Evaluative Linguistic Expressions Research Articles

Three-way decisions with evaluative linguistic expressions

The theory of three-way decisions (3WD) requires dividing a finite, non-empty universe into three disjoint sets called positive, negative, and boundary regions. Three types of decisions are then made on the objects in each region: acceptance, rejection, and abstention (or non-commitment), respectively. Until today, a large number of 3WD extensions and applications have been proposed; some of the most recent ones also include aspects of linguistics. In this article, we first propose an innovative linguistic interpretation of three-way decisions, where the positive, negative, and boundary regions are constructed by means of the so-called evaluative linguistic expressions. These are expressions of natural language, such as small, medium, very short, quite roughly strong, extremely good, etc., and they are described within a logical theory based on the formal system of higher-order fuzzy logic. Furthermore, in line with our linguistic 3WD approach, we introduce the novel notion of linguistic rough sets, thus contributing to the development of Rough Set Theory. Finally, we connect the theory of linguistic three-way decisions with the standard 3WD model based on probabilistic rough sets, establishing conditions under which the two approaches coincide. Our results highlight connections between two different research areas: three-way decisions and the theory of evaluative linguistic expressions.

Describing Linguistic Vagueness of Evaluative Expressions Using Fuzzy Natural Logic and Linguistic Constraints

In recent years, the study of evaluative linguistic expressions has crossed the field of theoretical linguistics and has aroused interest in very different research areas such as artificial intelligence, psychology or cognitive linguistics. The interest in this type of expressions may be due to its relevance in applications such as opinion mining or sentiment analysis. This paper brings together Fuzzy Natural Logic and Fuzzy Property Grammars to approach evaluative expressions. Our contribution includes the marriage of mathematical and linguistic methods for providing a formalism to deal with the linguistic vagueness of evaluative expressions by describing the syntax and semantics of these structures. We contribute to the study of evaluative linguistic expressions by proposing a formal characterization of them where the concepts of semantic prime, borderline evaluative expressions and markedness are defined and where the relation between the semantic constraints of evaluations and their sentiment can be established. A proof-of-concept of how to create a lexicon of evaluative expressions for future computational applications is presented. The results demonstrate that linguistic evaluative expressions are gradient, have sentiment, and that the evaluations work as a relation of hypernym and hyponym, the hypernym being a semantic prime. Our findings provide the basis for building an ontology of evaluative expressions for future computational applications.

Graded polygons of opposition in fuzzy formal concept analysis

Quantifier-based operators are fuzzy quantifiers that are, similarly to the intermediate quantifiers, based on the evaluative linguistic expressions not small, very big and extremely big. This article focuses mainly on achieving two goals. Firstly, quantifier-based operators are introduced to create extended fuzzy concept lattices that capture more detailed information from datasets compared to the existing ones. Then, graded extensions of Aristotle's square, named polygons of opposition, are constructed using quantifier-based operators. Our results highlight new connections between three different research areas: the theory of evaluative linguistic expressions, fuzzy formal concept analysis, and the studies on Aristotle's square.1

The theory of intermediate quantifiers in fuzzy natural logic revisited and the model of “Many”

The fuzzy natural logic (FNL) is a formal theory whose goal is to provide a mathematical model of natural human reasoning whose typical feature is the use of natural language. One of its tasks is to develop a mathematical model of a special class of linguistic quantifiers called intermediate ones. In our previous papers, we introduced a general principle of how intermediate quantifiers can be formed and suggested generalized definitions of the relations of contrary, contradictory, subcontrary, and subalterns between these quantifiers. Based on these relations and following Peterson's book [62], we were able to suggest a formal model of the 5-square of opposition with intermediate quantifiers. This paper picks up the threads of this work and has the following goals: it contributes to the development of the theory of fuzzy natural logic. First, it gets back to some concepts of the theory of evaluative linguistic expressions, introduces slight modifications, and proves some not yet presented properties. Furthermore, it improves the formal theory of intermediate quantifiers; some definitions are made more precise, and some new theorems are proved. Finally, it contributes to the theory of the intermediate quantifier “Many” and the analysis of its position in the mentioned 5-square. We will show that “Many” manifests an ambiguous relation towards the other quantifiers.

Linguistic Characterization of Natural Data by Applying Intermediate Quantifiers on Fuzzy Association Rules

The paper aims at applying fuzzy natural logic together with the Fuzzy GUHA method to analyse and linguistically characterise scientific data. Fuzzy GUHA is a tool for extracting linguistic association rules from data. Obtained associations are IF-THEN rules composed of evaluative linguistic expressions, which allow the quantities to be characterized with vague linguistic terms such as very small, big, medium etc. Originally, fuzzy GUHA provides several numerical indices of rule quality, which may not be easily understandable for domain experts that are not familiar with GUHA association rules. Therefore, we show in this paper that the theory of intermediate quantifiers (a constituent of fuzzy natural logic) can be applied to the results in an automatic manner in order to obtain natural linguistic summarization. We also present an idea of how the theory of generalized Aristotles's syllogisms can be used for a detailed data analysis. We also open the possibility to use fuzzy partial logic for cases where some data is missing or undefined.

Evaluative linguistic expressions vs. fuzzy categories

In this paper, we discuss the distinction between categories characterized by verbal labels taken from a fuzzy rating scale and special class of linguistic expressions, called evaluative. The latter form a general class of expressions that includes gradable and evaluative adjectives and their hedges. First, we will provide a brief linguistic analysis of them. Then we outline basic principles for construction of the mathematical model of semantics of evaluative expressions. In Section 3 we will analyze the concepts of rating scale with verbal labels (fuzzy rating scale), their semantics and demonstrate that the latter cannot be identified with the semantics of evaluative expressions. Finally, we suggest a method for construction of fuzzy rating scales on the basis of evaluative linguistic expressions. The main goal of this paper is to demonstrate the power of fuzzy set theory and to show that it is capable of providing tools for advanced modeling of linguistic semantics.

On modelling with words

In this paper, we discuss a class of methods encapsulated under the term modelling with words. The theoretical frame is mathematical fuzzy logic in broader sense, namely its constituents: formal logical theory of evaluative linguistic expressions, intermediate quantifiers, and the related concepts of linguistic description and perception-based logical deduction. We present various kinds of applications based on this theory: control of complex processes, managerial decision making, analysis, forecasting and linguistic evaluation of time series, mining linguistic associations, and also linguistic summarization and deduction based on intermediate quantifier theory.

Mining Linguistic Associations for Emergent Flood Prediction Adjustment

Floods belong to the most hazardous natural disasters and their disaster management heavily relies on precise forecasts. These forecasts are provided by physical models based on differential equations. However, these models do depend on unreliable inputs such as measurements or parameter estimations which causes undesirable inaccuracies. Thus, an appropriate data-mining analysis of the physical model and its precision based on features that determine distinct situations seems to be helpful in adjusting the physical model. An application of fuzzy GUHA method in flood peak prediction is presented. Measured water flow rate data from a system for flood predictions were used in order to mine fuzzy association rules expressed in natural language. The provided data was firstly extended by a generation of artificial variables (features). The resulting variables were later on translated into fuzzy GUHA tables with help of Evaluative Linguistic Expressions in order to mine associations. The found associations were interpreted as fuzzy IF-THEN rules and used jointly with the Perception-based Logical Deduction inference method to predict expected time shift of flow rate peaks forecasted by the given physical model. Results obtained from this adjusted model were statistically evaluated and the improvement in the forecasting accuracy was confirmed.

A fuzzy random periodic review system: a technique for real-life application

This paper presents a technique for the suitable quantification of the available demand information for inventory situations characterised by the limited availability of past demand data. As this lack of information makes it difficult to develop reliable estimates of the demand parameter, with experts preferring to give their estimates in terms of evaluative linguistic expressions, such inventory situations are characterised by the simultaneous presence of fuzziness and randomness. Therefore, this paper focuses on providing the decision-makers with the means of suitably quantifying this imprecise and uncertain information as a fuzzy random data set. The periodic review system has been utilised in this regard to provide an illustration of the proposed technique. A numerical example has also been provided for this purpose. This paper, therefore, presents a methodology for the implementation of a theoretical fuzzy random inventory model to a real-life situation.

A linguistic approach to time series modeling with the help of F-transform

In this paper, we describe an approach to modeling and forecasting time series that uses the theory of evaluative linguistic expressions, fuzzy/linguistic IF–THEN rules and the fuzzy transform method. We show that the use of a linguistic approach allows better readability and understandability without any significant deterioration in precision.

A comprehensive theory of trichotomous evaluative linguistic expressions

In this paper, a logical theory of the, so-called, trichotomous evaluative linguistic expressions (TEv-expressions) is presented. These are frequent expressions of natural language, such as “small, very small, roughly medium, extremely big”, etc. The theory is developed using the formal system of higher-order fuzzy logic, namely the fuzzy type theory (generalization of classical type theory). First, we discuss informally what are properties of the meaning of TEv-expressions. Then we construct step by step axioms of a formal logical theory T Ev of TEv-expressions and prove various properties of T Ev . All the proofs are syntactical and so, our theory is very general. We also outline construction of a canonical model of T Ev . The main elegancy of our theory consists in the fact that semantics of all kinds of evaluative expressions is modeled in a unified way. We also prove theorems demonstrating that essential properties of the vagueness phenomenon can be captured within our theory.

A formal theory of intermediate quantifiers

The paper provides a logical theory of a specific class of natural language expressions called intermediate quantifiers (most, a lot of, many, a few, a great deal of, a large part of, a small part of), which can be ranked among generalized quantifiers. The formal frame is the fuzzy type theory (FTT). Our main idea lays in the observation that intermediate quantifiers speak about elements taken from a class that is made “smaller” than the original universe in a specific way. Our theory is based on the formal theory of trichotomous evaluative linguistic expressions. Thus, an intermediate quantifier is obtained as a classical quantifier “for all” or “exists” but taken over a class of elements that is determined using an appropriate evaluative expression. In the paper we will characterize the behavior of intermediate quantifiers and prove many valid syllogisms that generalize classical Aristotle's ones.

Mining pure linguistic associations from numerical data

This paper contains a method for direct search of associations from numerical data that are expressed in natural language and so, we call them “linguistic associations”. The associations are composed of evaluative linguistic expressions, for example “small, very big, roughly medium”, etc. The main idea is to evaluate real-valued data by the corresponding linguistic expressions and then search for associations using some of the standard data-mining technique (we have used the GUHA method). One of essential outcomes of our theory is high understandability of the found associations because when formulated in natural language they are much closer to the way of thinking of experts from various fields. Moreover, associations characterizing real dependencies can be directly taken as fuzzy IF–THEN rules and used as expert knowledge about the problem.

Fuzzy transform in the analysis of data

Fuzzy transform is a novel, mathematically well founded soft computing method with many applications. In this paper, we present this technique with applications to data analysis. First, we show how it can be used for detection and characterization of dependencies among attributes. Second, we apply it to mining associations that have a functional character. Moreover, the mined associations are characterized linguistically which means that their antecedent consists of fuzzy numbers and the consequent is characterized using pure evaluative linguistic expressions (i.e. expressions such as small, very big, more or less medium, etc).