J. Tinguaro Rodríguez

An ordinal approach to computing with words and the preference-aversion model

Computing with words (CWW) explores the brains ability to handle and evaluate perceptions through language, i.e., by means of the linguistic representation of information and knowledge. On the other hand, standard preference structures examine decision problems through the decomposition of the preference predicate into the simpler situations of strict preference, indifference and incomparability. Hence, following the distinctive cognitive/neurological features for perceiving positive and negative stimuli in separate regions of the brain, we consider two separate and opposite poles of preference and aversion, and obtain an extended preference structure named the Preference-aversion (P-A) structure. In this way, examining the meaning of words under an ordinal scale and using CWWs methodology, we are able to formulate the P-A model under a simple and purely linguistic approach to decision making, obtaining a solution based on the preference and non-aversion order.

Some Properties of Consistency in the Families of Aggregation Operators

Properties related with aggregation operators functions have been widely studied in literature. Nevertheless, few efforts have been dedicated to analyze those properties related with the family of operators in a global way. What should be the relationship among the members of a family of aggregation operators? Is it possible to build the aggregation of n data with aggregation operators of lower dimension? Should it exist some consistency in the family of aggregation operators? In this work, we analyze two properties of consistency in a family of aggregation operators: Stability and Structural Relevance. The stability property for a family of aggregation operators tries to force a family to have a stable/continuous definition in the sense that the aggregation of n items should be similar to the aggregation of n + 1 items if the last item is the aggregation of the previous n items. Following this idea some definitions and results are given. The second concept presented in this work is related with the construction of the aggregation operator when the data that have to be aggregated has an inherent structure. The Structural Relevance property tries to give some ideas about the construction of the aggregation operator when the items are related by means of a graph.

Computational intelligence in decision making

In this preface we stress the relevance of the traditional collaboration between Engineering and any field of Mathematics in order to build intelligent decision-aid tools, as it is illustrated by the twelve papers contained in this Special Issue. These papers, selected by means of a standard peer review process after an open call, offer an interesting variety of models, approaches and techniques, to be applied within different specific problems. Each paper is introduced in this preface and is developed in the subsequent article. Moreover, in this preface we also claim for a more intense collaboration between decision engineers and other fields that study human brain behavior, like Neurology, Psychology, Sociology and Linguistics. Because if we really want to procure intelligent tools for decision aid, we should start by taking the human brain as our first reference, as it is the most efficient machinery we have found in order to deal with complex, uncertain, incomplete and even apparently inconsistent information. We hope that readers will enjoy this Special Issue devoted to Computational Intelligence in Decision Making.

Development of child's home environment indexes based on consistent families of aggregation operators with prioritized hierarchical information

The interventions aimed at the early childhood are of a main interest in educational policy, since it is in this period when it is possible to produce a major impact in the subsequent human development. The quality of childrens social environment is the main influence to consider in achieving sound child development, affecting throughout school life. For this reason, the development of childs environment indexes appears in a natural way in the evaluation of all kind of educational policy research and social programs. However, crisp measures and indexes, based on usual linear techniques, do not ensure an adequate representation of social reality, since this last has a fuzzy nature and a nonlinear behavior. The development of indexes can be seen as an aggregation problem. In this paper, we extend the notions of consistency and strict stability of a family of aggregation operators (FAO), proposed in a previous work of the authors for the case of an aggregation process in which the data have no particular structure, to the case in which the information has a prioritized hierarchical structure. This extended notion of strict stability is then used to address the construction of indexes. Particularly, we apply this approach to develop a construction method of childs home environment indexes in which a stable family of prioritized aggregation operators is used in order to ensure robustness of the aggregation process when the information has a lineal structure. These indexes are built using fuzzy data that fit into a hierarchical structure by means of a stable family of prioritized aggregation operators based on the prioritized operator formulated by Yager, where the order relationship over fuzzy information was defined by experts on child development.

Stability in Aggregation Operators

Aggregation functions have been widely studied in literature. Nevertheless, few efforts have been dedicated to analyze those properties related with the family of operators in a global way. In this work, we analyze the stability in a family of aggregation operators The stability property for a family of aggregation operators tries to force a family to have a stable/continuous definition in the sense that the aggregation of n − 1 items should be similar to the aggregation of n items if the last item is the aggregation of the previous n − 1 items. Following this idea some definitions and results are given.

Another paraconsistent algebraic semantics for Lukasiewicz–Pavelka logic

Abstract As recently proved in a previous work of Turunen, Tsoukias and Ozturk, starting from an evidence pair ( a , b ) on the real unit square and associated with a propositional statement α, we can construct evidence matrices expressed in terms of four values t, f, k, u that respectively represent the logical valuations true , false , contradiction (both true and false) and unknown (neither true nor false) regarding the statement α. The components of the evidence pair ( a , b ) are to be understood as evidence for and against α, respectively. Moreover, the set of all evidence matrices can be equipped with an injective MV-algebra structure. Thus, the set of evidence matrices can play the role of truth-values of a Lukasiewicz–Pavelka fuzzy logic, a rich and applicable mathematical foundation for fuzzy reasoning, and in such a way that the obtained new logic is paraconsistent. In this paper we show that a similar result can be also obtained when the evidence pair ( a , b ) is given on the real unit triangle. Since the real unit triangle does not admit a natural MV-structure, we introduce some mathematical results to show how this shortcoming can be overcome, and another injective MV-algebra structure in the corresponding set of evidence matrices is obtained. Also, we derive several formulas to explicitly calculate the evidence matrices for the operations associated to the usual connectives.

On the Semantics of Bipolarity and Fuzziness

This paper analyzes the relationship between fuzziness and bipolarity, notions which were devised to address different kinds of uncertainty: linguistic imprecision, in the former, and knowledge relevance and character or polarity, in the latter. Although different types of fuzziness and bipolarity have been defined, these relations are not always clear. This paper proposes the use of four-valued extensions to provide a formal method to rigorously define and compare the semantics and logical structure of diverse combinations of fuzziness and bipolarity types. As a result, this paper claims that these notions and their different types are independent and not semantically equivalent despite its possible formal equivalence.

A computational definition of aggregation rules

The currently-in-use definition of aggregation function is analyzed in this paper, noting that the introduced variability in the dimension of information does not avoid some obvious dysfunctions. In particular, a potential abuse of the mathematical formalism underlies such a definition, which could lead to solve a complex concept by means of a formal mathematical expression. In this paper we propose an alternative definition making emphasis on the practical implementation of aggregation functions, taking into account the objectives and limitations observed in the application of aggregation functions within the fuzzy context.

Approaches to learning strictly-stable weights for data with missing values

The problem of missing data is common in real-world applications of supervised machine learning such as classification and regression. Such data often gives rise to the need for functions defined for varying dimension. Here we propose optimization methods for learning the weights of quasi-arithmetic means in the context of data with missing values. We investigate some alternative approaches depending on the number of variables that have missing values and show results for several numerical experiments.

On Partial Comparability and Fuzzy Preference-Aversion Models

A general overview of partial comparability and preference theory allows examining the notion of bipolarity and its role in the development of some general preference structures. This bipolar approach comes natural to the framework of decision theory, where different preference structures can be initially explored according to the type of bipolar model that they follow. Therefore, we compare two general preference structures, the first one, referred to as the PCT structure, which results from a well known axiomatic model for partial comparability theory, and the second one, referred to as the P-A structure, which extends one particular standard fuzzy preference model, such that some basic differences as well as particular similarities are clearly identified.