Search results for "Fuzzy mathematics"

Introducing a Fuzzy-Pattern Operator in Fuzzy Time Series

2017

In this paper we introduce a fuzzy pattern operator and propose a new weighting fuzzy time series strategy for generating accurate ex-post forecasts. A decision support system is built for managing the weights of the information provided by the historical data, under a fuzzy time series framework. Our procedure analyzes the historical performance of the time series using different experiments, and it classifies the characteristics of the series through a fuzzy operator, providing a trapezoidal fuzzy number as one-step ahead forecast. We also present some numerical results related to the predictive performance of our procedure with time series of financial data sets.

Fuzzy functions: a fuzzy extension of the category SET and some related categories

2000

<p>In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -> L is distinguished which could be considered as fuzzy functions from an L-valued set (X,Ex) to an L-valued set (Y,Ey). We study basic properties of these functions, consider some properties of the corresponding category of L-valued sets and fuzzy functions as well as briefly describe some categories related to algebra and topology with fuzzy functions in the role of morphisms.</p>

On a Category of Extensional Fuzzy Rough Approximation L-valued Spaces

2016

We establish extensionality of some upper and lower fuzzy rough approximation operators on an L-valued set. Taking as the ground basic properties of these operators, we introduce the concept of an (extensional) fuzzy rough approximation L-valued space. We apply fuzzy functions satisfying certain continuity-type conditions, as morphisms between such spaces, and in the result obtain a category \(\mathcal{FRA}{} \mathbf{SPA}(L)\) of fuzzy rough approximation L-valued spaces. An interpretation of fuzzy rough approximation L-valued spaces as L-fuzzy (di)topological spaces is presented and applied for constructing examples in category \(\mathcal{FRA}{} \mathbf{SPA}(L)\).

Upper and lower approximations of general aggregation operators based on fuzzy rough sets

2015

Our paper deals with constructions of upper and lower general aggregation operators which act on fuzzy sets. These constructions are based on fuzzy rough sets and provide two approximations (upper and lower) of the pointwise extension and the t-extension of an ordinary aggregation operator. Considering two lattices of corresponding general aggregation operators we describe two approximate systems with respect to a lattice of fuzzy equivalence relations.

Ranking fuzzy interval numbers in the setting of random sets – further results

1999

Abstract We present some new properties of several fuzzy order relations, defined on the set of fuzzy numbers, from among those introduced in [S. Chanas, M. Delgado, J.L. Verdegay, M.A. Vila, Information Sciences 69 (1993) 201–217]. The main result is proving that four from among the relations considered in [S. Chanas, M. Delgado, J.L. Verdegay, M.A. Vila, Information Sciences 69 (1993) 201–217] are strongly transitive (s-transitive).

A Fuzzy Discrete Event Simulator for Fuzzy Production Environment Analysis

1998

Abstract Discrete Event Simulation is a powerful tool to help production managers in planning manufacturing systems. The necessity to rapid react to market conditions is pushing production planners to process requirements and information affected by vagueness. Vagueness is related with event definition, therefore it is not manageable through statistical tools, but more properly by using fuzzy mathematics. Production situations where uncertainty takes body in term of vagueness are referred as Fuzzy Production Environments. Classical Discrete Event simulators are not suitable to deal with fuzzy variables, therefore they cannot be used to model Fuzzy Production Environments. This paper aims to…

Application of the Morris method for screening the influential parameters of fuzzy controllers applied to wastewater treatment plants

2011

In this paper,we evaluate the application of a sensitivity analysis to help fine-tuning a fuzzy controller for a biological nitrogen and phosphorus removal (BNPR) plant. TheMorris Screeningmethod is proposed and evaluated as a prior step to obtain the parameter significance ranking. First, an iterative procedure has been performed in order to find out the proper repetition number of the elementary effects (r) of the method. The optimal repetition number found in this study (r = 60) is in direct contrast to previous applications of the Morris method, which usually use low repetition number, e.g. r = 10 ~ 20. Working with a non-proper repetition number (r) could lead to Type I error (identify…

Representation of knowledge using Fuzzy set theory

1989

Fuzzy methods for analysing fuzzy production environment

1998

Abstract Very recently, in production management research literature, the necessity to extend production systems analysis techniques, such as queue theory, Mean Value Analysis (MVA) and discrete simulation, to Fuzzy Production Environments, i.e. to those production situations in which data are vague, has emerged. Fuzzy set theory is a powerful tool to model vagueness and, therefore, fuzzy mathematics can be used to extend classical production system analysis techniques. This paper proposes a methodology based on fuzzy relation algebra to extend classical MVA and discrete event simulation.

A fuzzy framework to explain musical tuning in practice

2013

A theoretical tuning system is a set of pitches that can be used to play music. It is a fact that the human ear perceives notes with very close frequencies as if they were the same note. Therefore, in our approach a musical note and its pitch sensation are modeled as L-R fuzzy numbers with a modal interval and a bounded support. We pay particular attention to the 12-tone equal temperament (12-TET) for being the most widely used tuning system and we define the fuzzy 12-TET composed of 12 fuzzy notes. A similarity relation between a fuzzy note and a theoretical note can be defined, and subsequently a similarity class associated to each one of the fuzzy notes in the fuzzy 12-TET arises. Finall…