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ORDINAL SUMS IN INTERVAL-VALUED FUZZY SET THEORY [PDF]

New Mathematics and Natural Computation, 2005
Interval-valued fuzzy sets form an extension of fuzzy sets which assign to each element of the universe a closed subinterval of the unit interval. This interval approximates the "real", but unknown, membership degree. In fuzzy set theory, an important class of triangular norms is the class of those that satisfy the residuation principle.
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Cut Sets on Interval-Valued Intuitionistic Fuzzy Sets

2009 Sixth International Conference on Fuzzy Systems and Knowledge Discovery, 2009
The aim of this article is to study the cut sets of interval valued intuitionistic fuzzy sets. By considering the cut sets of an interval-valued intuitionistic fuzzy set as five valued fuzzy sets, the definitions of four cut sets on interval-valued intuitionistic fuzzy sets are given, which are the generalizations of cuts sets on Zadeh fuzzy sets and ...
Xue-Hai Yuan, Hong-xing Li
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Uninorms on Interval-Valued Fuzzy Sets

2016
This paper is a kind of continuation of the paper by G. Deschrijver ‘Uninorms which are neither conjunctive nor disjunctive in interval-valued fuzzy set theory’, which was published in Information Sciences in 2013. In that paper he constructed uninorms whose neutral element is arbitrary of the type \({\mathbf e}=(e,e)\) and annihilator, \(\mathbf {a}\),
Martin Kalina, Pavol Král
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Distances between interval-valued fuzzy sets

NAFIPS 2009 - 2009 Annual Meeting of the North American Fuzzy Information Processing Society, 2009
In this paper, some researches on distances of interval-valued fuzzy sets are made and some properties of metric space with respect to these distances are discussed.
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RELATING INTUITIONISTIC FUZZY SETS AND INTERVAL-VALUED FUZZY SETS THROUGH BILATTICES

Applied Computational Intelligence, 2004
In this paper, we show that bilattices are robust mathematical structures that provide a natural accommodation to, and bridge between, intuitionistic fuzzy sets and interval-valued fuzzy sets. In this way, we resolve the controversy surrounding the formal equivalence of these two models, and open up the path for a new tradition for representing ...
O. ARIELI, C. CORNELIS, G. DESCHRIJVER, E. E. KERRE   +3 more
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Interval-valued intuitionistic fuzzy sets and similarity measure

2017
Summary: 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, 1996
Let \(X\) 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, 1996
The 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, Walker, Carol, Walker, Elbert   +2 more
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An Interval-Valued Intuitionistic Fuzzy Rough Set Model

Fundamenta Informaticae, 2009
Given 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

2009
A 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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