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Interval-valued intuitionistic fuzzy sets and similarity measure
2017Summary: In this paper, the problem of measuring the degree of inclusion and similarity measure for two interval-valued intuitionistic fuzzy sets is considered. We propose inclusion and similarity measure by using order on interval-valued intuitionistic fuzzy sets connected with lexicographical order.
Pekala, Barbara, Balicki, Krzysztof
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Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets
Fuzzy Sets and Systems, 1996Let \(X\) be a nonempty fixed set (universe). An intuitionistic fuzzy set (IFS) \(A\) is an object having the form \(A=\{\langle x,\mu_A(x),\gamma_A(x)\rangle\): \(x\in X\}\) where the functions \(\mu_A:X\to [0,1]\) and \(\gamma_A:X\to [0,1]\) denote the degrees of membership and of non-membership of each element \(x\in X\) to the set \(A\), resp., and
Burillo, P., Bustince, H.
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Some comments on interval valued fuzzy sets
International Journal of Intelligent Systems, 1996The paper deals with fuzzy set theoretical models where the values of membership functions are open sub-intervals of \([0,1]\). The concepts of \(t\)-norm and \(t\)-conorm are used as the main theoretical tools for managing the described model. The adequacy of \(t\)-norms for the considered fuzzy set theoretical structures is shown by the main results ...
Gehrke, Mai +2 more
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An Interval-Valued Intuitionistic Fuzzy Rough Set Model
Fundamenta Informaticae, 2009Given a widespread interest in rough sets as being applied to various tasks of data analysis it is not surprising at all that we have witnessed a wave of further generalizations and algorithmic enhancements of this original concept. This paper proposes an interval-valued intuitionistic fuzzy rough model by means of integrating the classical Pawlak ...
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Entropy for Interval-Valued Fuzzy Sets
2009A non-probabilistic-type entropy measure for interval-valued fuzzy set (IVFS) is proposed. It is a result of a geometric interpretation of IVFS and uses a ratio of distances between them. It is also shown that the proposed measure can be defined in terms of the ratio of interval-valued fuzzy cardinalities: of F ∩ F c and F ∪ F c .
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On Interval Valued Intuitionistic Fuzzy Sets
2019In this chapter, the basic definitions of the concepts of Interval Valued Fuzzy Sets (IVFSs) and Interval Valued Intuitionistic Fuzzy Sets (IVIFSs) will be introduced. The relation between IFSs and IVFSs will be discussed.
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Algebraic structure through interval-valued fuzzy signature based on interval-valued fuzzy sets
Granular Computing, 2023Sangeetha Palanisamy +1 more
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Soft Interval-Valued Intuitionistic Fuzzy Rough Sets
2015The vagueness or the representation of imperfect knowledge has been a problem for a long time for the mathematicians. There are many mathematical tools for dealing with uncertainties; some of them are fuzzy set theory, rough set theory, and soft set theory.
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