scholarly journals Three-way decision based on canonical soft sets of hesitant fuzzy sets

2021 ◽  
Vol 7 (2) ◽  
pp. 2061-2083
Author(s):  
Feng Feng ◽  
◽  
Zhe Wan ◽  
José Carlos R. Alcantud ◽  
Harish Garg ◽  
...  
Keyword(s):  
Fuzzy Sets ◽  
Rough Sets ◽  
Efficient Solution ◽  
Unit Interval ◽  
Research Articles ◽  
Hesitant Fuzzy Sets ◽  
Soft Sets ◽  
Decision Method ◽  
Rough Model ◽  
Different Parts

<abstract><p>The theory of three-way decision is built on the philosophy of thinking in threes. The essence of three-way decision is trisecting the whole and taking different strategies for different parts accordingly. The theory of three-way decision has been successfully implemented to diverse fields since it provides an elegant and efficient solution for solving complicated problems. In this paper, a useful representation for hesitant fuzzy sets is obtained by means of canonical soft sets. We also define unit interval parameterized soft sets and their derived hesitant fuzzy sets. Mutual representations and inner connections between hesitant fuzzy sets and soft sets are examined. With the help of soft rough sets, a generalized rough model based on hesitant fuzzy sets is established. A novel three-way decision method is presented for solving decision-making problems by means of hesitant fuzzy sets and canonical soft sets. Finally, a numerical example regarding peer review of research articles is given to illustrate the validity and efficacy of the proposed method.</p></abstract>

scholarly journals Linear Diophantine Fuzzy Soft Rough Sets for the Selection of Sustainable Material Handling Equipment

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1215
Author(s):  
Muhammad Riaz ◽  
Masooma Raza Hashmi ◽  
Humaira Kalsoom ◽  
Dragan Pamucar ◽  
Yu-Ming Chu
Keyword(s):  
Fuzzy Sets ◽  
Rough Sets ◽  
Material Handling ◽  
Optimal Decision ◽  
Soft Sets ◽  
Sustainable Material ◽  
Material Handling Equipment ◽  
Core Set ◽  
Modeling Uncertainties ◽  
Selection Of

The concept of linear Diophantine fuzzy sets (LDFSs) is a new approach for modeling uncertainties in decision analysis. Due to the addition of reference or control parameters with membership and non-membership grades, LDFS is more flexible and reliable than existing concepts of intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy sets (PFSs), and q-rung orthopair fuzzy sets (q-ROFSs). In this paper, the notions of linear Diophantine fuzzy soft rough sets (LDFSRSs) and soft rough linear Diophantine fuzzy sets (SRLDFSs) are proposed as new hybrid models of soft sets, rough sets, and LDFS. The suggested models of LDFSRSs and SRLDFSs are more flexible to discuss fuzziness and roughness in terms of upper and lower approximation operators. Certain operations on LDFSRSs and SRLDFSs have been established to discuss robust multi-criteria decision making (MCDM) for the selection of sustainable material handling equipment. For these objectives, some algorithms are developed for the ranking of feasible alternatives and deriving an optimal decision. Meanwhile, the ideas of the upper reduct, lower reduct, and core set are defined as key factors in the proposed MCDM technique. An application of MCDM is illustrated by a numerical example, and the final ranking in the selection of sustainable material handling equipment is computed by the proposed algorithms. Finally, a comparison analysis is given to justify the feasibility, reliability, and superiority of the proposed models.

Intuitionistic Fuzzy Soft Ideals

2020 ◽  
pp. 91-104
Author(s):  
Shuker Khalil
Keyword(s):  
Social Science ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Sets ◽  
Real Life ◽  
Soft Sets ◽  
Vague Sets ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Sets Theory

The basic notions of soft sets theory are introduced by Molodtsov to deal with uncertainties when solving problems in practice as in engineering, social science, environment, and economics. This notion is convenient and easy to apply as it is free from the difficulties that appear when using other mathematical tools as theory of theory of fuzzy sets, rough sets, and theory of vague sets. The soft set theory has recently gaining significance for finding rational and logical solutions to various real-life problems, which involve uncertainty, impreciseness, and vagueness. The concepts of intuitionistic fuzzy soft left almost semigroups and the intuitionistic fuzzy soft ideal are introduced in this chapter, and some of their basic properties are studied.

Soft Sets and Its Applications

2016 ◽  
pp. 65-85 ◽  
Author(s):  
B. K. Tripathy ◽  
K. R. Arun
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Soft Set ◽  
Soft Sets ◽  
Practical Applications ◽  
Set Operations ◽  
New Models ◽  
Pros And Cons

Uncertainty is an inherent characteristic of modern day databases. In order to handle such databases with uncertainty, several new models have been introduced in the literature. Some new models like fuzzy sets introduced by Zadeh (1965), rough sets invented by Z. Pawlak (1982) and intuitionistic fuzzy sets extended by K.T. Atanassov (1986). All these models have their own pros and cons. However, one of the major problems with these models is the lack of sufficient number of parameters to deal with uncertainty. In order to add adequate number of parameters, soft set theory was introduced by Molodtsov in 1999. Since then the theoretical developments on soft set theory has attracted the attention of researchers. However, the practical applications of any theory are of enough importance to make use of it. In this chapter, the basic definitions of soft set, operations and properties are discussed. Also, the aim in this chapter is to discuss on the different applications of soft sets; like decision making, parameter reduction, data clustering and data dealing with incompleteness.

On Theory of Multisets and Applications

2016 ◽  
pp. 1-22
Author(s):  
B. K. Tripathy
Keyword(s):  
Fuzzy Sets ◽  
Model Uncertainty ◽  
Rough Sets ◽  
Real Life ◽  
Intuitionistic Fuzzy Sets ◽  
Current Status ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Mathematics ◽  
Basic Sets

Although multiple occurrences of elements are immaterial in sets, in real life situations repetition of elements is useful. So, the notion of multisets (also called as bags) was introduced, where repetition of elements is taken into account. Fuzzy set, intuitionistic (a misnomer here as intuitionistic mathematics has nothing to do with its fuzzy counterpart) fuzzy sets, rough sets and soft sets are extensions of the basic notion of sets as they model uncertainty in data. Following this multisets have been extended to fuzzy multisets, intuitionistic fuzzy sets, rough multisets and soft multisets. Many properties of basic sets have been extended to the context of multisets, fuzzy multisets, intuitionistic fuzzy sets, rough multisets and soft multisets. Several applications of different multisets mentioned above are found in literature. In this chapter, it is our aim to introduce the different concepts of multisets, their properties, current status and highlight their applications.

scholarly journals Hesitant Fuzzy Soft Subalgebras and Ideals inBCK/BCI-Algebras

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Young Bae Jun ◽  
Sun Shin Ahn ◽  
G. Muhiuddin
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Hesitant Fuzzy Sets ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets

As a link between classical soft sets and hesitant fuzzy sets, the notion of hesitant fuzzy soft sets is introduced and applied to a decision making problem in the papers by Babitha and John (2013) and Wang et al. (2014). The aim of this paper is to apply hesitant fuzzy soft set for dealing with several kinds of theories inBCK/BCI-algebras. The notions of hesitant fuzzy soft subalgebras and (closed) hesitant fuzzy soft ideals are introduced, and related properties are investigated. Relations between a hesitant fuzzy soft subalgebra and a (closed) hesitant fuzzy soft ideal are discussed. Conditions for a hesitant fuzzy soft set to be a hesitant fuzzy soft subalgebra are given, and conditions for a hesitant fuzzy soft subalgebra to be a hesitant fuzzy soft ideal are provided. Characterizations of a (closed) hesitant fuzzy soft ideal are considered.

Generalized Hesitant Fuzzy Soft Sets and Its Application to Decision Making

2019 ◽  
Vol 33 (12) ◽  
pp. 1950019 ◽  
Author(s):  
Chunquan Li ◽  
Dongxue Li ◽  
Jianhua Jin
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Hesitant Fuzzy Sets ◽  
Soft Sets ◽  
Fundamental Properties ◽  
Fuzzy Soft Sets

In this paper, we propose generalized hesitant fuzzy soft sets by integrating generalized fuzzy soft sets with hesitant fuzzy sets. Then we investigate several fundamental properties of generalized hesitant fuzzy soft sets. In particular, a system of all the generalized hesitant fuzzy soft sets with narrow strict union and generalized strict intersection operators turns out to be a lattice. Meanwhile, a system of all the generalized hesitant fuzzy soft sets with generalized strict union and narrow strict intersection operators is a lattice. Based on generalized hesitant fuzzy soft sets, we provide an effective approach to decision making. Finally, three examples are presented to illuminate the feasibility of the method.

Hesitant fuzzy β covering rough sets and applications in multi-attribute decision making

2021 ◽  
pp. 1-16
Author(s):  
Jia-Jia Zhou ◽  
Xiang-Yang Li
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Fuzzy Sets ◽  
Rough Sets ◽  
Fuzzy Information ◽  
Hesitant Fuzzy Sets ◽  
Application Model ◽  
Rough Approximation ◽  
Multi Attribute Decision Making ◽  
The Universe

 In present paper, we put forward four types of hesitant fuzzy β covering rough sets (HFβCRSs) by uniting covering based rough sets (CBRSs) and hesitant fuzzy sets (HFSs). We firstly originate hesitant fuzzy β covering of the universe, which can induce two types of neighborhood to produce four types of HFβCRSs. We then make further efforts to probe into the properties of each type of HFβCRSs. Particularly, the relationships of each type of rough approximation operators w.r.t. two different hesitant fuzzy β coverings are groped. Moreover, the relationships between our proposed models and some other existing related models are established. Finally, we give an application model, an algorithm, and an illustrative example to elaborate the applications of HFβCRSs in multi-attribute decision making (MADM) problems. By making comparative analysis, the HFβCRSs models proposed by us are more general than the existing models of Ma and Yang and are more applicable than the existing models of Ma and Yang when handling hesitant fuzzy information.

Soft sets combined with fuzzy sets and rough sets: a tentative approach

2009 ◽  
Vol 14 (9) ◽  
pp. 899-911 ◽  
Author(s):  
Feng Feng ◽  
Changxing Li ◽  
B. Davvaz ◽  
M. Irfan Ali
Keyword(s):  
Fuzzy Sets ◽  
Rough Sets ◽  
Soft Sets
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