Fuzzy measurement theory

Urbański, Michał; ̧sowski, Janusz Wa

doi:10.1016/j.measurement.2007.02.006

Cited by 12 publications

(3 citation statements)

References 9 publications

(18 reference statements)

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“…In our previous papers [8,10], we propose another way of unifying the error theory basing on the fuzzy set theory. We show that by using the fuzzy structure with arithmetic based on t-norms (or boundary weak t-norms [9]) it is possible to describe simultaneously two kinds of uncertainty: systematic and non-systematic.…”

Section: Discussionmentioning

confidence: 99%

Algebraic approach to extensive measurement based on direct comparison

Urbański

Wa̧sowski

2009

Measurement

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Section: Discussionmentioning

confidence: 99%

Algebraic approach to extensive measurement based on direct comparison

Urbański

Wa̧sowski

2009

Measurement

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“…However, as the aim of this paper is to propose operational processing for expert dam assessment, we will not study the concept of degradation "measurability" [31][32], but consider that a small group of experts agrees on a commensurate meaning of dam degradation scores.…”

Section: Dam Characteristicsmentioning

confidence: 99%

A dam assessment support system based on physical measurements, sensory evaluations and expert judgements

Curt¹,

Talon²,

Mauris

2011

Measurement

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In engineering system control, human beings can play various key roles, in particular concerning measurement, global assessment and decision. This paper focuses on methods that allow the representation and aggregation of heterogeneous data (sensory evaluations, physical measurements, outputs of mathematical models, etc.) used in a global dam assessment process.It is acknowledged that in such complex systems many of the variables involved are evaluated with uncertainty. We propose a possibility theory-based approach to deal with all the different uncertain pieces of information and propagate them in aggregation models for global dam assessment. Finally, decision-making and communication applications relating to dam safety are presented.

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“…A non-fuzzy set represents a systematic component of uncertainty and is obtained by use of expert method. Such an approach with an arithmetic based on t-norms was proposed in [24] and [25] and studied empirically in [26].…”

Section: Measures and Fuzzy Setsmentioning

confidence: 99%

Convergence, Strong Law of Large Numbers, and Measurement Theory in the Language of Fuzzy Variables

Bzowski,

Urbanski

2009

Preprint

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In the paper we define the convergence of compact fuzzy sets as a convergence of α-cuts in the topology of compact subsets of a metric space. Furthermore we define typical convergences of fuzzy variables and show relations with convergence of their fuzzy distributions. In this context we prove a general formulation of the Strong Law of Large Numbers for fuzzy sets and fuzzy variables with Archimedean t-norms. Next we dispute a structure of fuzzy logics and postulate a new definition of necessity measures. Finally, we prove fuzzy version of the Glivenko-Cantelli theorem and use it for a construction of a complete fuzzy measurement theory.

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Fuzzy measurement theory

Cited by 12 publications

References 9 publications

Algebraic approach to extensive measurement based on direct comparison

Algebraic approach to extensive measurement based on direct comparison

A dam assessment support system based on physical measurements, sensory evaluations and expert judgements

Convergence, Strong Law of Large Numbers, and Measurement Theory in the Language of Fuzzy Variables

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