Fuzzy Hypervector Spaces | Zendy

R. Ameri | Zendy; O. R. Dehghan | Zendy

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Fuzzy Hypervector Spaces

Author(s) -

R. Ameri,

O. R. Dehghan

Publication year - 2008

Publication title -

advances in fuzzy systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.38

H-Index - 19

eISSN - 1687-711X

pISSN - 1687-7101

DOI - 10.1155/2008/295649

Subject(s) - mathematics , fuzzy logic , fuzzy classification , fuzzy subalgebra , pure mathematics , space (punctuation) , defuzzification , generalization , discrete mathematics , fuzzy set , coset , fuzzy number , algebra over a field , computer science , mathematical analysis , artificial intelligence , operating system

The aim of this paper is the generalization of the notion of fuzzy vector spaces to fuzzy hypervector spaces. In this regard, by considering the notion of fuzzy hypervector spaces, we characterized a fuzzy hypervector space based on its level sub-hyperspace. The algebraic nature of fuzzy hypervector space under transformations is studied. Certain conditions are obtained under which a given fuzzy hypervector space can or cannot be realized as a union of two fuzzy hypervector spaces such that none is contained in the other. The construction of a fuzzy hypervector space generated by a given fuzzy subset of a hypervector space is given. The set of all fuzzy cosets of a fuzzy hypervector space is shown to be a hypervector space. Finally, a fuzzy quotient hypervector space is defined and an analogue of a consequence of the “fundamental theorem of homomorphisms” is obtained

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