GIS-based multi-criteria evaluation (MCE) procedure by extending the ANP using fuzzy quantifiers-guided ordered weighted averaging (OWA) operators. This extension, which generalizes the aggregation process used in the ANP, would provide a generic powerful decision-making tool that allows decision-makers to define a decision strategy on a continuum between pessimistic (risk-averse) and optimistic (risk-taking) strategies. By changing the linguistic quantifiers, the GIS-based ANP–OWA can generate a wide range of decision strategies taking into accounts the level of risk the decision-makers wish to assume in their MCE. A land-use suitability analysis in a region of Saudi Arabia is presented to demonstrate the application of the proposed procedure.

Anonymous Social Influence

We study a stochastic model of influence where agents have “yes” or “no” inclinations on some issue, and opinions may change due to mutual influence among the agents. Each agent independently aggregates the opinions of the other agents and possibly herself. We study influence processes modelled by ordered weighted averaging operators, which are anonymous: they only depend on how many agents share an opinion. For instance, this allows to study situations where the influence process is based on majorities, which are not covered by the classical approach of weighted averaging aggregation. We find a necessary and sufficient condition for convergence to consensus and characterize outcomes where the society ends up polarized. Our results can also be used to understand more general situations, where ordered weighted averaging operators are only used to some extent. We provide an analysis of the speed of convergence and the possible outcomes of the process. Furthermore, we apply our results to fuzzy linguistic quantifiers, i.e., expressions like “most” or “at least a few”.

Anonymous social influence

We study a stochastic model of influence where agents have “yes” or “no” inclinations on some issue, and opinions may change due to mutual influence among the agents. Each agent independently aggregates the opinions of the other agents and possibly herself. We study influence processes modeled by ordered weighted averaging operators, which are anonymous: they only depend on how many agents share an opinion. For instance, this allows to study situations where the influence process is based on majorities, which are not covered by the classical approach of weighted averaging aggregation. We find a necessary and sufficient condition for convergence to consensus and characterize outcomes where the society ends up polarized. Our results can also be used to understand more general situations, where ordered weighted averages are only used to some extent. Furthermore, we apply our results to fuzzy linguistic quantifiers, i.e., expressions like “most” or “at least a few”.

The green economy for sustainable development: a spatial multi-criteria analysis - ordered weighted averaging approach in the siting process for short rotation forestry in the Basilicata Region, Italy

Optimising bioenergy chains and the creation of a bio-energy district can make a positive contribution to territorial development, land use planning and employment, while reducing environmental pollution. Energy planning issues are complex problems with multiple decision makers and criteria. Given the spatial nature of the problem, the present paper proposes a spatial multi-criteria analysis approach for supporting decision makers in the site selection process for short rotation forestry planting in the Basilicata Region, southern Italy. The methodology applied in the decision-support system is ordered weighted averaging, extended by means of fuzzy linguistic quantifiers. The purpose of the research is to formulate a systematic procedure to analyse complex decision problems, while supplying decision makers with a flexible tool to decide on possible agro-energy policies. The outcomes of the analysis may support decision makers in defining targeted agro-energy policies and help the private sector to identify the most appropriate cropping plan.

Looking for Like-Minded Individuals in Social Networks Using Tagging and E Fuzzy Sets

The web is perceived as a new social platform. Very often, the users look at the web as a place where they can find an individual or group of people with the same or similar interests, or even find new friends. Such situation is reflected in one of the aspects of the web 2.0 called tagging. Tagging is a process of labeling (annotating) digital items-resources-by users. The labels-tags-assigned to those resources reflect users' ways of seeing, categorizing, and perceiving particular items. In general, a single user can label a number of items with a number of different tags. The results of this activity-labeled items and used tags-can be perceived as information characterizing the user. This paper describes an approach for constructing a user signature representing her interests and opinions based on used items and tags. The signature is determined as a fuzzy relation built on two fuzzy sets proposed here: a fuzzy set representing resource attractiveness, and a fuzzy set representing tag popularity. Furthermore, users' signatures are used to determine similarity between users, and potentially give users a method to find new web friends with similar interests and opinions. The paper also describes a process of building different signatures representing a group of users. Signatures of users that are members of the group are aggregated using OWA operator and different linguistic quantifiers to describe the group in a number of ways. A real-world case study illustrating the process of finding similar users and/or groups of users is included.

FAHSCEP: Fuzzy and Analogy Based Hybrid Software Cost Estimation Process

Estimation models in software engineering are used to predict some important attributes of future entities such as software development effort, software reliability and programmers productivity. Among these models, those estimating software effort have motivated considerable research in recent years. Estimation by analogy is one of the attractive techniques in software effort estimation field. However, the procedure used in estimation by analogy is not yet able to handle correctly categorical data. In this paper, we propose a new approach based on reasoning by analogy, fuzzy logic and linguistic quantifiers to estimate effort when the software project is described either by categorical or numerical data. Fuzzy logic-based cost estimation models are more appropriate when vague and imprecise information is to be accounted for. Fuzzy systems try to behave just like the processes of the brain with a rule base. In our proposed method the effort and the cost can be estimated using the Fuzzy logic based analogy method and the cost can be calculated. The performance of the proposed system is calculated using MARE (Mean Absolute Relative Error).

Ranking and selection of unsupervised learning marketing segmentation

This paper addresses the problem of choosing the most appropriate classification from a given set of classifications of a set of patterns. This is a relevant topic on unsupervised systems and clustering analysis because different classifications can in general be obtained from the same data set. The provided methodology is based on five fuzzy criteria which are aggregated using an Ordered Weighted Averaging (OWA) operator. To this end, a novel multi-criteria decision making (MCDM) system is defined, which assesses the degree up to which each criterion is met by all classifications. The corresponding single evaluations are then proposed to be aggregated into a collective one by means of an OWA operator guided by a fuzzy linguistic quantifier, which is used to implement the concept of fuzzy majority in the selection process. This new methodology is applied to a real marketing case based on a business to business (B2B) environment to help marketing experts during the segmentation process. As a result, a segmentation containing three segments consisting of 35, 98 and 127 points of sale respectively is selected to be the most suitable to endorse marketing strategies of the firm. Finally, an analysis of the managerial implications of the proposed methodology solution is provided.

A consensus support model based on linguistic information for the initial-self assessment of the EFQM in health care organizations

The improvement of the quality of the services is one of the primary sources of competitive advantage in health care organizations. As customers typically search for higher quality of care when choosing treatments, health plans and providers, the health care organizations strive to improve the quality of care and patient safety and satisfaction, as primary goals, with the resources that are available. To do so, the European Foundation for Quality Management (EFQM) Excellence Model for self-assessment has been used by the health care organizations to improve their services and their competitiveness in the global market. However, when the health care organizations address self-assessment processes for the first time, the initial effort needed presents many difficulties. The aim of this paper is to offer a consensus support model based on linguistic information to conduct the self-assessment of the EFQM Excellence Model when questionnaires are used. It is based on the use of linguistic information to provide the individuals’ opinions, which facilitates the individual responses, and on the use of fuzzy majority, represented by means of a linguistic quantifier, to compute the measures guiding the consensus reaching process.

Intégration de préférences dans la découverte et la sélection des services web

Les methodes actuelles pour la decouverte de services basees sur le comportement – decrit comme un processus metier (PM) – retournent encore un grand nombre de services offrant des fonctionnalites similaires. Dans cet article, nous proposons une strategie d’evaluation pour la recherche de services basee sur les quantificateurs linguistiques flous et qui prend en compte la similarite structurelle entre les PM de services et la satisfaction des preferences sur les attributs de qualite de services (QdS). La requete utilisateur et les PM cibles sont representes a l’aide de graphes annotes ; les preferences de QdS sont modelisees au moyen des ensembles flous.

Similarity classifier with ordered weighted averaging operators

In this article we extend the similarity classifier to cover also ordered weighted averaging (OWA) operators. Earlier, similarity classifier was mainly used with generalized mean operator, but in this article we extend this aggregation process to cover more general OWA operators. With OWA operators we concentrate on linguistic quantifier guided aggregation where several different quantifiers are studied and on how they best suite for the similarity classifier. Our proposed method is applied to real world medical data sets which are new thyroid, hypothyroid, lymphography and hepatitis data sets. Results are very promising and show improvement compared to the earlier used generalized mean operator. In this article we will show that by using OWA operators instead of generalized mean, we can improve classification accuracy with chosen data sets.

On the analysis of set-based fuzzy quantified reasoning using classical syllogistics

Syllogism is a type of deductive reasoning involving quantified statements. The syllogistic reasoning scheme in the classical Aristotelian framework involves three crisp term sets and four linguistic quantifiers, for which the main support is the linguistic properties of the quantifiers. A number of fuzzy approaches for defining an approximate syllogism have been proposed for which the main support is cardinality calculus. In this paper we analyze fuzzy syllogistic models previously described by Zadeh and Dubois et al. and compare their behavior with that of the classical Aristotelian framework to check which of the 24 classical valid syllogistic reasoning patterns or moods are particular crisp cases of these fuzzy approaches. This allows us to assess to what extent these approaches can be considered as either plausible extensions of the classical crisp syllogism or a basis for a general approach to the problem of approximate syllogism.

Wind farm land suitability indexing using multi-criteria analysis

Wind farm siting can be considered as Multi Criteria Decision Making (MCDM) problem that consists of set of alternative locations and set of selection criteria. This study applied multi-criteria decision making approach using Analytical Hierarchy Process with Ordered Weigh Averaging AHP-OWA aggregation function to derive wind farm land suitability index and classification under Geographical Information System (GIS) environment. Linguistic quantifier’s version of AHP-OWA aggregation function was used to classify lands based on their suitability for wind farm installation. Different selection criteria were considered including economical (distance to road, terrain slope), social (urban area), environmental (historical locations, wildlife and natural reserves) and technical (wind power density, energy demand matching, percentage of sustainable wind, turbulence intensity, sand dunes). A case study of the proposed approach is implemented and presented for Oman.

Autologistic regression and multicriteria evaluation models for the prediction of forest expansion

Land use changes are complex ecological processes driven by the interaction of biophysical and human related factors. The prediction of forest land use changes is important for sustainable forest management and biodiversity conservation. This study investigates the modelling process of the spatial dynamics of a forest ecosystem in north eastern Greece. For the prediction of forest expansion, based on land use data of the study area, a deterministic approach using logistic regression and heuristic methods of multi-criteria evaluation is adopted. The set of factors driving forest expansion are: the slope, the distance to roads, the distance to urban areas, the distance to forest, the soil depth, the soil erosion and the influence from the land uses of the neighbourhood. The spatial autocorrelation of driving factors is addressed using an autologistic regression model. The multicriteria evaluation approach is developed using weighted linear combination (WLC) and ordered weighted averaging (OWA) methods. In WLC method the relative importance of each factor was estimated using the analytical hierarchy process. In the OWA method, decision strategies are generated using a selection of relative linguistic quantifiers, which allow different Risk in decisions. The accuracy of the models produced was tested with real data for the year 2001 using the ROC validation method. All the methods produced satisfactory results. Autologistic regression showed slightly better performance than multicriteria evaluation methods due to higher degree of objectivity in defining the importance of driving factors for forest expansion.