Topic
Membership function
About: Membership function is a research topic. Over the lifetime, 15795 publications have been published within this topic receiving 418366 citations.
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TL;DR: The results of the experiments support the hypothesis that people often use compensatory procedures and suggest a new class of operators which varies with respect to a parameter of compensation.
911 citations
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TL;DR: This paper defines a broad family of fuzzy rough sets, each one of which, called an (I, J)-fuzzy rough set, is determined by an implicator I and a triangular norm J.
911 citations
01 Jan 1996
TL;DR: Lotfi Zadeh (1965) introduced fuzzy set theory and fuzzy logic, and promoted these as a way of reasoning about uncertainty in computer systems.
Abstract: Another approach to reasoning about uncertainty, with a different mathematical basis, is fuzzy logic. Brief history: Standard classical (Boolean) logic (Aristotle, c 50BC; Boole, 1854) uses two possible truth values: • A statement may be true (truth value 1) or false (truth value 0) Łukasiewicz logic (early 20th century): three truth values: • 2, 1 and 0 represent, respectively, “true”, “false” and “unknown” or “irrelevant” • This was further extended to an infinite-valued logic, where real numbers in the range [0,1] represent varying degrees of truth. Only of academic interest, until... Lotfi Zadeh (1965) introduced fuzzy set theory and fuzzy logic, and promoted these as a way of reasoning about uncertainty in computer systems.
901 citations
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TL;DR: Fuzzy set theory is applied to fuzzy linear programming problems and it is shown how fuzzylinear programming problems can be solved without increasing the computational effort.
Abstract: The concept of fuzzy sets is presented as a new tool for the formulation and solution of systems and decision problems which contain fuzzy components or fuzzy relationships. After a brief description of the basic theory of fuzzy sets, implications to systems theory and decision making are indicated. Fuzzy set theory is then applied to fuzzy linear programming problems and it is shown how fuzzy linear programming problems can be solved without increasing the computational effort. Some critical remarks concerning the presently existing axioms and necessary future research efforts conclude this introductionary paper.
899 citations
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TL;DR: A new image thresholding method based on minimizing the measures of fuzziness of an input image and a fuzzy range is defined to find the adequate threshold value within this range.
889 citations