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Symmetric difference on orthomodular lattices and Z 2 -valued states

Milan Matoušek, Pavel Pták (2009)

Commentationes Mathematicae Universitatis Carolinae

The investigation of orthocomplemented lattices with a symmetric difference initiated the following question: Which orthomodular lattice can be embedded in an orthomodular lattice that allows for a symmetric difference? In this paper we present a necessary condition for such an embedding to exist. The condition is expressed in terms of Z 2 -valued states and enables one, as a consequence, to clarify the situation in the important case of the lattice of projections in a Hilbert space.

Symmetric implicational restriction method of fuzzy inference

Yiming Tang, Wenbin Wu, Youcheng Zhang, Witold Pedrycz, Fuji Ren, Jun Liu (2021)

Kybernetika

The symmetric implicational method is revealed from a different perspective based upon the restriction theory, which results in a novel fuzzy inference scheme called the symmetric implicational restriction method. Initially, the SIR-principles are put forward, which constitute optimized versions of the triple I restriction inference mechanism. Next, the existential requirements of basic solutions are given. The supremum (or infimum) of its basic solutions is achieved from some properties of fuzzy...

Synthesis of membership functions to determine a radius of influence.

Vicenç Torra (1995)

Mathware and Soft Computing

In this work we study the synthesis of membership functions when they have been calculated from a set of observations according to the definition of (Zhang, 1993). The results obtained have been used to determine the radius of influence of a tramp for Podarcis lilfordi (a kind of saurians) in the island of Cabrera (Balearic Islands). The measure of this radius was used in a later work to estimate the density of these saurians in the island.

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