Fuzzy Logic is a multi-valued logic model based on fuzzy set theory, which may be considered as an extension of Boolean Logic. One of the fields of this theory is the Compensatory Fuzzy Logic, based on the removal of some axioms in order to achieve a sensitive and idempotent multi-valued system. This system is based on a quadruple of continuous operators: conjunction, disjunction, order and negation. In this work we present a new model of Compensatory Fuzzy Logic based on a different set of operators, conjunction and disjunction, than the ones used in the original definition, and then prove that this new model satisfies the required axioms. As an example, we present an application to decision-making, comparing the results against the ones based on the original model.
This paper aims to formally define a concept of interpretability according to natural language of a logical theory, and show advances for demonstrating that the logic system called Compensatory Fuzzy Logic is interpretable. A logical theory is interpretable according to natural language if the calculus based upon the elements of this logical theory can be understood in natural language and vice versa. We present conditions necessary for a logical theory to be called interpretable, especially Compensatory Fuzzy Logic.
This work presents a novel approach to prediction of financial asset prices. Its main contribution is the combination of compensatory fuzzy logic and the classical technical analysis to build an efficient prediction model. The interpretability properties of the model allow its users to incorporate and consider virtually any set of rules from technical analysis, in addition to the investors’ knowledge related to the actual market conditions. This knowledge can be incorporated into the model in the form of subjective assessments made by investors. Such assessments can be obtained, for example, from the graphical analysis commonly performed by traders. The effectiveness of the model was assessed through its systematic application in the stock and cryptocurrency markets. From the results, we conclude that when the model shows a high degree of recommendation, the actual financial assets show high effectiveness.
One of the advantages of Magnetic Resonance images is their ability to discriminate tissues for their subsequent quantification. In this work, magnetic resonance brain images are analyzed pixelwise by fuzzy logical predicates, reproducing in a computational way the considerations that experts employ when they interpret these images, in order to identify the tissues that pixels represent. We used Compensatory Fuzzy Logic operators to implement the logical connectives. The problem has been addressed as one pertaining to the discipline of decision-making support. The aim is to determine which tissue corresponds to each pixel. The system is optimized by a Genetic Algorithm that search an adequate set of parameters for fuzzy sets included in the predicates. It has been possible to successfully discriminate cerebrospinal fluid, gray matter and white matter in simulated and real images, validating the results using the Tanimoto Coefficient. As the operations involved are simple, processing time is short. The method can be expanded and adapted to be applied on other types of images and to recognize a greater number of tissues.
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