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In this paper, we propose a new mathematical model for image processing. It is a logarithmical one. We consider the bounded interval (-1, 1) as the set of gray levels. Firstly, we define two operations: addition 〈+〉 and real scalar multiplication 〈×〉. With these operations, the set of gray levels becomes a real vector space. Then, defining the scalar(More)
— This paper presents an extension of fuzzy set based on Łukasiewicz penta-valued logic. This new type of fuzzy set will be called penta-valued fuzzy set and will be defined by five scalar functions: the strong membership, the weak membership, the uncertainty, the weak non-membership and the strong non-membership. Also, the penta-valued fuzzy set represents(More)
In this paper, we propose a mathematical model for color image processing. It is a logarithmical one. We consider the cube (-1,1) 3 as the set of values for the color space. We define two operations: addition + and real scalar multiplication . With these operations the space of colors becomes a real vector space. Then, defining the scalar product (.|.)(More)