Displaying similar documents to “Mixed integer programming, general concept inclusions and fuzzy description logics.”

Formal Introduction to Fuzzy Implications

Adam Grabowski (2017)

Formalized Mathematics

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In the article we present in the Mizar system the catalogue of nine basic fuzzy implications, used especially in the theory of fuzzy sets. This work is a continuation of the development of fuzzy sets in Mizar; it could be used to give a variety of more general operations, and also it could be a good starting point towards the formalization of fuzzy logic (together with t-norms and t-conorms, formalized previously).

The limits of fuzzy logic.

Juan Luis Castro (1999)

Mathware and Soft Computing

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In this paper we try to answer the following questions: What can be made by applying fuzzy logic? and What can not be made by applying fuzzy logic? The question will be analyzed from both a theoretical and an applied point of view. A (partial) answer will be given for three topics: a) as calculus procedure b) as reasoning mechanism and c) as engineering tool.

From computing with numbers to computing with words - From manipulation of measurements to manipulation of perceptions

Lotfi Zadeh (2002)

International Journal of Applied Mathematics and Computer Science

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Computing, in its usual sense, is centered on manipulation of numbers and symbols. In contrast, computing with words, or CW for short, is a methodology in which the objects of computation are words and propositions drawn from a natural language, e.g., small, large, far, heavy, not very likely, the price of gas is low and declining, Berkeley is near San Francisco, it is very unlikely that there will be a significant increase in the price of oil in the near future, etc. Computing with...

Formalization of Provenes fuzzy functional dependency in fuzzy databases.

Nedzad Dukic, Zikrija Avdagic (2004)

Mathware and Soft Computing

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In this paper we establish equivalence between a theory of fuzzy functional dependences and a fragment of fuzzy logic. We give a way to interpret fuzzy functional dependences as formulas in fuzzy logic. This goal is realized in a few steps. Truth assignment of attributes is defined in terms of closeness between two tuples in a fuzzy relation. A corresponding fuzzy formula is associated to a fuzzy functional dependence. It is proved that if a relation satisfies a fuzzy functional dependence,...

Interpretability of linguistic variables: a formal account

Ulrich Bodenhofer, Peter Bauer (2005)

Kybernetika

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This contribution is concerned with the interpretability of fuzzy rule-based systems. While this property is widely considered to be a crucial one in fuzzy rule-based modeling, a more detailed formal investigation of what “interpretability” actually means is not available. So far, interpretability has most often been associated with rather heuristic assumptions about shape and mutual overlapping of fuzzy membership functions. In this paper, we attempt to approach this problem from a...