Complex fuzzy logic

Ramot, D.; Friedman, Menahem; Langholz, G.; Kandel, Abraham

doi:10.1109/tfuzz.2003.814832

Cited by 369 publications

(231 citation statements)

References 11 publications

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“…First, we recall complex fuzzy inference in [17] for convenience. Let U and V be two universes of discourse.…”

Section: Complex Fuzzy Inferencementioning

confidence: 99%

“…The amplitude term and the phase term of complex fuzzy implication relation µ A→B (x, y) in [17] are characterized by:…”

Section: Complex Fuzzy Inferencementioning

confidence: 99%

“…Functions (25)- (27) are introduced in [17] and Function (28) is a new adding method. Similar to Definition 2, the concept of orthogonality preserving complex fuzzy inference is formally expressed as follows.…”

Section: Complex Fuzzy Inferencementioning

confidence: 99%

“…Thus a complex fuzzy set is a set of vectors in the complex plane. This idea of membership vectors greatly inspired how definition of complex fuzzy sets operations [14,15] and complex fuzzy logic systems [16][17][18][19][20][21] and how to measures the difference between two complex fuzzy sets [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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The Orthogonality between Complex Fuzzy Sets and Its Application to Signal Detection

Dai

2017

Symmetry

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Abstract:A complex fuzzy set is a set whose membership values are vectors in the unit circle in the complex plane. This paper establishes the orthogonality relation of complex fuzzy sets. Two complex fuzzy sets are said to be orthogonal if their membership vectors are perpendicular. We present the basic properties of orthogonality of complex fuzzy sets and various results on orthogonality with respect to complex fuzzy complement, complex fuzzy union, complex fuzzy intersection, and complex fuzzy inference methods. Finally, an example application of signal detection demonstrates the utility of the orthogonality of complex fuzzy sets.

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“…First, we recall complex fuzzy inference in [17] for convenience. Let U and V be two universes of discourse.…”

Section: Complex Fuzzy Inferencementioning

confidence: 99%

“…The amplitude term and the phase term of complex fuzzy implication relation µ A→B (x, y) in [17] are characterized by:…”

Section: Complex Fuzzy Inferencementioning

confidence: 99%

Section: Complex Fuzzy Inferencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Orthogonality between Complex Fuzzy Sets and Its Application to Signal Detection

Dai

2017

Symmetry

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“…Buckley (1989) incorporated the concepts of fuzzy numbers and complex numbers under the name fuzzy complex numbers. This concept has become a famous research topic and a goal for many researchers (Buckley 1989;Ramot et al 2002Ramot et al , 2003. However, the concept given by Buckley has different range compared to the range of Ramot's et al definition for complex fuzzy set (CFS).…”

Section: Introductionmentioning

confidence: 99%