Special Issue "Fuzzy Techniques for Decision Making 2018"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: 30 November 2018

Special Issue Editor

Guest Editor
Prof. Dr. José Carlos R. Alcantud

Department of Economics and Economic History, University of Salamanca, Spain
Website | E-Mail
Phone: +34-923-294666
Fax: +34-923-294500 (ext 4666)
Interests: decision theory; social choice; mathematical economics;fuzzy set theory

Special Issue Information

Dear Colleagues,

Zadeh's fuzzy set theory incorporates impreciseness of data and evaluations by imputing the degrees to which objects belong to a set. Its appearance induced the rise of several related theories, which codify subjectivity, uncertainty, imprecision, or roughness of evaluations. Their rationale is to produce new and more flexible methodologies in order to realistically model a variety of concrete decision problems. This Special Issue invites contributions addressing novel tools, techniques and methodologies for decision making (e.g., group or multi-criteria decision making) in the context of these theories. Therefore we intend to garner articles in a variety of setups including fuzzy sets, fuzzy soft sets, type-2 fuzzy sets, interval-valued fuzzy sets, hesitant fuzzy sets, fuzzy rough sets and rough fuzzy sets. Extensive review papers which refer to the latest research findings, as well as application papers, are welcome.

Prof. Dr. José Carlos R. Alcantud
Guest Editor

Manuscript Submission Information

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Keywords

  • Fuzzy set
  • Fuzzy soft set
  • Type-2 fuzzy set
  • Interval-valued fuzzy set
  • Hesitant fuzzy set
  • Neutrosophic set
  • Aggregation operator
  • Similarity and distance measure
  • Group decision making
  • Multi-criteria decision making
  • Symmetrical decision model

Published Papers (23 papers)

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Research

Open AccessArticle On Approximation of Any Ordered Fuzzy Number by A Trapezoidal Ordered Fuzzy Number
Symmetry 2018, 10(10), 526; https://doi.org/10.3390/sym10100526
Received: 5 September 2018 / Revised: 16 October 2018 / Accepted: 18 October 2018 / Published: 21 October 2018
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Abstract
In this paper, the model of imprecise quantity information is an ordered fuzzy number. The purpose of our study is to propose some methods of approximating any ordered fuzzy number using a trapezoidal ordered fuzzy number. The information ambiguity is evaluated by means
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In this paper, the model of imprecise quantity information is an ordered fuzzy number. The purpose of our study is to propose some methods of approximating any ordered fuzzy number using a trapezoidal ordered fuzzy number. The information ambiguity is evaluated by means of an energy measure. The information indistinctness is evaluated by Kosko’s entropy measure. We discuss the problem of approximation of an arbitrary ordered fuzzy number by the nearest trapezoidal ordered fuzzy number. This way, we can simplify arithmetical operations on the linear space of ordered fuzzy numbers. The set of feasible trapezoidal ordered numbers is limited by the combination of the following conditions: invariance of energy measure, invariance of entropy measure, and invariance of information support. Evaluating the influence of individual limits combinations on the utility of given approximations, two combinations of those restraints, recommended for use, were chosen. It was also indicated that one of the recommended approximation problems can be used only for ordered fuzzy numbers characterized by a low level of entropy. The obtained results are currently used in such multi-criterial decision making models as financial portfolio management, evaluation of negotiations offers, the fuzzy TOPSIS model, and the fuzzy SAW model. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
Open AccessArticle Study on an Automatic Parking Method Based on the Sliding Mode Variable Structure and Fuzzy Logical Control
Symmetry 2018, 10(10), 523; https://doi.org/10.3390/sym10100523
Received: 29 September 2018 / Revised: 13 October 2018 / Accepted: 16 October 2018 / Published: 19 October 2018
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Abstract
This paper discusses an automatic parking control method based on the combination of the sliding mode variable structure control (SMVSC) and fuzzy logical control. SMVSC is applied to drive the vehicle from a random initial position and pose, to the designated parking position
[...] Read more.
This paper discusses an automatic parking control method based on the combination of the sliding mode variable structure control (SMVSC) and fuzzy logical control. SMVSC is applied to drive the vehicle from a random initial position and pose, to the designated parking position and pose. Then, the vehicle is driven from the designated parking position to the target parking slot using the method of fuzzy logical control, whose rules are limited to the range of the effective initial position. To combine SMVSC with the fuzzy logical control, the experimental results demonstrate that effective parking can be guaranteed, even if the initial position is out of the effective parking area of the fuzzy logical control. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessArticle An Emergency Decision Making Method for Different Situation Response Based on Game Theory and Prospect Theory
Symmetry 2018, 10(10), 476; https://doi.org/10.3390/sym10100476
Received: 20 September 2018 / Revised: 3 October 2018 / Accepted: 6 October 2018 / Published: 11 October 2018
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Abstract
Because of the continuous burst of emergency events (EEs) recently, emergency decision making (EDM) has become an active research topic due to its crucial role in relieving and reducing various losses and damages (property, lives, environment, etc.) caused by EEs. Current EDM studies
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Because of the continuous burst of emergency events (EEs) recently, emergency decision making (EDM) has become an active research topic due to its crucial role in relieving and reducing various losses and damages (property, lives, environment, etc.) caused by EEs. Current EDM studies based on prospect theory (PT) have considered decision maker’s (DM’s) psychological behavior, which is very important in the EDM process because it affects DM’s decision behavior directly, particularly under the uncertainty decision environment. However, those studies neglected an important fact that different emergency situations should be handled by different measures to show the pertinence and effectiveness of the emergency response in the real world, which has been taken into consideration in EDM studies based on game theory (GT). Different behavior experiments show that DMs usually have limited rationality when involved in risk and an uncertain decision environment, in which their psychological behavior has distinct impacts on their decision choice and behavior. Nevertheless, the existing studies of EDM based on GT build on an assumption that DMs are totally rational; however, it is obvious that such an assumption is unreasonable and far from the real-world situation. Motivated by these limitations pointed out previously, this study proposes a novel EDM method combining GT and PT that considers not only the DM’s psychological behavior, but also takes different situations’ handling for EEs into account, which is closer to the EDM problems in reality. An example and comparison with other methods are provided to demonstrate the validity and rationality of the proposed method for coping with real-world EDM problems. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessArticle Some q-Rung Dual Hesitant Fuzzy Heronian Mean Operators with Their Application to Multiple Attribute Group Decision-Making
Symmetry 2018, 10(10), 472; https://doi.org/10.3390/sym10100472
Received: 21 September 2018 / Revised: 6 October 2018 / Accepted: 7 October 2018 / Published: 10 October 2018
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Abstract
The q-rung orthopair fuzzy sets (q-ROFSs), originated by Yager, are good tools to describe fuzziness in human cognitive processes. The basic elements of q-ROFSs are q-rung orthopair fuzzy numbers (q-ROFNs), which are constructed by membership and
[...] Read more.
The q-rung orthopair fuzzy sets (q-ROFSs), originated by Yager, are good tools to describe fuzziness in human cognitive processes. The basic elements of q-ROFSs are q-rung orthopair fuzzy numbers (q-ROFNs), which are constructed by membership and nonmembership degrees. As realistic decision-making is very complicated, decision makers (DMs) may be hesitant among several values when determining membership and nonmembership degrees. By incorporating dual hesitant fuzzy sets (DHFSs) into q-ROFSs, we propose a new technique to deal with uncertainty, called q-rung dual hesitant fuzzy sets (q-RDHFSs). Subsequently, we propose a family of q-rung dual hesitant fuzzy Heronian mean operators for q-RDHFSs. Further, the newly developed aggregation operators are utilized in multiple attribute group decision-making (MAGDM). We used the proposed method to solve a most suitable supplier selection problem to demonstrate its effectiveness and usefulness. The merits and advantages of the proposed method are highlighted via comparison with existing MAGDM methods. The main contribution of this paper is that a new method for MAGDM is proposed. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessArticle New Similarity Measures of Single-Valued Neutrosophic Multisets Based on the Decomposition Theorem and Its Application in Medical Diagnosis
Symmetry 2018, 10(10), 466; https://doi.org/10.3390/sym10100466
Received: 16 September 2018 / Revised: 1 October 2018 / Accepted: 2 October 2018 / Published: 9 October 2018
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Abstract
Cut sets, decomposition theorem and representation theorem have a great influence on the realization of the transformation of fuzzy sets and classical sets, and the single-valued neutrosophic multisets (SVNMSs) as the generalization of fuzzy sets, which cut sets, decomposition theorem and representation theorem
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Cut sets, decomposition theorem and representation theorem have a great influence on the realization of the transformation of fuzzy sets and classical sets, and the single-valued neutrosophic multisets (SVNMSs) as the generalization of fuzzy sets, which cut sets, decomposition theorem and representation theorem have the similar effects, so they need to be studied in depth. In this paper, the decomposition theorem, representation theorem and the application of a new similarity measures of SVNMSs are studied by using theoretical analysis and calculations. The following are the main results: (1) The notions, operation and operational properties of the cut sets and strong cut sets of SVNMSs are introduced and discussed; (2) The decomposition theorem and representation theorem of SVNMSs are established and rigorously proved. The decomposition theorem and the representation theorem of SVNMSs are the theoretical basis for the development of SVNMSs. The decomposition theorem provides a new idea for solving the problem of SVNMSs, and points out the direction for the principle of expansion of SVNMSs. (3) Based on the decomposition theorem and representation theorem of SVNMSs, a new notion of similarity measure of SVNMSs is proposed by applying triple integral. And this new similarity is applied to the practical problem of multicriteria decision-making, which explains the efficacy and practicability of this decision-making method. The new similarity is not only a way to solve the problem of multi-attribute decision-making, but also contains an important mathematical idea, that is, the idea of transformation. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
Open AccessArticle Two Types of Intuitionistic Fuzzy Covering Rough Sets and an Application to Multiple Criteria Group Decision Making
Symmetry 2018, 10(10), 462; https://doi.org/10.3390/sym10100462
Received: 7 September 2018 / Revised: 23 September 2018 / Accepted: 29 September 2018 / Published: 4 October 2018
PDF Full-text (814 KB)
Abstract
Intuitionistic fuzzy rough sets are constructed by combining intuitionistic fuzzy sets with rough sets. Recently, Huang et al. proposed the definition of an intuitionistic fuzzy (IF) β-covering and an IF covering rough set model. In this paper, some properties of IF β
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Intuitionistic fuzzy rough sets are constructed by combining intuitionistic fuzzy sets with rough sets. Recently, Huang et al. proposed the definition of an intuitionistic fuzzy (IF) β -covering and an IF covering rough set model. In this paper, some properties of IF β -covering approximation spaces and the IF covering rough set model are investigated further. Moreover, we present a novel methodology to the problem of multiple criteria group decision making. Firstly, some new notions and properties of IF β -covering approximation spaces are proposed. Secondly, we study the characterizations of Huang et al.’s IF covering rough set model and present a new IF covering rough set model for crisp sets in an IF environment. The relationships between these two IF covering rough set models and some other rough set models are investigated. Finally, based on the IF covering rough set model, Huang et al. also defined an optimistic multi-granulation IF rough set model. We present a novel method to multiple criteria group decision making problems under the optimistic multi-granulation IF rough set model. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
Open AccessArticle A Novel Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets and Its Applications
Symmetry 2018, 10(10), 441; https://doi.org/10.3390/sym10100441
Received: 29 August 2018 / Revised: 21 September 2018 / Accepted: 25 September 2018 / Published: 27 September 2018
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Abstract
In this paper, a novel similarity measure for interval-valued intuitionistic fuzzy sets is introduced, which is based on the transformed interval-valued intuitionistic triangle fuzzy numbers. Its superiority is shown by comparing the proposed similarity measure with some existing similarity measures by some numerical
[...] Read more.
In this paper, a novel similarity measure for interval-valued intuitionistic fuzzy sets is introduced, which is based on the transformed interval-valued intuitionistic triangle fuzzy numbers. Its superiority is shown by comparing the proposed similarity measure with some existing similarity measures by some numerical examples. Furthermore, the proposed similarity measure is applied to deal with pattern recognition and medical diagnosis problems. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessArticle A New Method to Decision-Making with Fuzzy Competition Hypergraphs
Symmetry 2018, 10(9), 404; https://doi.org/10.3390/sym10090404
Received: 23 July 2018 / Revised: 6 September 2018 / Accepted: 12 September 2018 / Published: 16 September 2018
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Abstract
Hypergraph theory is the most developed tool for demonstrating various practical problems in different domains of science and technology. Sometimes, information in a network model is uncertain and vague in nature. In this paper, our main focus is to apply the powerful methodology
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Hypergraph theory is the most developed tool for demonstrating various practical problems in different domains of science and technology. Sometimes, information in a network model is uncertain and vague in nature. In this paper, our main focus is to apply the powerful methodology of fuzziness to generalize the notion of competition hypergraphs and fuzzy competition graphs. We introduce various new concepts, including fuzzy column hypergraphs, fuzzy row hypergraphs, fuzzy competition hypergraphs, fuzzy k-competition hypergraphs and fuzzy neighbourhood hypergraphs, strong hyperedges, kth strength of competition and symmetric properties. We design certain algorithms for constructing different types of fuzzy competition hypergraphs. We also present applications of fuzzy competition hypergraphs in decision support systems, including predator–prey relations in ecological niche, social networks and business marketing. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessArticle Symmetric Triangular Interval Type-2 Intuitionistic Fuzzy Sets with Their Applications in Multi Criteria Decision Making
Symmetry 2018, 10(9), 401; https://doi.org/10.3390/sym10090401
Received: 26 August 2018 / Revised: 7 September 2018 / Accepted: 11 September 2018 / Published: 14 September 2018
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Abstract
Type-2 intuitionistic fuzzy set (T2IFS) is a powerful and important extension of the classical fuzzy set, intuitionistic fuzzy set to measure the vagueness and uncertainty. In a practical decision-making process, there always occurs an inter-relationship among the multi-input arguments. To deal with this
[...] Read more.
Type-2 intuitionistic fuzzy set (T2IFS) is a powerful and important extension of the classical fuzzy set, intuitionistic fuzzy set to measure the vagueness and uncertainty. In a practical decision-making process, there always occurs an inter-relationship among the multi-input arguments. To deal with this point, the motivation of the present paper is to develop some new interval type-2 (IT2) intuitionistic fuzzy aggregation operators which can consider the multi interaction between the input argument. To achieve it, we define a symmetric triangular interval T2IFS (TIT2IFS), its operations, Hamy mean (HM) operator to aggregate the preference of the symmetric TIT2IFS and then shows its applicability through a multi-criteria decision making (MCDM). Several enviable properties and particular cases together with following different parameter values of this operator are calculated in detail. At last a numerical illustration is to given to exemplify the practicability of the proposed technique and a comparative analysis is analyzed in detail. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessArticle Probabilistic Hesitant Intuitionistic Linguistic Term Sets in Multi-Attribute Group Decision Making
Symmetry 2018, 10(9), 392; https://doi.org/10.3390/sym10090392
Received: 22 July 2018 / Revised: 31 August 2018 / Accepted: 3 September 2018 / Published: 10 September 2018
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Abstract
Decision making is the key component of people’s daily life, from choosing a mobile phone to engaging in a war. To model the real world more accurately, probabilistic linguistic term sets (PLTSs) were proposed to manage a situation in which several possible linguistic
[...] Read more.
Decision making is the key component of people’s daily life, from choosing a mobile phone to engaging in a war. To model the real world more accurately, probabilistic linguistic term sets (PLTSs) were proposed to manage a situation in which several possible linguistic terms along their corresponding probabilities are considered at the same time. Previously, in linguistic term sets, the probabilities of all linguistic term sets are considered to be equal which is unrealistic. In the process of decision making, due to the vagueness and complexity of real life, an expert usually hesitates and unable to express its opinion in a single term, thus making it difficult to reach a final agreement. To handle real life scenarios of a more complex nature, only membership linguistic decision making is unfruitful; thus, some mechanism is needed to express non-membership linguistic term set to deal with imprecise and uncertain information in more efficient manner. In this article, a novel notion called probabilistic hesitant intuitionistic linguistic term set (PHILTS) is designed, which is composed of membership PLTSs and non-membership PLTSs describing the opinions of decision makers (DMs). In the theme of PHILTS, the probabilities of membership linguistic terms and non-membership linguistic terms are considered to be independent. Then, basic operations, some governing operational laws, the aggregation operators, normalization process and comparison method are studied for PHILTSs. Thereafter, two practical decision making models: aggregation based model and the extended TOPSIS model for PHILTS are designed to classify the alternatives from the best to worst, as an application of PHILTS to multi-attribute group decision making. In the end, a practical problem of real life about the selection of the best alternative is solved to illustrate the applicability and effectiveness of our proposed set and models. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessArticle Intertemporal Choice of Fuzzy Soft Sets
Symmetry 2018, 10(9), 371; https://doi.org/10.3390/sym10090371
Received: 6 August 2018 / Revised: 24 August 2018 / Accepted: 27 August 2018 / Published: 1 September 2018
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Abstract
This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data
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This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theories. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
Open AccessArticle The New Similarity Measure and Distance Measure of a Hesitant Fuzzy Linguistic Term Set Based on a Linguistic Scale Function
Symmetry 2018, 10(9), 367; https://doi.org/10.3390/sym10090367
Received: 4 August 2018 / Revised: 18 August 2018 / Accepted: 24 August 2018 / Published: 29 August 2018
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Abstract
The existing cosine similarity measure for hesitant fuzzy linguistic term sets (HFLTSs) has an impediment as it does not satisfy the axiom of similarity measure. Due to this disadvantage, a new similarity measure combining the existing cosine similarity measure and the Euclidean distance
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The existing cosine similarity measure for hesitant fuzzy linguistic term sets (HFLTSs) has an impediment as it does not satisfy the axiom of similarity measure. Due to this disadvantage, a new similarity measure combining the existing cosine similarity measure and the Euclidean distance measure of HFLTSs is proposed, which is constructed based on a linguistic scale function; the related properties are also given. According to the relationship between the distance measure and the similarity measure, a corresponding distance measure between HFLTSs is obtained. Furthermore, we generalize the technique for order preference by similarity to an ideal solution (TOPSIS) method to the obtained distance measure of the HFLTSs. The principal advantages of the proposed method are that it cannot only effectively transform linguistic information in different semantic environments, but it can also avoid the shortcomings of existing the cosine similarity measure. Finally, a case study is conducted to illustrate the feasibility and effectiveness of the proposed method, which is compared to the existing methods. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessArticle A Three-Dimensional Constrained Ordered Weighted Averaging Aggregation Problem with Lower Bounded Variables
Symmetry 2018, 10(8), 339; https://doi.org/10.3390/sym10080339
Received: 25 July 2018 / Revised: 9 August 2018 / Accepted: 9 August 2018 / Published: 13 August 2018
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Abstract
We consider the constrained ordered weighted averaging (OWA) aggregation problem with a single constraint and lower bounded variables. For the three-dimensional constrained OWA aggregation problem with lower bounded variables, we present four types of solution depending on the number of zero elements. According
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We consider the constrained ordered weighted averaging (OWA) aggregation problem with a single constraint and lower bounded variables. For the three-dimensional constrained OWA aggregation problem with lower bounded variables, we present four types of solution depending on the number of zero elements. According to the computerized experiment we perform, the lower bounds can affect the solution types, thereby affecting the optimal solution of the three-dimensional constrained OWA aggregation problem with lower bounded variables. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
Open AccessArticle A Multi-Level Privacy-Preserving Approach to Hierarchical Data Based on Fuzzy Set Theory
Symmetry 2018, 10(8), 333; https://doi.org/10.3390/sym10080333
Received: 28 July 2018 / Revised: 8 August 2018 / Accepted: 9 August 2018 / Published: 10 August 2018
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Abstract
Nowadays, more and more applications are dependent on storage and management of semi-structured information. For scientific research and knowledge-based decision-making, such data often needs to be published, e.g., medical data is released to implement a computer-assisted clinical decision support system. Since this data
[...] Read more.
Nowadays, more and more applications are dependent on storage and management of semi-structured information. For scientific research and knowledge-based decision-making, such data often needs to be published, e.g., medical data is released to implement a computer-assisted clinical decision support system. Since this data contains individuals’ privacy, they must be appropriately anonymized before to be released. However, the existing anonymization method based on l-diversity for hierarchical data may cause serious similarity attacks, and cannot protect data privacy very well. In this paper, we utilize fuzzy sets to divide levels for sensitive numerical and categorical attribute values uniformly (a categorical attribute value can be converted into a numerical attribute value according to its frequency of occurrences), and then transform the value levels to sensitivity levels. The privacy model ( α l e v h , k)-anonymity for hierarchical data with multi-level sensitivity is proposed. Furthermore, we design a privacy-preserving approach to achieve this privacy model. Experiment results demonstrate that our approach is obviously superior to existing anonymous approach in hierarchical data in terms of utility and security. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessArticle Multiple-Attribute Decision-Making Method Using Similarity Measures of Hesitant Linguistic Neutrosophic Numbers Regarding Least Common Multiple Cardinality
Symmetry 2018, 10(8), 330; https://doi.org/10.3390/sym10080330
Received: 10 July 2018 / Revised: 5 August 2018 / Accepted: 7 August 2018 / Published: 9 August 2018
Cited by 4 | PDF Full-text (749 KB) | HTML Full-text | XML Full-text
Abstract
Linguistic neutrosophic numbers (LNNs) are a powerful tool for describing fuzzy information with three independent linguistic variables (LVs), which express the degrees of truth, uncertainty, and falsity, respectively. However, existing LNNs cannot depict the hesitancy of the decision-maker (DM). To solve this issue,
[...] Read more.
Linguistic neutrosophic numbers (LNNs) are a powerful tool for describing fuzzy information with three independent linguistic variables (LVs), which express the degrees of truth, uncertainty, and falsity, respectively. However, existing LNNs cannot depict the hesitancy of the decision-maker (DM). To solve this issue, this paper first defines a hesitant linguistic neutrosophic number (HLNN), which consists of a few LNNs regarding an evaluated object due to DMs’ hesitancy to represent their hesitant and uncertain information in the decision-making process. Then, based on the least common multiple cardinality (LCMC), we present generalized distance and similarity measures of HLNNs, and then develop a similarity measure-based multiple-attribute decision-making (MADM) method to handle the MADM problem in the HLNN setting. Finally, the feasibility of the proposed approach is verified by an investment decision case. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessArticle Picture Hesitant Fuzzy Set and Its Application to Multiple Criteria Decision-Making
Symmetry 2018, 10(7), 295; https://doi.org/10.3390/sym10070295
Received: 21 June 2018 / Revised: 17 July 2018 / Accepted: 18 July 2018 / Published: 20 July 2018
Cited by 1 | PDF Full-text (727 KB) | HTML Full-text | XML Full-text
Abstract
To address the complex multiple criteria decision-making (MCDM) problems in practice, this article proposes the picture hesitant fuzzy set (PHFS) theory based on the picture fuzzy set and the hesitant fuzzy set. First, the concept of PHFS is put forward, and its operations
[...] Read more.
To address the complex multiple criteria decision-making (MCDM) problems in practice, this article proposes the picture hesitant fuzzy set (PHFS) theory based on the picture fuzzy set and the hesitant fuzzy set. First, the concept of PHFS is put forward, and its operations are presented, simultaneously. Second, the generalized picture hesitant fuzzy weighted aggregation operators are developed, and some theorems and reduced operators of them are discussed. Third, the generalized picture hesitant fuzzy prioritized weighted aggregation operators are put forward to solve the MCDM problems that the related criteria are at different priorities. Fourth, two novel MCDM methods combined with the proposed operators are constructed to determine the best alternative in real life. Finally, two numerical examples and an application of web service selection are investigated to illustrate the effectiveness of the proposed methods. The sensitivity analysis shows that the different values of the parameter λ affect the ranking of alternatives, and the proposed operators are compared with several existing MCDM methods to illustrate their advantages. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessArticle Selecting the Optimal Mine Ventilation System via a Decision Making Framework under Hesitant Linguistic Environment
Symmetry 2018, 10(7), 283; https://doi.org/10.3390/sym10070283
Received: 15 June 2018 / Revised: 10 July 2018 / Accepted: 10 July 2018 / Published: 13 July 2018
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Abstract
Ventilation systems are amongst the most essential components of a mine. As the indicators of ventilation systems are in general of ambiguity or uncertainty, the selection of ventilation systems can therefore be regarded as a complex fuzzy decision making problem. In order to
[...] Read more.
Ventilation systems are amongst the most essential components of a mine. As the indicators of ventilation systems are in general of ambiguity or uncertainty, the selection of ventilation systems can therefore be regarded as a complex fuzzy decision making problem. In order to solve such problems, a decision making framework based on a new concept, the hesitant linguistic preference relation (HLPR), is constructed. The basic elements in the HLPR are hesitant fuzzy linguistic numbers (HFLNs). At first, new operational laws and aggregation operators of HFLNs are defined to overcome the limitations in existing literature. Subsequently, a novel comparison method based on likelihood is proposed to obtain the order relationship of two HFLNs. Then, a likelihood-based consistency index is introduced to represent the difference between two hesitant linguistic preference relations (HLPRs). It is a new way to express the consistency degree for the reason that the traditional consistency indices are almost exclusively based on distance measures. Meanwhile, a consistency-improving model is suggested to attain acceptable consistent HLPRs. In addition, a method to receive reasonable ranking results from HLPRs with acceptable consistency is presented. At last, this method is used to pick out the best mine ventilation system under uncertain linguistic decision conditions. A comparison and a discussion are conducted to demonstrate the validity of the presented approach. The results show that the proposed method is effective for selecting the optimal mine ventilation system, and provides references for the construction and management of mines. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
Open AccessArticle Intuitionistic Fuzzy Multiple Attribute Decision-Making Model Based on Weighted Induced Distance Measure and Its Application to Investment Selection
Symmetry 2018, 10(7), 261; https://doi.org/10.3390/sym10070261
Received: 11 June 2018 / Revised: 28 June 2018 / Accepted: 2 July 2018 / Published: 4 July 2018
Cited by 1 | PDF Full-text (262 KB) | HTML Full-text | XML Full-text
Abstract
This paper investigates an intuitionistic fuzzy multiple attribute decision-making method based on weighted induced distance and its application to investment selection. Specifically, an intuitionistic fuzzy weighted induced ordered weighted averaging operator is proposed to eliminate the drawbacks of existing methods by extending the
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This paper investigates an intuitionistic fuzzy multiple attribute decision-making method based on weighted induced distance and its application to investment selection. Specifically, an intuitionistic fuzzy weighted induced ordered weighted averaging operator is proposed to eliminate the drawbacks of existing methods by extending the functions of the order-induced variables. The main advantage of the proposed operator is its dual roles of the order-inducing variables that can simultaneously induce arguments and moderate associated weights. A further extension of the proposed operator is its adaptation towards measuring intuitionistic fuzzy information more effectively. In addition, a multiple attribute decision-making model based on the proposed distance operators is proposed. Finally, the practicability and validity of the proposed model are illustrated by using a numerical example related to investment selection. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
Open AccessArticle Complex Fuzzy Geometric Aggregation Operators
Symmetry 2018, 10(7), 251; https://doi.org/10.3390/sym10070251
Received: 15 June 2018 / Revised: 25 June 2018 / Accepted: 28 June 2018 / Published: 2 July 2018
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Abstract
A complex fuzzy set is an extension of the traditional fuzzy set, where traditional [0,1]-valued membership grade is extended to the complex unit disk. The aggregation operator plays an important role in many fields, and this paper presents several complex fuzzy geometric aggregation
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A complex fuzzy set is an extension of the traditional fuzzy set, where traditional [0,1]-valued membership grade is extended to the complex unit disk. The aggregation operator plays an important role in many fields, and this paper presents several complex fuzzy geometric aggregation operators. We show that these operators possess the properties of rotational invariance and reflectional invariance. These operators are also closed on the upper-right quadrant of the complex unit disk. Based on the relationship between Pythagorean membership grades and complex numbers, these operators can be applied to the Pythagorean fuzzy environment. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessArticle A Hybrid Fuzzy Analytic Network Process (FANP) and Data Envelopment Analysis (DEA) Approach for Supplier Evaluation and Selection in the Rice Supply Chain
Symmetry 2018, 10(6), 221; https://doi.org/10.3390/sym10060221
Received: 18 May 2018 / Revised: 12 June 2018 / Accepted: 12 June 2018 / Published: 14 June 2018
Cited by 1 | PDF Full-text (2025 KB) | HTML Full-text | XML Full-text
Abstract
In the market economy, competition is typically due to the difficulty in selecting the most suitable supplier, one that is capable to help a business to develop a profit to the highest value threshold and capable to meet sustainable development features. In addition,
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In the market economy, competition is typically due to the difficulty in selecting the most suitable supplier, one that is capable to help a business to develop a profit to the highest value threshold and capable to meet sustainable development features. In addition, this research discusses a wide range of consequences from choosing an effective supplier, including reducing production cost, improving product quality, delivering the product on time, and responding flexibly to customer requirements. Therefore, the activities noted above are able to increase an enterprise’s competitiveness. It can be seen that selecting a supplier is complex in that decision-makers must have an understanding of the qualitative and quantitative features for assessing the symmetrical impact of the criteria to reach the most accurate result. In this research, the multi-criteria group decision-making (MCGDM) approach was proposed to solve supplier selection problems. The authors collected data from 25 potential suppliers, and the four main criteria within contain 15 sub-criteria to define the most effective supplier, which has viewed factors, including financial efficiency guarantee, quality of materials, ability to deliver on time, and the conditioned response to the environment to improve the efficiency of the industry supply chain. Initially, fuzzy analytic network process (ANP) is used to evaluate and rank these criteria, which are able to be utilized to clarify important criteria that directly affect the profitability of the business. Subsequently, data envelopment analysis (DEA) models, including the Charnes Cooper Rhodes model (CCR model), Banker Charnes Cooper model (BCC model), and slacks-based measure model (SBM model), were proposed to rank suppliers. The result of the model has proposed 7/25 suppliers, which have a condition response to the enterprises’ supply requirements. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessFeature PaperArticle Hesitant Fuzzy Linguistic Aggregation Operators Based on the Hamacher t-norm and t-conorm
Symmetry 2018, 10(6), 189; https://doi.org/10.3390/sym10060189
Received: 11 May 2018 / Revised: 26 May 2018 / Accepted: 30 May 2018 / Published: 31 May 2018
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Abstract
Hesitant fuzzy linguistic (HFL) term set, as a very flexible tool to represent the judgments of decision makers, has attracted the attention of many researchers. In recent years, some HFL aggregation operators have been developed to aggregate the HFL information. However, most of
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Hesitant fuzzy linguistic (HFL) term set, as a very flexible tool to represent the judgments of decision makers, has attracted the attention of many researchers. In recent years, some HFL aggregation operators have been developed to aggregate the HFL information. However, most of these operators are proposed based on the Algebraic product and Algebraic sum. In this paper, we presented some HFL aggregation operators to handle HFL information based on Hamacher triangle norms. We first define new operational laws on the HFL element according to Hamacher triangle norms. Then we present a family of HFL Hamacher aggregation operators, including the HFL Hamacher weighted averaging, HFL Hamacher weighted geometric, HFL Hamacher power weighted averaging and HFL Hamacher power weighted geometric operators and their generalized forms. We also investigate some special cases and properties of these operators in detail. Furthermore, we develop two approaches based on the proposed operators to deal with the multi-criteria decision-making problem with HFL information. Finally, a numerical example with regard to choosing a suitable city to release sharing car is provided to illustrate the feasibility of the proposed method, and the advantages of the proposed methods are shown by conducting a sensitivity and comparative analysis. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessArticle A Novel Approach to Multi-Attribute Group Decision-Making with q-Rung Picture Linguistic Information
Symmetry 2018, 10(5), 172; https://doi.org/10.3390/sym10050172
Received: 20 April 2018 / Revised: 10 May 2018 / Accepted: 14 May 2018 / Published: 18 May 2018
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Abstract
The proposed q-rung orthopair fuzzy set (q-ROFS) and picture fuzzy set (PIFS) are two powerful tools for depicting fuzziness and uncertainty. This paper proposes a new tool, called q-rung picture linguistic set (q-RPLS) to deal with vagueness
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The proposed q-rung orthopair fuzzy set (q-ROFS) and picture fuzzy set (PIFS) are two powerful tools for depicting fuzziness and uncertainty. This paper proposes a new tool, called q-rung picture linguistic set (q-RPLS) to deal with vagueness and impreciseness in multi-attribute group decision-making (MAGDM). The proposed q-RPLS takes full advantages of q-ROFS and PIFS and reflects decision-makers’ quantitative and qualitative assessments. To effectively aggregate q-rung picture linguistic information, we extend the classic Heronian mean (HM) to q-RPLSs and propose a family of q-rung picture linguistic Heronian mean operators, such as the q-rung picture linguistic Heronian mean (q-RPLHM) operator, the q-rung picture linguistic weighted Heronian mean (q-RPLWHM) operator, the q-rung picture linguistic geometric Heronian mean (q-RPLGHM) operator, and the q-rung picture linguistic weighted geometric Heronian mean (q-RPLWGHM) operator. The prominent advantage of the proposed operators is that the interrelationship between q-rung picture linguistic numbers (q-RPLNs) can be considered. Further, we put forward a novel approach to MAGDM based on the proposed operators. We also provide a numerical example to demonstrate the validity and superiorities of the proposed method. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Open AccessArticle Some Interval Neutrosophic Linguistic Maclaurin Symmetric Mean Operators and Their Application in Multiple Attribute Decision Making
Symmetry 2018, 10(4), 127; https://doi.org/10.3390/sym10040127
Received: 10 April 2018 / Revised: 15 April 2018 / Accepted: 17 April 2018 / Published: 22 April 2018
Cited by 1 | PDF Full-text (381 KB) | HTML Full-text | XML Full-text
Abstract
There are many practical decision-making problems in people’s lives, but the information given by decision makers (DMs) is often unclear and how to describe this information is of critical importance. Therefore, we introduce interval neutrosophic linguistic numbers (INLNs) to represent the less clear
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There are many practical decision-making problems in people’s lives, but the information given by decision makers (DMs) is often unclear and how to describe this information is of critical importance. Therefore, we introduce interval neutrosophic linguistic numbers (INLNs) to represent the less clear and uncertain information and give their operational rules and comparison methods. In addition, since the Maclaurin symmetric mean (MSM) operator has the special characteristic of capturing the interrelationships among multi-input arguments, we further propose an MSM operator for INLNs (INLMSM). Furthermore, considering the weights of attributes are the important parameters and they can influence the decision results, we also propose a weighted INLMSM (WINLMSM) operator. Based on the WINLMSM operator, we develop a multiple attribute decision making (MADM) method with INLNs and some examples are used to show the procedure and effectiveness of the proposed method. Compared with the existing methods, the proposed method is more convenient to express the complex and unclear information. At the same time, it is more scientific and flexible in solving the MADM problems by considering the interrelationships among multi-attributes. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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