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Interval-valued intuitionistic fuzzy soft sets and their properties [PDF]

Computers and Mathematics With Applications, 2010
Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. However, it has been pointed out that classical soft sets are not appropriate to deal with imprecise and fuzzy parameters ...
Yuncheng Jiang
exaly   +2 more sources

Interval Type-2 Fuzzy Sets are Generalization of Interval-Valued Fuzzy Sets: Toward a Wider View on Their Relationship [PDF]

IEEE Transactions on Fuzzy Systems, 2015
In this paper, we will present a wider view on the relationship between interval-valued fuzzy sets and interval type-2 fuzzy sets, where we will show that interval-valued fuzzy sets are a particular case of the interval type-2 fuzzy sets. For this reason,
Edurne Barrenechea, Hani Hagras, Francisco Herrera   +2 more
exaly   +2 more sources

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APPLICATION OF INTERVAL VALUED FUZZY SET AND SOFT SET

jnanabha, 2020
Molodtsov was a father of soft set approach. We can’t easily settle the membership degree in some practical application. So it must be much better to describe interval-valued data instead of explaining membership degree. In this paper, we introduce the latest approach of the interval-valued fuzzy soft set by combining the interval-valued fuzzy set and ...
Rheem, Abdul, Ahmad, Musheer
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On the cardinalities of interval-valued fuzzy sets

Fuzzy Sets and Systems, 2007
The paper deals with one of the possible extensions of axiomatic theory of scalar cardinalities of fuzzy sets with finite support. The extension is related to the interval-valued fuzzy sets. Their cardinality is introduced as a mapping to the set of closed subintervals of non-negative real numbers.
Glad Deschrijver, Pavol Král
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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
Pedro J. Burillo, Humberto Bustince
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Note on Interval-Valued Fuzzy Set

2005
In this note, we introduce the concept of cut set of interval-valued fuzzy set and discuss some properties of cut set of interval-valued fuzzy set, propose three decomposition theorems of interval-valued fuzzy set and investigate some properties of cut set of interval-valued fuzzy set and mapping H in detail.
Wenyi Zeng, Yu Shi
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REPRESENTATION THEOREM OF INTERVAL-VALUED FUZZY SET

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2006
In this paper, we introduce the concept of interval-valued nested set on the universal set X, propose two representation theorems and equivalent classification theorem of interval-valued fuzzy set. These works can be used in setting up the basic theory of interval-valued fuzzy set.
Wenyi Zeng, Yu Shi, Hongxing Li 0004
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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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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, Hongxing Li 0004
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Some comments on interval valued fuzzy sets

International Journal of Intelligent Systems, 1998
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 ...
Mai Gehrke, Carol L. Walker, Elbert A. Walker   +2 more
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