Generalized and Customizable Sets in R

We present data structures and algorithms for sets and some generalizations thereof (fuzzy sets, multisets, and fuzzy multisets) available for R through the sets package. Fuzzy (multi-)sets are based on dynamically bound fuzzy logic families. Further extensions include user-definable iterators and matching functions.

Generalized Bonferroni mean operators in multi-criteria aggregation

In this paper we provide a systematic investigation of a family of composed aggregation functions which generalize the Bonferroni mean. Such extensions of the Bonferroni mean are capable of modeling the concepts of hard and soft partial conjunction and disjunction as well as that of k-tolerance and k-intolerance. There are several interesting special cases with quite an intuitive interpretation for application

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches

Quasi Conjunction, Quasi Disjunction, T-norms and T-conorms: Probabilistic Aspects

We make a probabilistic analysis related to some inference rules which play an important role in nonmonotonic reasoning. In a coherence-based setting, we study the extensions of a probability assessment defined on $n$ conditional events to their quasi conjunction, and by exploiting duality, to their quasi disjunction. The lower and upper bounds coincide with some well known t-norms and t-conorms: minimum, product, Lukasiewicz, and Hamacher t-norms and their dual t-conorms. On this basis we obtain Quasi And and Quasi Or rules. These are rules for which any finite family of conditional events p-entails the associated quasi conjunction and quasi disjunction. We examine some cases of logical dependencies, and we study the relations among coherence, inclusion for conditional events, and p-entailment. We also consider the Or rule, where quasi conjunction and quasi disjunction of premises coincide with the conclusion. We analyze further aspects of quasi conjunction and quasi disjunction, by computing probabilistic bounds on premises from bounds on conclusions. Finally, we consider biconditional events, and we introduce the notion of an $n$-conditional event. Then we give a probabilistic interpretation for a generalized Loop rule. In an appendix we provide explicit expressions for the Hamacher t-norm and t-conorm in the unitary hypercube

Applying the Generalized Dombi Operator Family to the Speech Recognition Task

In the automatic speech recognition (ASR) problem, the task of constructing one word- or sentence-level probability from the available phoneme-level probabilities is a very important one. Here we try to improve the performance of ASR systems by applying operators taken from fuzzy logic which have the sort of properties this problem requires. In this paper we do this by using the Generalized Dombi Operator, which, by its two adjustable parameters and incorporating other well-known fuzzy operators, seems quite suitable. To properly adjust these parameters, we used the public optimization package called Snobfit. The results show that our approach is surprisingly successful: we were able to reduce the overall error rate by 53.4%

Appropriate choice of aggregation operators in fuzzy decision support systems

Fuzzy logic provides a mathematical formalism for a unified treatment of vagueness and imprecision that are ever present in decision support and expert systems in many areas. The choice of aggregation operators is crucial to the behavior of the system that is intended to mimic human decision making. This paper discusses how aggregation operators can be selected and adjusted to fit empirical data&mdash;a series of test cases. Both parametric and nonparametric regression are considered and compared. A practical application of the proposed methods to electronic implementation of clinical guidelines is presented<br /

Fitting ST-OWA operators to empirical data

The OWA operators gained interest among researchers as they provide a continuum of aggregation operators able to cover the whole range of compensation between the minimum and the maximum. In some circumstances, it is useful to consider a wider range of values, extending below the minimum and over the maximum. ST-OWA are able to surpass the boundaries of variation of ordinary compensatory operators. Their application requires identification of the weighting vector, the t-norm, and the t-conorm. This task can be accomplished by considering both the desired analytical properties and empirical data.<br /