Displaying similar documents to “On the resolution of bipolar max-min equations”

(T, ⊥, N) fuzzy logic.

Y. Xu, J. Lin, Da Ruan (2001)

Mathware and Soft Computing

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To investigate more reasonable fuzzy reasoning model in expert systems as well as more effective logical circuit in fuzzy control, a (T, ⊥, N) fuzzy logic is proposed in this paper by using T-norm, ⊥-norm and pseudo-complement N as the logical connectives. Two aspects are discussed: (1) some concepts of (T, ⊥, N) fuzzy logic are introduced and some properties of (T, ⊥, N) fuzzy logical formulae are discussed. (2) G-fuzzy truth (falsity) of (T, ⊥, N) fuzzy logical formulae are investigated...

Generation of fuzzy mathematical morphologies.

Pedro J. Burillo López, Noé Frago Paños, Ramón Fuentes González (2001)

Mathware and Soft Computing

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Fuzzy Mathematical Morphology aims to extend the binary morphological operators to grey-level images. In order to define the basic morphological operations fuzzy erosion, dilation, opening and closing, we introduce a general method based upon fuzzy implication and inclusion grade operators, including as particular case, other ones existing in related literature. In the definition of fuzzy erosion and dilation we use several fuzzy implications (Annexe A, Table of fuzzy implications),...

Fuzzy numbers, definitions and properties.

Miguel Delgado, José Luis Verdegay, M. Amparo Vila (1994)

Mathware and Soft Computing

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Two different definitions of a Fuzzy number may be found in the literature. Both fulfill Goguen's Fuzzification Principle but are different in nature because of their different starting points. The first one was introduced by Zadeh and has well suited arithmetic and algebraic properties. The second one, introduced by Gantner, Steinlage and Warren, is a good and formal representation of the concept from a topological point of view. The objective of this paper is...

On completeness and direction in fuzzy relational systems.

Pedro J. Burillo López, Ramón Fuentes-González, León A. González Sotos (1998)

Mathware and Soft Computing

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The concepts of bounded subset, complete subset and directed subset, wich are well known in the context of partially ordered sets (X,≤), are extended in order to become appliable, with coherence, in fuzzy relational systems (X,R). The properties of these generalized structures are analyzed and operative exemples of them are presented.

Similarity in fuzzy reasoning.

Frank Klawonn, Juan Luis Castro (1995)

Mathware and Soft Computing

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Fuzzy set theory is based on a `fuzzification' of the predicate in (element of), the concept of membership degrees is considered as fundamental. In this paper we elucidate the connection between indistinguishability modelled by fuzzy equivalence relations and fuzzy sets. We show that the indistinguishability inherent to fuzzy sets can be computed and that this indistinguishability cannot be overcome in approximate reasoning. For our investigations we generalize from the unit interval...

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).