6,486 research outputs found
Eigenlogic: a Quantum View for Multiple-Valued and Fuzzy Systems
We propose a matrix model for two- and many-valued logic using families of
observables in Hilbert space, the eigenvalues give the truth values of logical
propositions where the atomic input proposition cases are represented by the
respective eigenvectors. For binary logic using the truth values {0,1} logical
observables are pairwise commuting projectors. For the truth values {+1,-1} the
operator system is formally equivalent to that of a composite spin 1/2 system,
the logical observables being isometries belonging to the Pauli group. Also in
this approach fuzzy logic arises naturally when considering non-eigenvectors.
The fuzzy membership function is obtained by the quantum mean value of the
logical projector observable and turns out to be a probability measure in
agreement with recent quantum cognition models. The analogy of many-valued
logic with quantum angular momentum is then established. Logical observables
for three-value logic are formulated as functions of the Lz observable of the
orbital angular momentum l=1. The representative 3-valued 2-argument logical
observables for the Min and Max connectives are explicitly obtained.Comment: 11 pages, 2 table
Fuzzy logic as a decision-making support system for the indication of bariatric surgery based on an index (OBESINDEX) generated by the association between body fat and body mass index
Background: A Fuzzy Obesity Index (OBESINDEX) for use as an alternative in bariatric surgery indication (BSI) is presented. The search for a more accurate method to evaluate obesity and to indicate a better treatment is important in the world health context. BMI (body mass index) is considered the main criteria for obesity treatment and BSI. Nevertheless, the fat excess related to the percentage of Body Fat (%BF) is actually the principal harmful factor in obesity disease that is usually neglected. This paper presents a new fuzzy mechanism for evaluating obesity by associating BMI with %BF that yields a fuzzy obesity index for obesity evaluation and treatment and allows building up a Fuzzy Decision Support System (FDSS) for BSI.

Methods: Seventy-two patients were evaluated for both BMI and %BF. These data are modified and treated as fuzzy sets. Afterwards, the BMI and %BF classes are aggregated yielding a new index (OBESINDEX) for input linguistic variable are considered the BMI and %BF, and as output linguistic variable is employed the OBESINDEX, an obesity classification with entirely new classes of obesity in the fuzzy context as well is used for BSI.

Results: There is a gradual, smooth obesity classification and BSI when using the proposed fuzzy obesity index when compared with other traditional methods for dealing with obesity.

Conclusion: The BMI is not adequate for surgical indication in all the conditions and fuzzy logic becomes an alternative for decision making in bariatric surgery indication based on the OBESINDEX
Fuzzy logic as a decision-making support system for the indication of bariatric surgery based on an index (MAFOI) generated by the association between body fat and body mass index.
Background: A fuzzy obesity index (MAFOI) for use as an alternative to bariatric surgery indication (BSI) is presented. The search for a more accurate method to evaluate obesity and to indicate a better treatment is important in the world health context. BMI (body mass index) is considered the main criteria for obesity treatment and BSI. Nevertheless, the fat excess related to the percentage of Body Fat (%BF) is actually the principal harmful factor in obesity disease that is usually neglected. This paper presents a new fuzzy mechanism for evaluating obesity by associating BMI with %BF that yields a fuzzy obesity index for obesity evaluation and treatment and allows building up a Fuzzy Decision Support System (FDSS) for BSI. Methods: Seventy-two patients were evaluated for both BMI and %BF. These data are modified and treated as fuzzy sets. Afterwards, the BMI and %BF classes are aggregated yielding a new index (MAFOI) for input linguistic variable are considered the BMI and %BF, and as output linguistic variable is employed the MAFOI, an obesity classification with entirely new classes of obesity in the fuzzy context as well as is used for BSI. Results: There is gradual, smooth obesity classification and BSI when using the proposed fuzzy obesity index when compared with other traditional methods for dealing with obesity.
Conclusion: The BMI is not adequate for surgical indication in all the conditions and fuzzy logic becomes an alternative for decision making in bariatric surgery indication based on the MAFOI
Dual Logic Concepts based on Mathematical Morphology in Stratified Institutions: Applications to Spatial Reasoning
Several logical operators are defined as dual pairs, in different types of
logics. Such dual pairs of operators also occur in other algebraic theories,
such as mathematical morphology. Based on this observation, this paper proposes
to define, at the abstract level of institutions, a pair of abstract dual and
logical operators as morphological erosion and dilation. Standard quantifiers
and modalities are then derived from these two abstract logical operators.
These operators are studied both on sets of states and sets of models. To cope
with the lack of explicit set of states in institutions, the proposed abstract
logical dual operators are defined in an extension of institutions, the
stratified institutions, which take into account the notion of open sentences,
the satisfaction of which is parametrized by sets of states. A hint on the
potential interest of the proposed framework for spatial reasoning is also
provided.Comment: 36 page
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