José L. Verdegay

Tackling Real-Coded Genetic Algorithms: Operators and Tools for Behavioural Analysis

Genetic algorithms play a significant role, as search techniques forhandling complex spaces, in many fields such as artificial intelligence, engineering, robotic, etc. Genetic algorithms are based on the underlying genetic process in biological organisms and on the naturalevolution principles of populations. These algorithms process apopulation of chromosomes, which represent search space solutions,with three operations: selection, crossover and mutation.Under its initial formulation, the search space solutions are coded using the binary alphabet. However, the good properties related with these algorithms do not stem from the use of this alphabet; other coding types have been considered for the representation issue, such as real coding, which would seem particularly natural when tackling optimization problems of parameters with variables in continuous domains. In this paper we review the features of real-coded genetic algorithms. Different models of genetic operators and some mechanisms available for studying the behaviour of this type of genetic algorithms are revised and compared.

Direct approach processes in group decision making using linguistic OWA operators

Abstract In a linguistic framework, several group decision making processes by direct approach are presented. These processes are designed using the linguistic ordered weighted averaging (LOWA) operator. To do so, first a study is made of the properties and the axiomatic of LOWA operator, showing the rationality of its aggregation way. And secondly, we present the use of LOWA operator to solve group decision making problems from individuals linguistic preference relations.

A sequential selection process in group decision making with a linguistic assessment approach

In this paper, a sequential selection process in group decision making under linguistic assessments is presented, where a set of linguistic preference relations represents individuals preferences. A collective linguistic preference is obtained by means of a defined linguistic ordered weighted averaging operator whose weights are chosen according to the concept of fuzzy majority, specified by a fuzzy linguistic quantifier. Then we define the concepts of linguistic non-dominance, linguistic dominance, and strict dominance degrees as parts of the sequential selection process. The solution alternative(s) is obtained by applying these concepts.

On aggregation operations of linguistic labels

This article is devoted to defining some aggregation operations between linguistic labels. First, from some remarks about the meaning of label addition, a formal and general definition of a label space is introduced. After, addition, difference, and product by a positive real number are formally defined on that space. the more important properties of these operations are studied, paying special attention to the convex combination labels. the article concludes with some numerical examples.

Tuning fuzzy logic controllers by genetic algorithms

The performance of a fuzzy logic controller depends on its control rules and membership functions. Hence, it is very important to adjust these parameters to the process to be controlled. A method is presented for tuning fuzzy control rules by genetic algorithms to make the fuzzy logic control systems behave as closely as possible to the operator or expert behavior in a control process. The tuning method fits the membership functions of the fuzzy rules given by the experts with the inference system and the defuzzification strategy selected, obtaining high-performance membership functions by minimizing an error function defined using a set of evaluation input-output data. Experimental results show the methods good performance.

Linguistic decision-making models

Using linguistic values to assess results and information about external factors is quite usual in real decision situations. In this article we present a general model for such problems. Utilities are evaluated in a term set of labels and the information is supposed to be a linguistic evidence, that is, is to be represented by a basic assignment of probability (in the sense of Dempster‐Shafer) but taking its values on a term set of linguistic likelihoods. Basic decision rules, based on fuzzy risk intervals, are developed and illustrated by several examples. the last section is devoted to analyzing the suitability of considering a hierarchical structure (represented by a tree) for the set of utility labels.

Linear programming problems and ranking of fuzzy numbers

Abstract In this paper linear programming problems with fuzzy constraints and fuzzy coefficients in both matrix and right hand side of the constraint set are considered. Because of fuzzy coefficients in both members of each constraint, ranking methods for fuzzy numbers must be considered. The diversity of such methods provides a lot of different models of conventional linear programming problems from which fuzzy solutions to the former problem can be obtained.

A learning process for fuzzy control rules using genetic algorithms

Abstract The purpose of this paper is to present a genetic learning process for learning fuzzy control rules from examples. It is developed in three stages: the first one is a fuzzy rule genetic generating process based on a rule learning iterative approach, the second one combines two kinds of rules, experts rules if there are and the previously generated fuzzy control rules, removing the redundant fuzzy rules, and the thrid one is a tuning process for adjusting the membership functions of the fuzzy rules. The three components of the learning process are developed formulating suitable genetic algorithms.

A dual approach to solve the fuzzy linear programming problem

Abstract A concept of fuzzy objective based on the Fuzzification Principle is presented. In accordance with this concept, the Fuzzy Linear Mathematical Programming problem is easily solved. A relationship of duality among fuzzy constraints and fuzzy objectives is given. The dual problem of a Fuzzy Linear Programming problem is also defined.

A procedure for ranking fuzzy numbers using fuzzy relations

Abstract This paper presents a method to give fuzzy order relations between fuzzy numbers. These are founded on the concept of ‘comparison function’ (defined in the paper), and the use of fuzzy measures related with the same numbers. The link of such relations with fuzzy operations is investigated too.