Juan Vicente Riera

A new linguistic computational model based on discrete fuzzy numbers for computing with words

In recent years, several different linguistic computational models for dealing with linguistic information in processes of computing with words have been proposed. However, until now all of them rely on the special semantics of the linguistic terms, usually fuzzy numbers in the unit interval, and the linguistic aggregation operators are based on aggregation operators in [0,1]. In this paper, a linguistic computational model based on discrete fuzzy numbers whose support is a subset of consecutive natural numbers is presented ensuring the accuracy and consistency of the model. In this framework, no underlying membership functions are needed and several aggregation operators defined on the set of all discrete fuzzy numbers are presented. These aggregation operators are constructed from aggregation operators defined on a finite chain in accordance with the granularity of the linguistic term set. Finally, an example of a multi-expert decision-making problem in a hierarchical multi-granular linguistic context is given to illustrate the applicability of the proposed method and its advantages.

Some interesting properties of the fuzzy linguistic model based on discrete fuzzy numbers to manage hesitant fuzzy linguistic information

Graphical abstractDisplay Omitted HighlightsProperties of the fuzzy linguistic model based on discrete fuzzy numbers are analysed.This model is used to handle hesitant fuzzy linguistic information.This model includes the hesitant fuzzy linguistic term sets model.Some advantages of the model based on discrete fuzzy numbers are pointed out.A fuzzy decision making model based on discrete fuzzy numbers is proposed. The management of hesitant fuzzy information is a topic of special interest in fuzzy decision making. In this paper, we focus on the use and properties of the fuzzy linguistic modelling based on discrete fuzzy numbers to manage hesitant fuzzy linguistic information. Among these properties, we can highlight the existence of aggregation functions with no need of transformations or the possibility of a greater flexibilization of the opinions of the experts, even using different linguistic chains (multigranularity). Furthermore, based on these properties we perform a comparison between this model and the one based on hesitant fuzzy linguistic term sets, showing the advantages of the former with respect to the latter. Finally, a fuzzy decision making model based on discrete fuzzy numbers is proposed.

A model based on subjective linguistic preference relations for group decision making problems

In a group decision making problem, experts often express their opinions through the so-called preference relations. In recent years, several different definitions of preference relations depending on the framework and the nature of the problem have been introduced. These approaches vary from interval-valued fuzzy preference relations to incomplete fuzzy linguistic preference relations. In this paper, a novel definition of preference relation, the so-called subjective linguistic preference relation, is proposed. These preference relations are based on the concept of subjective evaluations, introduced in the linguistic computational model based on discrete fuzzy numbers. In this framework, the experts have more flexibility to express their opinions and the solid mathematical background of this model is a guarantee of no loss of information. Finally, an example of a multi-expert decision making problem with a hierarchical multi-granular linguistic context is analyzed to illustrate the potential of the proposed method and its advantages with respect to other methods.

Some Remarks on the Fuzzy Linguistic Model Based on Discrete Fuzzy Numbers

In this article, some possible interpretations of the computational model based on discrete fuzzy numbers are given. In particular, some advantages of this model based on the aggregation process as well as on a greater flexibilization of the linguistic expressions are analysed. Finally, a fuzzy decision making model based on this kind on fuzzy subsets is proposed.

Uninorms and nullnorms on the set of discrete fuzzy numbers

In this paper a method to extend discrete uninorms and nullnorms on the finite chain L = {0,...,n}, to uninorms and nullnorms defined on the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers contained in L is presented. Some basic properties of discrete uninorms and nullnorms are preserved by this extension method and the structure of these kinds of aggregations is maintained too. Finally, we develop an application to obtain the group consensus opinion based on the extension of discrete uninorms and nullnorms.

On Fuzzy Polynomial Implications

In this work, the class of fuzzy polynomial implications is introduced as those fuzzy implications whose expression is given by a polynomial of two variables. Some properties related to the values of the coefficients of the polynomial are studied in order to obtain a fuzzy implication. The polynomial implications with degree less or equal to 3 are fully characterized. Among the implications obtained in these results, there are some well-known implications such as the Reichenbach implication.

Fuzzy implications defined on the set of discrete fuzzy numbers

Given an implication function I defined on the finite chain L = {0,...,n}, a method for extending I to the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers contained in L (denoted by A L ) is given. The resulting extension is in fact a fuzzy implication on A L preserving some boundary properties. Moreover, if the initial implication I is an S, QL or D-implication on L then its extension is also an S, QL or D-implication on A L , respectively.

A New Look on the Ordinal Sum of Fuzzy Implication Functions

Fuzzy implication functions are logical connectives commonly used to model fuzzy conditional and consequently they are essential in fuzzy logic and approximate reasoning. From the theoretical point of view, the study of how to construct new implication functions from old ones is one of the most important topics in this field. In this paper new ordinal sum construction methods of implication functions based on fuzzy negations N are presented. Some general properties are analysed and particular cases when the considered fuzzy negation is the classical one or any strong negation are highlighted.

A New Vision of Zadeh’s Z -numbers

From their introduction Z-numbers have been deeply studied and many investigations have appeared trying to reduce the inherent complexity in their computation. In this line, this paper presents a new vision of Z-numbers based on discrete fuzzy numbers with support in a finite chain \(L_n\). In this new approach, a Z-number associated with a variable, X, is a pair \((A,\,B)\) of discrete fuzzy numbers, where A is interpreted as a fuzzy restriction on X, while the estimation of the reliability of A is interpreted as a linguistic valuation based on the discrete fuzzy number B. In this non-probabilistic approach an aggregation method is proposed with the aim of applying it in group decision making problems.

On rational fuzzy implication functions

The proposal of new classes of fuzzy implication functions must take into account the final expression of the operator to be potentially used in a concrete application. In particular, fuzzy implication functions with simple expressions have low computational cost and they reduce the spreading of numerical errors. Following this line of research, in this work, the class of fuzzy rational implications is introduced as those fuzzy implication functions whose expression is given by the quotient of two polynomials of two variables. Since not all quotients of polynomials are adequate to generate a fuzzy implication function, some necessary properties related to the values of the coefficients of the polynomials are given to ensure obtaining a fuzzy implication function. In addition, we characterize all fuzzy rational implications constructed from polynomials of some fixed degrees. Finally, several construction methods of these implications and relationships with other families of fuzzy implication functions are given.