Interval-Valued and Interval Type-2 Fuzzy Sets: A Subjective Comparison

Niewiadomski, Adam

doi:10.1109/fuzzy.2007.4295537

Cited by 13 publications

(13 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For computational reasons, most practical applications of Type-2 fuzzy sets are indeed only concerned with the subclass of interval Type-2 fuzzy sets [52,53,84]. For most authors interval Type-2 fuzzy sets and intervalvalued fuzzy sets (IVFSs) [34,42,66,89] are two equivalent concepts although there are some conceptual differences regarding notions such as cardinality and support of interval Type-2 fuzzy sets and interval-valued fuzzy sets [60]. Recall that an interval-valued fuzzy set corresponds to a map-ping A from X into the class of intervals [µ 1 , µ 2 ] ⊆ [0, 1].…”

Section: Introductionmentioning

confidence: 99%

Interval-Valued and Intuitionistic Fuzzy Mathematical Morphologies as Special Cases of $\mathbb{L}$ -Fuzzy Mathematical Morphology

et al. 2011

View full text Add to dashboard Cite

Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted.The concept of L-fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov's intuitionistic fuzzy set. In addition, the class of L-fuzzy sets forms a complete lattice whenever the underlying set L constitutes a complete lattice. Based on these observations, we develop a general approach towards L-fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of L-fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction Grants or other notes.Peter Sussner and Estevão Esmi University of Campinas, Department of Applied Mathematics, Campinas, SP, 13083-859, Brazil Tel.: +55-19-3521 5959 Fax: +55-19-3289-5766 E-mail: sussner,ra050652@ime.unicamp.br Mike Nachtegael, Tom Mélange, Glad Deschrijver, and Etienne Kerre Ghent University, Department of Applied Mathematics and Computer Science, Krijgslaan 281 -S9, 9000 Ghent, Belgium Tel.: +32-9-264 4765 Fax: +32-9-264 4995 E-mail: Mike.Nachtegael,Tom.Melange,Glad.Deschrijver,Etienne.Kerre @UGent.be techniques in terms of interval-valued fuzzy image processing.

show abstract

Section: Introductionmentioning

confidence: 99%

Interval-Valued and Intuitionistic Fuzzy Mathematical Morphologies as Special Cases of $\mathbb{L}$ -Fuzzy Mathematical Morphology

et al. 2011

View full text Add to dashboard Cite

show abstract

“…If the linguistic summarizers are labeled with IT2FSs, the quantifier and the qualifier are labeled with T1FSs, then type-I quantified sentence becomes "Q Y s are/ haveS I [T ]" and type-II quantified sentence becomes "Q S g Y s are/ haveS I [T ]". Niewiadomski [64], [65] extended the scalar cardinality based degree of truth proposed by Zadeh [3] to IT2F environment for evaluating linguistic summaries for the both cases.…”

Section: B Linguistic Summarization With Interval Type-2 Fuzzy Sets:mentioning

confidence: 99%

“…Niewiadomski [64], [65] stated that at least one of Q and S should be labeled with a T1FS in linguistic summarization, and the degree of truth is equal to an interval value. When the quantifier is labeled with an IT2FS and the summarizers are labeled with T1FSs, type-I quantified sentence becomes "Q I Y s are/ have S [T ]" and type-II quantified sentence becomes "Q I S g Y s are/ have S [T ]".…”

Section: B Linguistic Summarization With Interval Type-2 Fuzzy Sets:mentioning

confidence: 99%

See 1 more Smart Citation

A Generic Method for the Evaluation of Interval Type-2 Fuzzy Linguistic Summaries

Boran

Akay

2014

IEEE Trans. Cybern.

View full text Add to dashboard Cite

Linguistic summarization has turned out to be an important knowledge discovery technique by providing the most relevant natural language-based sentences in a human consistent manner. While many studies on linguistic summarization have handled ordinary fuzzy sets [type-1 fuzzy set (T1FS)] for modeling words, only few of them have dealt with interval type-2 fuzzy sets (IT2FS) even though IT2FS is better capable of handling uncertainties associated with words. Furthermore, the existent studies work with the scalar cardinality based degree of truth which might lead to inconsistency in the evaluation of interval type-2 fuzzy (IT2F) linguistic summaries. In this paper, to overcome this shortcoming, we propose a novel probabilistic degree of truth for evaluating IT2F linguistic summaries in the forms of type-I and type-II quantified sentences. We also extend the properties that should be fulfilled by any degree of truth on linguistic summarization with T1FS to IT2F environment. We not only prove that our probabilistic degree of truth satisfies the given properties, but also illustrate by examples that it provides more consistent results when compared to the existing degree of truth in the literature. Furthermore, we carry out an application on linguistic summarization of time series data of Europe Brent Spot Price, along with a comparison of the results achieved with our approach and that of the existing degree of truth in the literature.

show abstract

“…Recently, Niewiadomski [48] presented a comparison analysis between the IT2FSs and IVFSs, the conclusion shows the fact that IVFSs and IT2FSs are not fully equivalent, despite the numerous similarities between them. For example, the cardinality of the IVFSs is an interval number, while the cardinality of the IT2FSs is a real number.…”

Section: Introductionmentioning

confidence: 97%

Multi-attribute group decision making using combined ranking value under interval type-2 fuzzy environment

Qin

Liu

2015

Information Sciences

124

View full text Add to dashboard Cite

Interval-Valued and Interval Type-2 Fuzzy Sets: A Subjective Comparison

Cited by 13 publications

References 14 publications

Interval-Valued and Intuitionistic Fuzzy Mathematical Morphologies as Special Cases of $\mathbb{L}$ -Fuzzy Mathematical Morphology

Interval-Valued and Intuitionistic Fuzzy Mathematical Morphologies as Special Cases of $\mathbb{L}$ -Fuzzy Mathematical Morphology

A Generic Method for the Evaluation of Interval Type-2 Fuzzy Linguistic Summaries

Multi-attribute group decision making using combined ranking value under interval type-2 fuzzy environment

Contact Info

Product

Resources

About