Article
Approximations of fuzzy numbers by trapezoidal fuzzy numbers preserving the ambiguity and value.
Computers & Mathematics with Applications (Impact Factor: 2.07). 01/2011; 61:13791401. DOI: 10.1016/j.camwa.2011.01.005
Source: DBLP

Article: Nearest interval, triangular and trapezoidal approximation of a fuzzy number preserving ambiguity
[Show abstract] [Hide abstract]
ABSTRACT: The ambiguity was introduced to simplify the task of representing and handling of fuzzy numbers. We find the nearest real interval, nearest triangular (symmetric) fuzzy number, nearest trapezoidal (symmetric) fuzzy number of a fuzzy number, with respect to average Euclidean distance, preserving the ambiguity. A simpler and elementary method, to avoid the Karush–Kuhn–Tucker theorem and the laborious calculus associated with it and to prove the continuity is used. We give algorithms for calculus and several examples. The approximations are discussed in relation to data aggregation.International Journal of Approximate Reasoning 07/2012; 53(5):805–836. · 1.73 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We prove that some important properties of convex subsets of vector topological spaces remain valid in the space of fuzzy numbers endowed with the Euclidean distance. We use these results to obtain a characterization of fuzzy numbervalued Lipschitz functions. This fact helps us to find the best Lipschitz constant of the trapezoidal approximation operator preserving the value and ambiguity introduced in a recent paper. Finally, applications in finding within a reasonable error the trapezoidal approximation of a fuzzy number preserving the value and ambiguity in the case when the direct formula is not applicable and an estimation for the defect of additivity of the trapezoidal approximation preserving the value and ambiguity are given.Fuzzy Sets and Systems 08/2012; 200:116–135. · 1.75 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: This paper focuses on modelling fuzzy numbers with meaningful membership functions. More precisely, it proposes a method to construct trapezoidal fuzzy number approximations from raw discrete data. In many applications, input information is numerical, and therefore, particular fuzzy sets, such as fuzzy numbers, hold great interest and relevance in managing data imprecision and vagueness. The proposed technique provides an efficient way to obtain trapezoidal numbers using linear regression. The technique is simple, fast, and effective. Preliminary tests are performed using different types of input data: a Gaussian function, a Sigmoidal function, three datasets of synthetic discrete data, and an histogram obtained from a colour satellite image.Information Sciences 06/2013; 233:1–14. · 3.64 Impact Factor
Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.