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2015•International Journal of Energy Information and CommunicationsOpen access

Theory of Fuzzy Sets: Construction of Membership Surfaces of Normal Fuzzy Vectors

Hemanta K. Baruah

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Abstract

Fuzzy vectors have been studied almost since the beginning of the theory of fuzzy sets.However, just as a fuzzy number has to be defined with reference to a membership function, every fuzzy vector too has to be defined with reference to a membership surface.Nothing however is available in the literature about the membership surface when a fuzzy vector is defined.In this article, using the Randomness-Fuzziness Consistency Principle, it would be shown how to construct the membership surface of a normal fuzzy vector.

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Fuzzy vectors have been studied almost since the beginning of the theory of fuzzy sets.However, just as a fuzzy number has to be defined with reference to a membership function, every fuzzy vector too has to be defined with reference to a membership surface.Nothing however is available in the literature about the membership surface when a fuzzy vector is defined.In this article, using the Randomness-Fuzziness Consistency Principle, it would be shown how to construct the membership surface of a normal fuzzy vector.

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Available abstract

Fuzzy vectors have been studied almost since the beginning of the theory of fuzzy sets.However, just as a fuzzy number has to be defined with reference to a membership function, every fuzzy vector too has to be defined with reference to a membership surface.Nothing however is available in the literature about the membership surface when a fuzzy vector is defined.In this article, using the Randomness-Fuzziness Consistency Principle, it would be shown how to construct the membership surface of a normal fuzzy vector.

Key concepts: Fuzzy logic, Fuzzy set, Mathematics, Fuzzy classification, Fuzzy mathematics, Fuzzy set operations, Defuzzification, Fuzzy number

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