A Fuzzy Petri Nets Model for Computing With Words

Motivated by Zadeh's paradigm of computing with words rather than numbers, several formal models of computing with words have recently been proposed. These models are based on automata and thus are not well-suited for concurrent computing. In this paper, we incorporate the well-known model of concurrent computing, Petri nets, together with fuzzy set theory and thereby establish a concurrency model of computing with words--fuzzy Petri nets for computing with words (FPNCWs). The new feature of such fuzzy Petri nets is that the labels of transitions are some special words modeled by fuzzy sets. By employing the methodology of fuzzy reasoning, we give a faithful extension of an FPNCW which makes it possible for computing with more words. The language expressiveness of the two formal models of computing with words, fuzzy automata for computing with words and FPNCWs, is compared as well. A few small examples are provided to illustrate the theoretical development.Comment: double columns 14 pages, 8 figure

Retraction and Generalized Extension of Computing with Words

Fuzzy automata, whose input alphabet is a set of numbers or symbols, are a formal model of computing with values. Motivated by Zadeh's paradigm of computing with words rather than numbers, Ying proposed a kind of fuzzy automata, whose input alphabet consists of all fuzzy subsets of a set of symbols, as a formal model of computing with all words. In this paper, we introduce a somewhat general formal model of computing with (some special) words. The new features of the model are that the input alphabet only comprises some (not necessarily all) fuzzy subsets of a set of symbols and the fuzzy transition function can be specified arbitrarily. By employing the methodology of fuzzy control, we establish a retraction principle from computing with words to computing with values for handling crisp inputs and a generalized extension principle from computing with words to computing with all words for handling fuzzy inputs. These principles show that computing with values and computing with all words can be respectively implemented by computing with words. Some algebraic properties of retractions and generalized extensions are addressed as well.Comment: 13 double column pages; 3 figures; to be published in the IEEE Transactions on Fuzzy System

Managing Interacting Criteria: Application to Environmental Evaluation Practices

The need for organizations to evaluate their environmental practices has been recently increasing. This fact has led to the development of many approaches to appraise such practices. In this paper, a novel decision model to evaluate company’s environmental practices is proposed to improve traditional evaluation process in different facets. Firstly, different reviewers’ collectives related to the company’s activity are taken into account in the process to increase company internal efficiency and external legitimacy. Secondly, following the standard ISO 14031, two general categories of environmental performance indicators, management and operational, are considered. Thirdly, since the assumption of independence among environmental indicators is rarely verified in environmental context, an aggregation operator to bear in mind the relationship among such indicators in the evaluation results is proposed. Finally, this new model integrates quantitative and qualitative information with different scales using a multi-granular linguistic model that allows to adapt diverse evaluation scales according to appraisers’ knowledge

On Vague Computers

Vagueness is something everyone is familiar with. In fact, most people think that vagueness is closely related to language and exists only there. However, vagueness is a property of the physical world. Quantum computers harness superposition and entanglement to perform their computational tasks. Both superposition and entanglement are vague processes. Thus quantum computers, which process exact data without "exploiting" vagueness, are actually vague computers

On fuzzy-qualitative descriptions and entropy

This paper models the assessments of a group of experts when evaluating different magnitudes, features or objects by using linguistic descriptions. A new general representation of linguistic descriptions is provided by unifying ordinal and fuzzy perspectives. Fuzzy qualitative labels are proposed as a generalization of the concept of qualitative labels over a well-ordered set. A lattice structure is established in the set of fuzzy-qualitative labels to enable the introduction of fuzzy-qualitative descriptions as L-fuzzy sets. A theorem is given that characterizes finite fuzzy partitions using fuzzy-qualitative labels, the cores and supports of which are qualitative labels. This theorem leads to a mathematical justification for commonly-used fuzzy partitions of real intervals via trapezoidal fuzzy sets. The information of a fuzzy-qualitative label is defined using a measure of specificity, in order to introduce the entropy of fuzzy-qualitative descriptions. (C) 2016 Elsevier Inc. All rights reserved.Peer ReviewedPostprint (author's final draft

A model for providing emotion awareness and feedback using fuzzy logic in online learning

Monitoring users’ emotive states and using that information for providing feedback and scaffolding is crucial. In the learning context, emotions can be used to increase students’ attention as well as to improve memory and reasoning. In this context, tutors should be prepared to create affective learning situations and encourage collaborative knowledge construction as well as identify those students’ feelings which hinder learning process. In this paper, we propose a novel approach to label affective behavior in educational discourse based on fuzzy logic, which enables a human or virtual tutor to capture students’ emotions, make students aware of their own emotions, assess these emotions and provide appropriate affective feedback. To that end, we propose a fuzzy classifier that provides a priori qualitative assessment and fuzzy qualifiers bound to the amounts such as few, regular and many assigned by an affective dictionary to every word. The advantage of the statistical approach is to reduce the classical pollution problem of training and analyzing the scenario using the same dataset. Our approach has been tested in a real online learning environment and proved to have a very positive influence on students’ learning performance.Peer ReviewedPostprint (author's final draft