L-fuzzy Sets and Intuitionistic Fuzzy Sets

DOI: 10.1007/978-3-540-72687-6_16 In book: Computational Intelligence Based on Lattice Theory, Publisher: Springer, pp.325-339

ABSTRACT Summary. In this article we firstly summarize some notions on L-fuzzy sets, where L denotes a complete lattice. We then study a special case of L-fuzzy sets, namely the “intuitionistic fuzzy sets”. The importance of these sets comes from the fact that the negation is
being defined independently from the fuzzy membership function. The latter implies both flexibility and e.ectiveness in fuzzy
inference applications. We additionally show several practical applications on intuitionistic fuzzy sets, in the context of
computational intelligence.

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    ABSTRACT: research of fuzzy set theory, which is applied in fuzzy topology [2-3], fuzzy algebras [4- 5], fuzzy measure and analysis [6-10], fuzzy optimization and decision [11-1 2], fuzzy reasoning [1314], fuzzy logic [1 5]and related domains. The cut
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    ABSTRACT: In this paper, we study a generalization of group, hypergroup and n-ary group. Firstly, we define interval-valued fuzzy (anti fuzzy) n-ary sub-hypergroup with respect to a t-norm T (t-conorm S). We give a necessary and sufficient condition for, an interval-valued fuzzy subset to be an interval-valued fuzzy (anti fuzzy) n-ary sub-hypergroup with respect to a t-norm T (t-conorm S). Secondly, using the notion of image (anti image) and inverse image of a homomorphism, some new properties of interval-valued fuzzy (anti fuzzy) n-ary sub-hypergroup are obtained with respect to infinitely ∨-distributive t-norms T (∧-distributive t-conorms S). Also, we obtain some results of T-product (S-product) of the interval-valued fuzzy subsets for infinitely ∨-distributive t-norms T (∧-distributive t-conorms S). Lastly, we investigate some properties of interval-valued fuzzy subsets of the fundamental n-ary group with infinitely ∨-distributive t-norms T (∧-distributive t-conorms S).
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    ABSTRACT: in systems in addition to the mainstream models like fuzzy sets. The greyness in a grey number reflects the fact that our information is incomplete to determine its value, and it is different from the vaguness in a fuzzy set where complete information is available but the boundary of the set is ambiguous. Grey sets apply the basic concepts of grey numbers in grey systems, and consider the characteristic function values of a set as grey numbers. Due to the adoption of grey numbers, the usual rules of fuzzy set operations are not applicable in grey sets, and it is necessary to investigate the special operation rules of grey sets. Most research works in literature use intervals to represent grey numbers, and it brings a common misunderstanding of grey sets as another name for interval-valued fuzzy sets. An investigation on the operation of grey sets is beneficial to the understanding of the difference between a grey set and an interval-valued fuzzy set as well.


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Oct 2, 2014