We use a semantical method of complete residuated lattice-valued logic to give a general- ization of fuzzy topology as a partial answer to a problem by Rosser and Turquette.
Despite half a century of fuzzy sets and fuzzy logic progress, as fuzzy sets address complex and uncertain information through the lens of human knowledge and subjectivity, more progress is needed in the semantics of ...Despite half a century of fuzzy sets and fuzzy logic progress, as fuzzy sets address complex and uncertain information through the lens of human knowledge and subjectivity, more progress is needed in the semantics of fuzzy sets and in exploring the multi-modal aspect of fuzzy logic due to the different cognitive, emotional and behavioral angles of assessing truth. We lay here the foundations of a postmodern fuzzy set and fuzzy logic theory addressing these issues by deconstructing fuzzy truth values and fuzzy set membership functions to re-capture the human knowledge and subjectivity structure in membership function evaluations. We formulate a fractal multi-modal logic of Kabbalah which integrates the cognitive, emotional and behavioral levels of humanistic systems into epistemic and modal, deontic and doxastic and dynamic multi-modal logic. This is done by creating a fractal multi-modal Kabbalah possible worlds semantic frame of Kripke model type. The Kabbalah possible worlds semantic frame integrates together both the multi-modal logic aspects and their Kripke possible worlds model. We will not focus here on modal operators and axiom sets. We constructively define a fractal multi-modal Kabbalistic L-fuzzy set as the central concept of the postmodern fuzzy set theory based on Kabbalah logic and semantics.展开更多
The primary objective of this study is to apply the Evaluation Grid Method(EGM)and the continuous fuzzy Kano quality model to explore the cognitive preferences of Taiwan China residents regarding the beauty of Taiwan...The primary objective of this study is to apply the Evaluation Grid Method(EGM)and the continuous fuzzy Kano quality model to explore the cognitive preferences of Taiwan China residents regarding the beauty of Taiwan’s China landscape paintings.The aim is to contribute to the development of social and cultural art and promote the widespread appeal of art products.Through a literature review,consultations with aesthetic experts,and the application of Miryoku Engineering’s EGM,this paper consolidates the factors that contribute to the attractiveness of painting art products among Taiwan China residents,taking into account various aesthetic qualities.Simultaneously,the paper introduces the use of the triangular fuzzy golden ratio scale semantics,specifically the equal-ratio aesthetic scale semantics,as a replacement for the traditional subjective consciousness model.Departing from the traditional discrete Kano model that employs the mode as the standard for evaluating quality,this study applies triangular fuzzy numbers to the continuous Kano quality model to analyze the diverse preferences and evaluation standards of the public.The hope is that this research methodology will not only deepen Taiwan China residents’understanding and aesthetic literacy of painting art but also serve as a reference for the popularization of art products.展开更多
Classical decision tree model is one of the classical machine learning models for its simplicity and effectiveness in applications. However, compared to the DT model, probability estimation trees （PETs） give a bette...Classical decision tree model is one of the classical machine learning models for its simplicity and effectiveness in applications. However, compared to the DT model, probability estimation trees （PETs） give a better estimation on class probability. In order to get a good probability estimation, we usually need large trees which are not desirable with respect to model transparency. Linguistic decision tree （LDT） is a PET model based on label semantics. Fuzzy labels are used for building the tree and each branch is associated with a probability distribution over classes. If there is no overlap between neighboring fuzzy labels, these fuzzy labels then become discrete labels and a LDT with discrete labels becomes a special case of the PET model. In this paper, two hybrid models by combining the naive Bayes classifier and PETs are proposed in order to build a model with good performance without losing too much transparency. The first model uses naive Bayes estimation given a PET, and the second model uses a set of small-sized PETs as estimators by assuming the independence between these trees. Empirical studies on discrete and fuzzy labels show that the first model outperforms the PET model at shallow depth, and the second model is equivalent to the naive Bayes and PET.展开更多
The relationship among diverse fuzzy semantics vs. the corresponding logic consequence operators has been analyzed systematically The results that compactness and logical compactness of fuzzy semantics are equivalent ...The relationship among diverse fuzzy semantics vs. the corresponding logic consequence operators has been analyzed systematically The results that compactness and logical compactness of fuzzy semantics are equivalent to compactness and continuity of the logic consequence operator induced by the semantics respectively have been proved under certain conditions. A general compactness theorem of fuzzy semantics have been established which says that every fuzzy semantics defined on a free algebra with members corresponding to continuous functions is compact.展开更多
基金supported by the National Foundation for Distionguished Young Scholars(Grant No:69725004)Rrsearch and Development Project of High-Technology(Grant No:863-306-ZT06-04-3)+1 种基金Foundation of Natural Sciences(Grant No:6982001) of ChinaFOK Ying-Tung Edu
文摘We use a semantical method of complete residuated lattice-valued logic to give a general- ization of fuzzy topology as a partial answer to a problem by Rosser and Turquette.
文摘Despite half a century of fuzzy sets and fuzzy logic progress, as fuzzy sets address complex and uncertain information through the lens of human knowledge and subjectivity, more progress is needed in the semantics of fuzzy sets and in exploring the multi-modal aspect of fuzzy logic due to the different cognitive, emotional and behavioral angles of assessing truth. We lay here the foundations of a postmodern fuzzy set and fuzzy logic theory addressing these issues by deconstructing fuzzy truth values and fuzzy set membership functions to re-capture the human knowledge and subjectivity structure in membership function evaluations. We formulate a fractal multi-modal logic of Kabbalah which integrates the cognitive, emotional and behavioral levels of humanistic systems into epistemic and modal, deontic and doxastic and dynamic multi-modal logic. This is done by creating a fractal multi-modal Kabbalah possible worlds semantic frame of Kripke model type. The Kabbalah possible worlds semantic frame integrates together both the multi-modal logic aspects and their Kripke possible worlds model. We will not focus here on modal operators and axiom sets. We constructively define a fractal multi-modal Kabbalistic L-fuzzy set as the central concept of the postmodern fuzzy set theory based on Kabbalah logic and semantics.
文摘The primary objective of this study is to apply the Evaluation Grid Method(EGM)and the continuous fuzzy Kano quality model to explore the cognitive preferences of Taiwan China residents regarding the beauty of Taiwan’s China landscape paintings.The aim is to contribute to the development of social and cultural art and promote the widespread appeal of art products.Through a literature review,consultations with aesthetic experts,and the application of Miryoku Engineering’s EGM,this paper consolidates the factors that contribute to the attractiveness of painting art products among Taiwan China residents,taking into account various aesthetic qualities.Simultaneously,the paper introduces the use of the triangular fuzzy golden ratio scale semantics,specifically the equal-ratio aesthetic scale semantics,as a replacement for the traditional subjective consciousness model.Departing from the traditional discrete Kano model that employs the mode as the standard for evaluating quality,this study applies triangular fuzzy numbers to the continuous Kano quality model to analyze the diverse preferences and evaluation standards of the public.The hope is that this research methodology will not only deepen Taiwan China residents’understanding and aesthetic literacy of painting art but also serve as a reference for the popularization of art products.
文摘Classical decision tree model is one of the classical machine learning models for its simplicity and effectiveness in applications. However, compared to the DT model, probability estimation trees （PETs） give a better estimation on class probability. In order to get a good probability estimation, we usually need large trees which are not desirable with respect to model transparency. Linguistic decision tree （LDT） is a PET model based on label semantics. Fuzzy labels are used for building the tree and each branch is associated with a probability distribution over classes. If there is no overlap between neighboring fuzzy labels, these fuzzy labels then become discrete labels and a LDT with discrete labels becomes a special case of the PET model. In this paper, two hybrid models by combining the naive Bayes classifier and PETs are proposed in order to build a model with good performance without losing too much transparency. The first model uses naive Bayes estimation given a PET, and the second model uses a set of small-sized PETs as estimators by assuming the independence between these trees. Empirical studies on discrete and fuzzy labels show that the first model outperforms the PET model at shallow depth, and the second model is equivalent to the naive Bayes and PET.
文摘The relationship among diverse fuzzy semantics vs. the corresponding logic consequence operators has been analyzed systematically The results that compactness and logical compactness of fuzzy semantics are equivalent to compactness and continuity of the logic consequence operator induced by the semantics respectively have been proved under certain conditions. A general compactness theorem of fuzzy semantics have been established which says that every fuzzy semantics defined on a free algebra with members corresponding to continuous functions is compact.
