On (TS,N)-fuzzy implications

This paper proposes a new class of fuzzy implications, built according to the well-known (S,N) scheme but in such a way that the t-conorm S is replaced with a compensatory TS function (an aggregation function combining a t-norm and a t-conorm). The basic properties of such implications are studied, and different examples are provided.

Aggregating fuzzy implications to measure group consensus

We approach the problem of measuring consensus for a set of real inputs by aggregating the fuzzy implication degrees between each pair of inputs. We compare our operator with existing consensus measures in terms of their satisfaction of desirable properties. The appeal of such an approach lies in the interpretability and flexibility that results from component-wise construction which we modeled on the Bonferroni mean. We also outline some intentions for future research.

(S,N)-implications on bounded lattices

Since the birth of the fuzzy sets theory several extensions have been proposed. For these extensions, different sets of membership functions were considered. Since fuzzy connectives, such as conjunctions, negations and implications, play an important role in the theory and applications of fuzzy logics, these connectives have also been extended. An extension of fuzzy logic, which generalizes the ones considered up to the present, was proposed by Joseph Goguen in 1967. In this extension, the membership values are drawn from arbitrary bounded lattices. The simplest and best studied class of fuzzy implications is the class of (S,N)-implications, and in this chapter we provide an extension of (S,N)-implications in the context of bounded lattice valued fuzzy logic, and we show that several properties of this class are preserved in this more general framework.

On Fuzzy Implication Classes - Towards Extensions of Fuzzy Rule-Based Systems

Atualmente, há diferentes definições de implicações fuzzy aceitas na literatura. Do ponto de vista teórico, esta falta de consenso demonstra que há discordâncias sobre o real significado de "implicação lógica" nos contextos Booleano e fuzzy. Do ponto de vista prático, isso gera dúvidas a respeito de quais "operadores de implicação" os engenheiros de software devem considerar para implementar um Sistema Baseado em Regras Fuzzy (SBRF). Uma escolha ruim destes operadores pode implicar em SBRF's com menor acurácia e menos apropriados aos seus domínios de aplicação. Uma forma de contornar esta situação e conhecer melhor os conectivos lógicos fuzzy. Para isso se faz necessário saber quais propriedades tais conectivos podem satisfazer. Portanto, a m de corroborar com o significado de implicação fuzzy e corroborar com a implementação de SBRF's mais apropriados, várias leis Booleanas têm sido generalizadas e estudadas como equações ou inequações nas lógicas fuzzy. Tais generalizações são chamadas de leis Boolean-like e elas não são comumente válidas em qualquer semântica fuzzy. Neste cenário, esta dissertação apresenta uma investigação sobre as condições suficientes e necessárias nas quais três leis Booleanlike like — y ≤ I(x, y), I(x, I(y, x)) = 1 e I(x, I(y, z)) = I(I(x, y), I(x, z)) — se mantém válidas no contexto fuzzy, considerando seis classes de implicações fuzzy e implicações geradas por automorfismos. Além disso, ainda no intuito de implementar SBRF's mais apropriados, propomos uma extensão para os mesmos

A review of the relationships between implication, negation and aggregation functions from the point of view of material implication

Implication and aggregation functions play important complementary roles in the field of fuzzy logic. Both have been intensively investigated since the early 1980s, revealing a tight relationship between them. However, the main results regarding this relationship, published by Fodor and Demirli DeBaets in the 1990s, have been poorly disseminated and are nowadays somewhat obsolete due to the subsequent advances in the field. The present paper deals with the translation of the classical logical equivalence p → q = ¬pvq, often called material implication, to the fuzzy framework, which establishes a one-to-one correspondence between implication functions and disjunctors (the class of aggregation functions that extend the Boolean disjunction to the unit interval). The construction of implication functions from disjunctors via negation functions, and vice versa, is reviewed, stressing the properties of disjunctors (respectively, implication functions) that ensure certain properties of implication functions (disjunctors).

Fuzzy Coherence: Making Sense of Continuity in Hypertext Narratives

Hypertexts are digital texts characterized by interactive hyperlinking and a fragmented textual organization. Increasingly prominent since the early 1990s, hypertexts have become a common text type both on the Internet and in a variety of other digital contexts. Although studied widely in disciplines like hypertext theory and media studies, formal linguistic approaches to hypertext continue to be relatively rare. This study examines coherence negotiation in hypertext with particularly reference to hypertext fiction. Coherence, or the quality of making sense, is a fundamental property of textness. Proceeding from the premise that coherence is a subjectively evaluated property rather than an objective quality arising directly from textual cues, the study focuses on the processes through which readers interact with hyperlinks and negotiate continuity between hypertextual fragments. The study begins with a typological discussion of textuality and an overview of the historical and technological precedents of modern hypertexts. Then, making use of text linguistic, discourse analytical, pragmatic, and narratological approaches to textual coherence, the study takes established models developed for analyzing and describing conventional texts, and examines their applicability to hypertext. Primary data derived from a collection of hyperfictions is used throughout to illustrate the mechanisms in practice. Hypertextual coherence negotiation is shown to require the ability to cognitively operate between local and global coherence by means of processing lexical cohesion, discourse topical continuities, inferences and implications, and shifting cognitive frames. The main conclusion of the study is that the style of reading required by hypertextuality fosters a new paradigm of coherence. Defined as fuzzy coherence, this new approach to textual sensemaking is predicated on an acceptance of the coherence challenges readers experience when the act of reading comes to involve repeated encounters with referentially imprecise hyperlinks and discourse topical shifts. A practical application of fuzzy coherence is shown to be in effect in the way coherence is actively manipulated in hypertext narratives.

A guided rule reduction system for prioritization of failures in fuzzy FMEA

Traditional Failure Mode and Effect Analysis (FMEA) utilizes the Risk Priority Number (RPN) ranking system to evaluate the risk level of failures, to rank failures, and to prioritize actions. Although this method is simple, it suffers from several shortcomings. In this paper, use of fuzzy inference techniques for RPN determination in an attempt to overcome the weaknesses associated with the traditional RPN ranking system is investigated. However, the fuzzy RPN model, suffers from the combinatorial rule explosion problem. As a result, a generic rule reduction approach, i.e. the Guided Rule Reduction System (GRRS), is proposed to reduce the number of rules that need to be provided by users during the fuzzy RPN modeling process. The proposed approach is evaluated using real-world case studies pertaining to semiconductor manufacturing. The results are analyzed, and implications of the proposed approach are discussed.

Fuzzy FMEA with a guided rules reduction system for prioritization of failures

Purpose – To propose a generic method to simplify the fuzzy logic-based failure mode and effect analysis (FMEA) methodology by reducing the number of rules that needs to be provided by FMEA users for the fuzzy risk priority number (RPN) modeling process.

Design/methodology/approach – The fuzzy RPN approach typically requires a large number of rules, and it is a tedious task to obtain a full set of rules. The larger the number of rules provided by the users, the better the prediction accuracy of the fuzzy RPN model. As the number of rules required increases, ease of use of the model decreases since the users have to provide a lot of information/rules for the modeling process. A guided rules reduction system (GRRS) is thus proposed to regulate the number of rules required during the fuzzy RPN modeling process. The effectiveness of the proposed GRRS is investigated using three real-world case studies in a semiconductor manufacturing process.

Findings – In this paper, we argued that not all the rules are actually required in the fuzzy RPN model. Eliminating some of the rules does not necessarily lead to a significant change in the model output. However, some of the rules are vitally important and cannot be ignored. The proposed GRRS is able to provide guidelines to the users which rules are required and which can be eliminated. By employing the GRRS, the users do not need to provide all the rules, but only the important ones when constructing the fuzzy RPN model. The results obtained from the case studies demonstrate that the proposed GRRS is able to reduce the number of rules required and, at the same time, to maintain the ability of the Fuzzy RPN model to produce predictions that are in agreement with experts' knowledge in risk evaluation, ranking, and prioritization tasks.

Research limitations/implications – The proposed GRRS is limited to FMEA systems that utilize the fuzzy RPN model.

Practical implications – The proposed GRRS is able to simplify the fuzzy logic-based FMEA methodology and make it possible to be implemented in real environments.

Originality/value – The value of the current paper is on the proposal of a GRRS for rule reduction to enhance the practical use of the fuzzy RPN model in real environments.

An adaptive fuzzy min-max conflict-resolving classifier

This paper describes a novel adaptive network, which agglomerates a procedure based on the fuzzy min-max clustering method, a supervised ART (Adaptive Resonance Theory) neural network, and a constructive conflict-resolving algorithm, for pattern classification. The proposed classifier is a fusion of the ordering algorithm, Fuzzy ARTMAP (FAM) and the Dynamic Decay Adjustment (DDA) algorithm. The network, called Ordered FAMDDA, inherits the benefits of the trio, viz . an ability to identify a fixed order of training pattern presentation for good generalisation; stable and incrementally learning architecture; and dynamic width adjustment of the weights of hidden nodes of conflicting classes. Classification performance of the Ordered FAMDDA is assessed using two benchmark datasets. The performances are analysed and compared with those from FAM and Ordered FAM. The results indicate that the Ordered FAMDDA classifier performs at least as good as the mentioned networks. The proposed Ordered FAMDDA network is then applied to a condition monitoring problem in a power generation station. The process under scrutiny is the Circulating Water (CW) system, with prime attention to condition monitoring of the heat transfer efficiency of the condensers. The results and their implications are analysed and discussed.

Rule pruning in a fuzzy rule-based classification system

In this paper, we purpose a rule pruning strategy to reduce the number of rules in a fuzzy rule-based classification system.A confidence factor, which is formulated based on the compatibility of the rules with the input patterns is under deployed for rule pruning.The pruning strategy aims at reducing the complexity of the fuzzy classification system and, at the same time, maintaining the accuracy rate at a good level.To evaluate the effectiveness of the pruning strategy, two benchmark data sets are first tested. Then, a fault classification problem with real senor measurements collected from a power generation plant is evaluated.The results obtained are analyzed and explained, and implications of the proposed rule pruning strategy to the fuzzy classification system are discussed.

A new fuzzy peer assessment methodology for cooperative learning of students

In this paper, a new fuzzy peer assessment methodology that considers vagueness and imprecision of words used throughout the evaluation process in a cooperative learning environment is proposed. Instead of numerals, words are used in the evaluation process, in order to provide greater flexibility. The proposed methodology is a synthesis of perceptual computing (Per-C) and a fuzzy ranking algorithm. Per-C is adopted because it allows uncertainties of words to be considered in the evaluation process. Meanwhile, the fuzzy ranking algorithm is deployed to obtain appropriate performance indices that reflect a student's contribution in a group, and subsequently rank the student accordingly. A case study to demonstrate the effectiveness of the proposed methodology is described. Implications of the results are analyzed and discussed. The outcomes clearly demonstrate that the proposed fuzzy peer assessment methodology can be deployed as an effective evaluation tool for cooperative learning of students.

Fuzzy subset approach in coupled population dynamics of blowflies

This paper is a study on the population dynamics of blowflies employing a density-dependent. non-linear mathematical model and a coupled population formalism. In this Study, we investigated the coupled population dynamics applying fuzzy subsets to model the Population trajectory. analyzing demographic parameters such as fecundity, Survival, and migration. The main results suggest different possibilities in terms of dynamic behavior produced by migration in coupled Populations between distinct environments and the rescue effect generated by the connection between populations. It was possible to conclude that environmental heterogeneity can play an important role in blowfly metapopulation systems. The implications of these results for population dynamics of blowflies are discussed.

Uma aplicação da lógica Fuzzy

Pós-graduação em Matemática Universitária - IGCE