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Fuzzy similarity measures and measurement theory
2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2019We consider objects associated with a fuzzy set-based representation. By using a classic method of measurement introduced by Tversky, we establish necessary and sufficient conditions for the existence of a particular class of fuzzy similarity measures, agreeing with an ordering relation among pairs of objects which express the idea that two objects are
Coletti, Giulianella +1 more
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Measurement, 2008
Abstract Exact measurement is a mapping f0 from the structure of physical objects into the structure of real numbers R representing the results of measurement. In the framework of the fuzzy theory of measurement an inexact measurement is represented by a mapping f from a physical objects into a structure of fuzzy intervals.
Michał K. Urbański, Janusz Wa¸sowski
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Abstract Exact measurement is a mapping f0 from the structure of physical objects into the structure of real numbers R representing the results of measurement. In the framework of the fuzzy theory of measurement an inexact measurement is represented by a mapping f from a physical objects into a structure of fuzzy intervals.
Michał K. Urbański, Janusz Wa¸sowski
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Fuzzy measure based on decomposition theory
Fuzzy Sets and Systems, 2000The authors define a fuzzy measure \({\mathfrak M}^*\) for fuzzy numbers \(D\) by the formula \({\mathfrak M}^*(D)= \int^1_0(D_r(\alpha)- D_1(\alpha)) d\alpha\), where \(D_r(\alpha)\) and \(D_1(\alpha)\) are, respectively, the upper and lower bound of the \(\alpha\)-cut \(\{x\in \mathbb{R}:D(x)\geq \alpha\}= [D_1(\alpha), D_r(\alpha)]\).
Jing-Shing Yao, San-Chyi Chang
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Intuitionistic fuzzy similarity measure: Theory and applications
Journal of Intelligent & Fuzzy Systems, 2015First we give notion of integral of intuitionistic fuzzy set and introduce intuitionistic fuzzy implicator and intuitionistic fuzzy inclusion measure. Then we propose a new measure of similarity between two intuitionistic fuzzy sets based on intuitionistic fuzzy inclusion measure.
Ismat Beg, Tabasam Rashid
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Fuzzy approach to the theory of measurement inexactness
Measurement, 2003Abstract In this paper we propose the t -norm based arithmetics to describe the propagation of both systematic and statistical inexactness. Evaluation of measurement inexactness occurs in three steps: (1) estimation of inexactness of single ‘pure’ measurement results, (2) propagation of inexactness due to statistical evaluation, (3) estimation of ...
Michał K. Urbanski, Janusz Wa̧sowski
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The role of fuzzy scales in measurement theory
Measurement, 2013The introduction of the representational theory of measurement by Stevens initiated a new way to understand what measurement is and was followed by an intense scientific activity. Ludwik Finkelstein mainly contributed to this activity through several synthetic surveys and his formalisation of this theory includes a generalisation of the representation ...
Benoit, Eric, Foulloy, Laurent
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Duality and ordinality in fuzzy measure theory
Fuzzy Sets and Systems, 2003For a finite fuzzy measure \(m\) (i.e., a non-decreasing set function defined on a sigma-algebra \({\mathcal A}\) of a universe \(X\) vanishing at the empty set), its dual \(m^{\text{d}}:{\mathcal A}\to[0,\infty[\;\) is given by \(m^{\text{d}}(A)=m (X)-m(A^c)\).
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Fuzzy Subset Theory in the Measurement of Poverty
Philippine Journal of Development, 1992What has not been explored in the traditional measures of poverty is the extensive set of categorical variables that indicate standard of living and are already available from existing survey data. What precluded researchers from deriving poverty and welfare gauges from these data is the difficulty of incorporating these indicators in their measurement.
Bantilan, Maria Cynthia S. +2 more
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Imperfect Pattern Recognition Using the Fuzzy Measure Theory
2009This paper aims to provide a unified framework to deal with information imperfection and heterogeneity using possibility theory, in addition to information conflict and scarcity using Dempster-Shafer theory in order to classify imperfectly-described medical images. The proposed method is very robust and general.
Dahabiah, Anas +2 more
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Fuzzy intervals as a basis for measurement theory
NAFIPS/IFIS/NASA '94. Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference. The Industrial Fuzzy Control and Intelligent Systems Conference, and the NASA Joint Technology Wo, 2002We describe the problem of error estimation for indirect measurements, one of the main problems of measurement theory. We show why statistical approach is not always adequate, why interval and fuzzy approaches have their own problem, and propose a new paradigm: using fuzzy intervals as a basis for measurement theory. >
G.N. Solopchenko +2 more
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