International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

An alternative theory of linguistic variables is introduced based on voting model semantics. This theory is then applied to computing with words whereby a calculus is introduced for inference from linguistic facts and rules.

In this paper we study the extension of Choquet integrals to ordinal scales. We show that two different integrals can be defined on the basis of two different but equivalent expressions in the numerical case. We prove some properties of the Choquet integrals and show their application to aggregation.

The Fuzzy Linguistic Approach has been applied successfully to different areas. The use of linguistic information for modelling expert preferences implies the use of processes of Computing with Words. To accomplish these processes different approaches has been proposed in the literature: (i) Computational model based on the Extension Principle, (ii) the symbolic one(also called ordinal approach), and (iii) the 2-tuple linguistic computational model. The main problem of the classical approaches, (i) and (ii), is the loss of information and lack of precision during the computational processes. In this paper, we want to compare the linguistic description, accuracy and consistency of the results obtained using each model over the rest ones. To do so, we shall solve a Multiexpert Multicriteria Decision-Making problem defined in a multigranularity linguistic context using the different computational approaches. This comparison helps us to decide what model is more adequated for computing with words.

In common language, as well as in knowledge–based systems, the truth of a proposition can be evaluated in a qualitative manner using adverbs usually represented on a scale of symbolic degrees. To combine or aggregate such symbolic degrees, we may need scales of different precision levels. We propose to model small variations inside a degree scale using linguistic modifiers in a symbolic framework. We formally define such modifiers and we distinguish three families: reinforcing, weakening and central modifiers. We also introduce the original notion of intensity rate associated to a linguistic degree on a scale base. After that, we propose a generalization of our modifiers, so we obtain more sophisticated tools. These have been used, in particular, in an application on colorimetry that allows us to alter the color slightly. The importance of our work is that most of our linguistic modifiers verify some interesting properties on their intensity rate: notably, they assume a certain order relation.

In this paper an ordinal Information Retrieval model is proposed, which is formalised within fuzzy set theory and is based on the notion of linguistic granules of information. Linguistic expressions are defined to represent and manage the importance of both the index terms as descriptors of the information items and the query terms (content selectors) as descriptors of users' needs. The advantage of this approach with respect to the (numeric) fuzzy IR models is that the query evaluation mechanism and the definition of the importance semantics are simplified.

An Information Retrieval (IR) model defined using an ordinal fuzzy linguistic approach is proposed. It accepts ordinal linguistic weighted queries based on two weighting elements: the query terms and the query sub-expressions. In such a way, users may easily express simultaneously several semantic restrictions in a query. A symmetrical threshold semantic is associated to the weights of the query terms and an importance semantic is associated to the weights of the query sub-expressions. The advantage of this IR model with respect to others is the facility for expressing different semantic restrictions on the desired documents simultaneously, incorporating more flexibility in the user-IR system interaction.

A fuzzy preference relation is a popular model to represent both individual and group preferences. However, what is often sought is a subset of alternatives that is an ultimate solution of a decision problem. In order to arrive at such a final solution individal and/or group choice rules may be employed. There is a wealth of such rules devised in the context of the classical, crisp preference relations. Originally, most of the popular group decision making rules were conceived for classical (crisp) preference relations (orderings), and then extended to the case of traditional fuzzy preference relations. Moreover, they often differ in their assumptions about the properties o the preference relations to be processed. In the paper we pursue the path towards a universal representation of such rules that provides an effective generalization of the classical rules for the fuzzy case. Moreover, it leads to a meaningful extension to the linguistic preferences, in the spirit of the computing with words paradigm.

Today the evaluation of service quality is one of the most important management issues for every organization. An important feature of the service process is the degree of customer influence on the service process. A characteristic of service quality evaluation is that it consists of both tangible and intangible factors. In this paper the customers' subjective opinions and the weights of factors are described by linguistic labels which can be expressed in trapezoidal fuzzy numbers. After aggregating these linguistic labels, a linguistic decision–making method is proposed to evaluate the service quality level of each organization. Finally, a numerical example is shown to highlight the procedure of the proposed method at the end of this paper.

This paper addresses fuzzy evaluation issues as applied in a decision–making procedure of process planning. General framework of fuzzy partitioning of system variables, evaluation procedure, and system variables, evaluation procedure, and system parameters aggregation have been described in detail for two classes and three distinguishing types of evaluation. Classes of evaluation include (a) linguistic, and (b) fuzzy (Choquet) integral based evaluation. Within these classes we distinguish between: (1) single criterion evaluation, (2) global multicriteria evaluation, and (3) global integral evaluation. First type relates to fuzzification of system parameters and matching procedure of a system's parameters input values to linguistic values in pre–defined dictionary. Multicriteria evaluation provides aggregation protocol of an object's attributes values and their significance yielding its suitability measure. We can use this measure to select the most appropriate linguistic value from pre–defined dictionary for further propagation through reasoning system, as well as for ranking of possible alternatives since it provides their global rank. Both types belong to linguistic evaluation class. Finally, global integral evaluation employs fuzzy integrals (here Choquet integral) for overall assessment of alternatives status. This type of evaluation belongs to fuzzy integral based class. Each type of evaluation is illustrated by an example from the real industrial practice concerning metal cutting process planning. The whole methodology should be seen as an upgrade of traditional expert systems used for this purpose. Relaxation of some system constraints provides more generality to traditional approaches, puts more "naturality" in assessment of parameters values, and reduces knowledge bases.