Search results for "Fuzzy number"

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.

A Decomposition Theorem for the Fuzzy Henstock Integral

2012

We study the fuzzy Henstock and the fuzzy McShane integrals for fuzzy-number valued functions. The main purpose of this paper is to establish the following decomposition theorem: a fuzzy-number valued function is fuzzy Henstock integrable if and only if it can be represented as a sum of a fuzzy McShane integrable fuzzy-number valued function and of a fuzzy Henstock integrable fuzzy number valued function generated by a Henstock integrable function.

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).

Optimal Control Under Fuzzy Conditions for Dynamical Systems Associated with the Second Order Linear Differential Equations

2020

This paper is devoted to an optimal trajectory planning problem with uncertainty in location conditions considered as a problem of constrained optimal control for dynamical systems. Fuzzy numbers are used to incorporate uncertainty of constraints into the classical setting of the problem under consideration. The proposed approach applied to dynamical systems associated with the second order linear differential equations allows to find an optimal control law at each \(\alpha \)-level using spline-based methods developed in the framework of the theory of splines in convex sets. The solution technique is illustrated by numerical examples.

fuzzy approach to the robust facility layout in uncertain production environments

2001

The proposed method approaches the problem of the optimal facility layout using fuzzy theory. The optimal layout is a robust layout that minimizes the total material handling cost, when the product market demands are uncertain variables, which are defined as fuzzy numbers. Since each department has a limited production capacity, not all possible combinations, deriving from each product's market demand, are taken into account because some combination could exceed the overall department's productivity. Therefore, the optimal solution results by solving a 'constrained' fuzzy optimization problem, in which the fuzzy material handling costs corresponding to the layouts are evaluated, and a ranki…

Risk Assessment of a compound feed process based on HAZOP analysis and linguistic terms

2016

[EN] The size and complexity of industrial plants, along with the characteristics of the products used, require a study, analysis and control of the existing risks in every industrial process. In this paper, a methodology for risk assessment in industrial plants, based on the combination of risks identification through the Hazard and Operability (HAZOP) analysis and the risks evaluation through linguistic variables and fuzzy numbers is applied to a case study consisting on a compound feed plant located in the town of Silla (Valencia, Spain). The results from this study show that the main risk in the compound feed production process is the formation of explosive atmospheres (ATEX). Therefore…

A Simultaneous Approach for IMS Design: a Possibility Based Approach

1999

IMS investments are characterised by high fixed costs and long life cycles. On the other hand, their redditivity and risk coverage depend on their manufacturing efficiency that is mainly defined during the design phase by fixing the system configuration. Due to the flexibility required to IMS, system configuration depends not only from technological information, such as product routing table and service times, but also from marketing data such as the typology of products to be manufacture and their production volumes. Moreover, the evaluation of the redditivity and the risk of the investment depends on market information such as product prices as well. Such interdependencies make the invest…

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…