Topic
Fuzzy associative matrix
About: Fuzzy associative matrix is a research topic. Over the lifetime, 8027 publications have been published within this topic receiving 194790 citations.
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01 Feb 2006TL;DR: In this paper, a new fuzzy rough set approach is proposed, which does not use any fuzzy logical connectives (t-norm, t-conorm, fuzzy implication) to reduce the part of arbitrary in the fuzzy rough approximation.
Abstract: We propose a new fuzzy rough set approach which, differently from most known fuzzy set extensions of rough set theory, does not use any fuzzy logical connectives (t-norm, t-conorm, fuzzy implication). As there is no rationale for a particular choice of these connectives, avoiding this choice permits to reduce the part of arbitrary in the fuzzy rough approximation. Another advantage of the new approach is that it is based on the ordinal properties of fuzzy membership degrees only. The concepts of fuzzy lower and upper approximations are thus proposed, creating a base for induction of fuzzy decision rules having syntax and semantics of gradual rules. The proposed approach to rule induction is also interesting from the viewpoint of philosophy supporting data mining and knowledge discovery, because it is concordant with the method of concomitant variations by John Stuart Mill. The decision rules are induced from lower and upper approximations defined for positive and negative relationships between credibility degrees of multiple premises, on one hand, and conclusion, on the other hand.
132 citations
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TL;DR: The concepts of inconsistency, validity, prime implicant and prime implicate are extended to fuzzy logic and various properties of these notions in the context of fuzzy logic are established.
Abstract: In this paper, the fuzzy set ZZadeh (1965)] is viewed as a multivalued logic with a continuum of truth values in the interval Z0, 1]. The concepts of inconsistency, validity, prime implicant and prime implicate are extended to fuzzy logic and various properties of these notions in the context of fuzzy logic are established. It is proved that a formula is valid (inconsistent) in fuzzy logic iff it is valid (inconsistent) in two-valued logic. An algorithm that generates fuzzy prime implicants (implicates) is introduced. A proof of the completeness of this algorithm is also given.
132 citations
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23 Jul 2007
TL;DR: The development and design of a graphical user interface and a command line programming toolbox for construction, edition and observation of interval type-2 fuzzy inference systems are presented.
Abstract: This paper presents the development and design of a graphical user interface and a command line programming toolbox for construction, edition and observation of interval type-2 fuzzy inference systems. The interval type-2 fuzzy logic system toolbox (IT2FLS), is an environment for interval type-2 fuzzy logic inference system development. Tools that cover the different phases of the fuzzy system design process, from the initial description phase, to the final implementation phase, build the toolbox. The toolbox's best qualities are the capacity to develop complex systems and the flexibility that permits the user to extend the availability of functions for working with the use of type-2 fuzzy operators, linguistic variables, interval type-2 membership functions, defuzzification methods and the evaluation of interval type-2 fuzzy inference systems.
132 citations
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TL;DR: A weighted fuzzy backward reasoning algorithm, based on WFSN P systems, is developed, which can accomplish dynamic fuzzy reasoning of a rule-based system more flexibly and intelligently.
Abstract: Spiking neural P systems (SN P systems) are a new class of computing models inspired by the neurophysiological behavior of biological spiking neurons. In order to make SN P systems capable of representing and processing fuzzy and uncertain knowledge, we propose a new class of spiking neural P systems in this paper called weighted fuzzy spiking neural P systems (WFSN P systems). New elements, including fuzzy truth value, certain factor, weighted fuzzy logic, output weight, threshold, new firing rule, and two types of neurons, are added to the original definition of SN P systems. This allows WFSN P systems to adequately characterize the features of weighted fuzzy production rules in a fuzzy rule-based system. Furthermore, a weighted fuzzy backward reasoning algorithm, based on WFSN P systems, is developed, which can accomplish dynamic fuzzy reasoning of a rule-based system more flexibly and intelligently. In addition, we compare the proposed WFSN P systems with other knowledge representation methods, such as fuzzy production rule, conceptual graph, and Petri nets, to demonstrate the features and advantages of the proposed techniques.
131 citations
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18 Aug 1985TL;DR: Prolog-ELF incorporating fuzzy logic and several useful functions into Prolog has been implemented as a basic language for building knowledge systems with uncertainty or fuzziness.
Abstract: Prolog-ELF incorporating fuzzy logic and several useful functions into Prolog has been implemented as a basic language for building knowledge systems with uncertainty or fuzziness. Prolog-ELF inherits all the desirable basic features of Prolog. In addition to assertions with truth-values between 1.0 and 0.5 (0 for exceptional cases), fuzzy sets can be very easily manipulated. An application of fuzzy logical database is illustrated.
131 citations