Proceedings Article10.1109/FUZZY.2009.5276884
On hesitant fuzzy sets and decision
Vicenç Torra,Yasuo Narukawa +1 more
- 02 Oct 2009
- pp 1378-1382
1.1K
TL;DR: The hesitant fuzzy sets as mentioned in this paper are a generalization of fuzzy sets where the membership is an interval, instead of being a single value, and they have been used in decision making.
read more
Abstract: Intuitionistic Fuzzy Sets (IFS) are a generalization of fuzzy sets where the membership is an interval. That is, membership, instead of being a single value, is an interval. A large number of operations have been defined for this type of fuzzy sets, and several applications have been developed in the last years. In this paper we describe hesitant fuzzy sets. They are another generalization of fuzzy sets. Although similar in intention to IFS, some basic differences on their interpretation and on their operators exist. In this paper we review their definition, the main results and we present an extension principle, which permits to generalize existing operations on fuzzy sets to this new type of fuzzy sets. We also discuss their use in decision making.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Hesitant intuitionistic fuzzy soft sets
Admi Nazra,Syafruddin,Riri Lestari,Gandung Catur Wicaksono +3 more
- 01 Sep 2017
Abstract: This paper aims to extend the hesitant fuzzy soft sets to hesitant intuitionistic fuzzy soft sets by merging the concept of hesitant intuitionistic fuzzy sets and soft sets. The authors define some operations on hesitant intuitionistic fuzzy sets, such as complement, union and intersection, and obtain related properties. The similar operations are defined on hesitant intuitionistic fuzzy soft sets, and also some properties such as assosiative and De Morgan’s laws are obtained.
Decision-Making Analysis Under Interval-Valued q-Rung Orthopair Dual Hesitant Fuzzy Environment
TL;DR: The novel idea of interval-valued q-rung orthopair dual hesitant fuzzy graphs, in the light of Hamacher operator, is proposed and the new concepts of Zagreb energy and Harmonic energy of IV q-RODHFHGs are developed.
Linguistic hesitant intuitionistic fuzzy cross-entropy measures
TL;DR: Two new multiple attribute decision making methods have been presented based on the new cross-entropy measures in which attribute values are given in the form of linguistic hesitant intuitionistic fuzzy values to reflect human hesitantation and fuzzy thinking comprehensively.
Group consistency and group decision making under uncertain probabilistic hesitant fuzzy preference environment
TL;DR: This study proposes the uncertain probabilistic hesitant fuzzy element (UPHFE), a generalized fuzzy number, which includes four types of HFEs, and introduces the UPHFPRs and these methods into a group decision-making process, for which two operators are proposed to aggregate the UHFEs and ensure that the aggregated preference relations can remain UPHfPRs.
Dual hesitant fuzzy interaction operators and their application to group decision making
Yejun Xu,Dou Rui,Huimin Wang +2 more
TL;DR: In this paper, a new class of dual hesitant fuzzy aggregation operators are developed, including a weighted interaction averaging operator, a weighted weighted interaction geometric operator, and a hybrid interaction operator.
References
•Book
Fuzzy sets
Lotfi A. Zadeh
- 01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
53.2K
Intuitionistic fuzzy sets
TL;DR: Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
15.7K
Detecting change in vague interpretations of landscapes
TL;DR: It is suggested that the mappings derived express subtle variations in land cover types and change in those types as well as in ecotones, which may be related more conclusively to an ecological process than are Boolean mappings with associated linear boundaries.
10.7K
Distances between intuitionistic fuzzy sets
Eulalia Szmidt,Janusz Kacprzyk +1 more
TL;DR: It is shown that all three parameters describing intuitionistic fuzzy sets should be taken into account while calculating those distances between intuitionistically fuzzy sets.
1.6K
Some properties of fuzzy sets of type 2
Masaharu Mizumoto,Kokichi Tanaka +1 more
TL;DR: This paper investigates the algebraic structures of fuzzy grades under the operations of join ⊔, meet ⊓, and negation ┐ which are defined by using the extension principle, and shows that convex fuzzy grades form a commutative semiring and normal convex fuzzies form a distributive lattice under ⊢ and ⊡.
787