Abstract: We discuss matrix associative memories. We also introduce holographic matrix associative memories. We show how the first class allows for interpolation while the holographic kind does not. We provide a general class of matrix associative memories that allows us to move between these two extremes. We next look at fuzzy associative memories and introduce a general fuzzy holographic memory. Finally, we describe a number of methods for measuring the degree of association between an input and a primary memory stimulus.
Abstract: Knowledge representation plays a fundamental role in the construction of artificial intelligence for modeling commonsense reasoning. We emphasize the role fuzzy logic can play in extending some of the models of AI. Some basic ideas from the fuzzy set based theory of approximate reasoning are introduced. We then discuss two extensions of the theory of approximate reasoning, possibilistic logic and effectation logic.
Abstract: Consonant belief structures provide a representation for fuzzy sets because their plausibility measures are possibility measures. However, in general the aggregation of these consonant belief structures are not consonant, not fuzzy sets. In this article, we attempt to overcome this problem. We first note that two belief structures are equivalent if their plausibility and belief functions are equal. This observation allows us to provide different equivalent representations for any belief structure. This allows us to induce for different consonant belief structures commensurate representations. We show that if we represent two consonant belief structures in a commensurate manner their aggregations are…also consonant if we impose the additional requirement that the underlying probability distributions satisfy the condition of synonyminity, that is, they are completely correlated. The results of this work allow us to use belief structure representations to manipulate fuzzy subsets.
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Abstract: A new form of uncertainty called possibilistic uncertainty is introduced. As opposed to probabilistic uncertainty, which is based upon an additive measure and is applicable in cases of repeated experiments, possibilistic uncertainty is based upon a non-additive measure and is a generalization of the idea of ease of attainment in a situation. We discuss the properties of possibilistic uncertainty and describe some prototypical examples. We also discuss the idea of language as being a generator of possibilistic variables. We introduce fuzzy subsets as a means of translating linguistic values into possibility distributions and the idea of approximate reasoning as a…means of simulating a large class of human reasoning operations. We introduce a measure of specificity of a possibility distribution and discuss applications of fuzzy set theory to intelligent quering of data bases and multiple criteria decision making. Finally, we introduce some ideas from fuzzy arithmetic.
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Keywords: Linguistic information, uncertainty, fuzzy sets, multiple criteria, approximate inference
Abstract: In this paper, we develop a relationship between two approaches to combining evidence: the Ordered Abelian Group (OAG) approach and the uninorm approach. We show that while there exist uninorms that are not extended OAG's it turns out that for operations which are continuous (in some reasonable sense), these two approaches coincide.
Abstract: We present a general way to select an optimal alternative when there is some uncertainty about the state of the world. It is shown how this method can be applied whatever the uncertainty representation used to model the information about the state of nature: probability distribution, fuzzy set, possibility distribution, a Dempster–Shafer belief structure, or a fuzzy Dempster–Shafer structure. In this general formulation, we show the role of the OWA operators to model the decision maker's attitude.
Abstract: The increasing use of computers for transactions and communication have created mountains of data that contain potentially valuable knowledge. To search for this knowledge we have to develop a new generation of tools, which have the ability of flexible querying and intelligent searching. In this paper we will introduce an extension of a fuzzy query language called Summary SQL which can be used for knowledge discovery and data mining. We show how it can be used to search for fuzzy rules.
Keywords: Knowledge discovery, Data mining, Fuzzy query, Linguistic summary, Fuzzy rules
Abstract: The Analytical Hierarchy Process (AHP) provides a comprehensive methodology for the solution of multicriteria decision problems which makes considerable use of comparison generated importances to help in the aggregation of lower order concepts in the formulation of higher order concepts. We introduce an extension of the Analytical Hierarchy Process using the Ordered Weighted Averaging (OWA) operators. This extension, which generalizes the aggregation process used in the AHP, allows more flexibility in the formulation of higher order concepts and provides the AHP an even greater facility for modeling human decision making. Using the OWA operators we are able to model situations…where the number of sub-criteria needed to satisfy a higher order concept can be expressed in terms of linguistic quantifiers.
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Abstract: Fermatean fuzzy sets (FFSs), proposed by Senapati and Yager (2019a), can handle uncertain information more easily in the process of decision making. They defined basic operations over the Fermatean fuzzy sets. Here we shall introduce three new operations: subtraction, division, and Fermatean arithmetic mean operations over Fermatean fuzzy sets. We discuss their properties in details. Later, we develop a Fermatean fuzzy weighted product model to solve the multi-criteria decision-making problem. Finally, an illustrative example of selecting a suitable bridge construction method is given to verify the approach developed by us and to demonstrate its practicability and effectiveness.
Keywords: Fermatean fuzzy set, subtraction operation, division operation, Fermatean arithmetic mean operation, multiple criteria decision making (MCDM), weighted product model (WPM)
Citation: Informatica,
vol. 30, no. 2, pp. 391-412, 2019
Abstract: A new variable step size least mean squares (LMS) algorithm using fuzzy logic (FVSS-LMS) is presented. The change of the step size at each iteration, which increases or decreases according to the degree of misadaption, is computed by a proportional fuzzy logic controller. As a result the algorithm has very good convergence speed while preserving low misadjustment. The norm of the cross correlation between the estimation error and input data is used as a measure of misadaption. Simulation results are presented to verify the performance of the proposed algorithm.