Special Issue "Fuzzy Techniques for Decision Making"

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

Deadline for manuscript submissions: closed (30 September 2017)

Printed Edition Available!
A printed edition of this Special Issue is available here.

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,

The successful Bellman-Zadeh concept of a symmetrical decision model in a fuzzy environment, with full symmetry between constraints and objective functions, has been an inspiration for researchers on the general field of fuzzy decision making. Since Zadeh introduced the notion of fuzzy set many other types and extensions of fuzzy sets have been proposed and applied to make decisions.

This Special Issue invites contributions addressing novel techniques and tools for decision making (e.g., group or multi-criteria decision making) with notions that overcome the problem of finding the membership degree of each element in Zadeh’s original model. 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 set, 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

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Fuzzy set

  • Fuzzy soft set

  • Type-2 fuzzy set

  • Interval-valued fuzzy set

  • Hesitant fuzzy set

  • Aggregation operator

  • Similarity and distance measure

  • Group decision making

  • Multi-criteria decision making

  • Symmetrical decision model

Published Papers (22 papers)

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Editorial

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Open AccessEditorial Fuzzy Techniques for Decision Making
Symmetry 2018, 10(1), 6; https://doi.org/10.3390/sym10010006
Received: 22 December 2017 / Revised: 22 December 2017 / Accepted: 25 December 2017 / Published: 27 December 2017
Cited by 1 | PDF Full-text (173 KB) | HTML Full-text | XML Full-text
Abstract
This book contains the successful invited submissions [1–21] to a Special Issue of Symmetry on the subject area of “Fuzzy Techniques for Decision Making”.[...] Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making) Printed Edition available

Research

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Open AccessArticle Probabilistic Linguistic Power Aggregation Operators for Multi-Criteria Group Decision Making
Symmetry 2017, 9(12), 320; https://doi.org/10.3390/sym9120320
Received: 4 November 2017 / Revised: 13 December 2017 / Accepted: 13 December 2017 / Published: 19 December 2017
Cited by 3 | PDF Full-text (291 KB) | HTML Full-text | XML Full-text
Abstract
As an effective aggregation tool, power average (PA) allows the input arguments being aggregated to support and reinforce each other, which provides more versatility in the information aggregation process. Under the probabilistic linguistic term environment, we deeply investigate the new power aggregation (PA)
[...] Read more.
As an effective aggregation tool, power average (PA) allows the input arguments being aggregated to support and reinforce each other, which provides more versatility in the information aggregation process. Under the probabilistic linguistic term environment, we deeply investigate the new power aggregation (PA) operators for fusing the probabilistic linguistic term sets (PLTSs). In this paper, we firstly develop the probabilistic linguistic power average (PLPA), the weighted probabilistic linguistic power average (WPLPA) operators, the probabilistic linguistic power geometric (PLPG) and the weighted probabilistic linguistic power geometric (WPLPG) operators. At the same time, we carefully analyze the properties of these new aggregation operators. With the aid of the WPLPA and WPLPG operators, we further design the approaches for the application of multi-criteria group decision-making (MCGDM) with PLTSs. Finally, we use an illustrated example to expound our proposed methods and verify their performances. Full article
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Open AccessArticle New Applications of m-Polar Fuzzy Matroids
Symmetry 2017, 9(12), 319; https://doi.org/10.3390/sym9120319
Received: 1 November 2017 / Revised: 7 December 2017 / Accepted: 11 December 2017 / Published: 18 December 2017
Cited by 3 | PDF Full-text (386 KB) | HTML Full-text | XML Full-text
Abstract
Mathematical modelling is an important aspect in apprehending discrete and continuous physical systems. Multipolar uncertainty in data and information incorporates a significant role in various abstract and applied mathematical modelling and decision analysis. Graphical and algebraic models can be studied more precisely when
[...] Read more.
Mathematical modelling is an important aspect in apprehending discrete and continuous physical systems. Multipolar uncertainty in data and information incorporates a significant role in various abstract and applied mathematical modelling and decision analysis. Graphical and algebraic models can be studied more precisely when multiple linguistic properties are dealt with, emphasizing the need for a multi-index, multi-object, multi-agent, multi-attribute and multi-polar mathematical approach. An m-polar fuzzy set is introduced to overcome the limitations entailed in single-valued and two-valued uncertainty. Our aim in this research study is to apply the powerful methodology of m-polar fuzzy sets to generalize the theory of matroids. We introduce the notion of m-polar fuzzy matroids and investigate certain properties of various types of m-polar fuzzy matroids. Moreover, we apply the notion of the m-polar fuzzy matroid to graph theory and linear algebra. We present m-polar fuzzy circuits, closures of m-polar fuzzy matroids and put special emphasis on m-polar fuzzy rank functions. Finally, we also describe certain applications of m-polar fuzzy matroids in decision support systems, ordering of machines and network analysis. Full article
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Open AccessArticle Fishmeal Supplier Evaluation and Selection for Aquaculture Enterprise Sustainability with a Fuzzy MCDM Approach
Symmetry 2017, 9(11), 286; https://doi.org/10.3390/sym9110286
Received: 29 October 2017 / Revised: 11 November 2017 / Accepted: 14 November 2017 / Published: 21 November 2017
Cited by 3 | PDF Full-text (1335 KB) | HTML Full-text | XML Full-text
Abstract
In the aquaculture industry, feed that is of poor quality or nutritionally imbalanced can cause problems including low weight, poor growth, poor palatability, and increased mortality, all of which can induce a decrease in aquaculture production. Fishmeal is considered a better source of
[...] Read more.
In the aquaculture industry, feed that is of poor quality or nutritionally imbalanced can cause problems including low weight, poor growth, poor palatability, and increased mortality, all of which can induce a decrease in aquaculture production. Fishmeal is considered a better source of protein and its addition as an ingredient in the aquafeed makes aquatic animals grow fast and healthy. This means that fishmeal is the most important feed ingredient in aquafeed for the aquaculture industry. For the aquaculture industry in Taiwan, about 144,000 ton/USD $203,245,000 of fishmeal was imported, mostly from Peru, in 2016. Therefore, the evaluation and selection of fishmeal suppliers is a very important part of the decision-making process for a Taiwanese aquaculture enterprise. This study constructed a multiple criteria decision-making evaluation model for the selection of fishmeal suppliers using the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) approach based on the weights obtained with the entropy method in a fuzzy decision-making environment. This hybrid approach could effectively and conveniently measure the comprehensive performance of the main Peruvian fishmeal suppliers for practical applications. In addition, the results and processes described herein function as a good reference for an aquaculture enterprise in making decisions when purchasing fishmeal. Full article
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Open AccessArticle A New Multi-Attribute Decision-Making Method Based on m-Polar Fuzzy Soft Rough Sets
Symmetry 2017, 9(11), 271; https://doi.org/10.3390/sym9110271
Received: 19 October 2017 / Revised: 1 November 2017 / Accepted: 1 November 2017 / Published: 10 November 2017
Cited by 8 | PDF Full-text (279 KB) | HTML Full-text | XML Full-text
Abstract
We introduce notions of soft rough m-polar fuzzy sets and m-polar fuzzy soft rough sets as novel hybrid models for soft computing, and investigate some of their fundamental properties. We discuss the relationship between m-polar fuzzy soft rough approximation operators
[...] Read more.
We introduce notions of soft rough m-polar fuzzy sets and m-polar fuzzy soft rough sets as novel hybrid models for soft computing, and investigate some of their fundamental properties. We discuss the relationship between m-polar fuzzy soft rough approximation operators and crisp soft rough approximation operators. We also present applications of m-polar fuzzy soft rough sets to decision-making. Full article
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Open AccessArticle A Recourse-Based Type-2 Fuzzy Programming Method for Water Pollution Control under Uncertainty
Symmetry 2017, 9(11), 265; https://doi.org/10.3390/sym9110265
Received: 29 September 2017 / Revised: 29 October 2017 / Accepted: 31 October 2017 / Published: 4 November 2017
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Abstract
In this study, a recourse-based type-2 fuzzy programming (RTFP) method is developed for supporting water pollution control of basin systems under uncertainty. The RTFP method incorporates type-2 fuzzy programming (TFP) within a two-stage stochastic programming with recourse (TSP) framework to handle uncertainties expressed
[...] Read more.
In this study, a recourse-based type-2 fuzzy programming (RTFP) method is developed for supporting water pollution control of basin systems under uncertainty. The RTFP method incorporates type-2 fuzzy programming (TFP) within a two-stage stochastic programming with recourse (TSP) framework to handle uncertainties expressed as type-2 fuzzy sets (i.e., a fuzzy set in which the membership function is also fuzzy) and probability distributions, as well as to reflect the trade-offs between conflicting economic benefits and penalties due to violated policies. The RTFP method is then applied to a real case of water pollution control in the Heshui River Basin (a rural area of China), where chemical oxygen demand (COD), total nitrogen (TN), total phosphorus (TP), and soil loss are selected as major indicators to identify the water pollution control strategies. Solutions of optimal production plans of economic activities under each probabilistic pollutant discharge allowance level and membership grades are obtained. The results are helpful for the authorities in exploring the trade-off between economic objective and pollutant discharge decision-making based on river water pollution control. Full article
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Open AccessArticle Correlation Coefficients of Probabilistic Hesitant Fuzzy Elements and Their Applications to Evaluation of the Alternatives
Symmetry 2017, 9(11), 259; https://doi.org/10.3390/sym9110259
Received: 25 September 2017 / Revised: 28 October 2017 / Accepted: 29 October 2017 / Published: 2 November 2017
Cited by 8 | PDF Full-text (324 KB) | HTML Full-text | XML Full-text
Abstract
Correlation coefficient is one of the broadly use indexes in multi-criteria decision-making (MCDM) processes. However, some important issues related to correlation coefficient utilization within probabilistic hesitant fuzzy environments remain to be addressed. The purpose of this study is introduced a MCDM method based
[...] Read more.
Correlation coefficient is one of the broadly use indexes in multi-criteria decision-making (MCDM) processes. However, some important issues related to correlation coefficient utilization within probabilistic hesitant fuzzy environments remain to be addressed. The purpose of this study is introduced a MCDM method based on correlation coefficients utilize probabilistic hesitant fuzzy information. First, the covariance and correlation coefficient between two PHFEs is introduced, the properties of the proposed covariance and correlation coefficient are discussed. In addition, the northwest corner rule to obtain the expected mean related to the multiply of two PHFEs is introduced. Second, the weighted correlation coefficient is proposed to make the proposed MCDM method more applicable. And the properties of the proposed weighted correlation coefficient are also discussed. Finally, an illustrative example is demonstrated the practicality and effectiveness of the proposed method. An illustrative example is presented to demonstrate the correlation coefficient propose in this paper lies in the interval [−1, 1], which not only consider the strength of relationship between the PHFEs but also whether the PHFEs are positively or negatively related. The advantage of this method is it can avoid the inconsistency of the decision-making result due to the loss of information. Full article
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Open AccessArticle Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random Variables
Symmetry 2017, 9(11), 254; https://doi.org/10.3390/sym9110254
Received: 7 September 2017 / Revised: 6 October 2017 / Accepted: 6 October 2017 / Published: 30 October 2017
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Abstract
This paper considers linear programming problems (LPPs) where the objective functions involve discrete fuzzy random variables (fuzzy set-valued discrete random variables). New decision making models, which are useful in fuzzy stochastic environments, are proposed based on both possibility theory and probability theory. In
[...] Read more.
This paper considers linear programming problems (LPPs) where the objective functions involve discrete fuzzy random variables (fuzzy set-valued discrete random variables). New decision making models, which are useful in fuzzy stochastic environments, are proposed based on both possibility theory and probability theory. In multi-objective cases, Pareto optimal solutions of the proposed models are newly defined. Computational algorithms for obtaining the Pareto optimal solutions of the proposed models are provided. It is shown that problems involving discrete fuzzy random variables can be transformed into deterministic nonlinear mathematical programming problems which can be solved through a conventional mathematical programming solver under practically reasonable assumptions. A numerical example of agriculture production problems is given to demonstrate the applicability of the proposed models to real-world problems in fuzzy stochastic environments. Full article
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Open AccessFeature PaperArticle Valuation Fuzzy Soft Sets: A Flexible Fuzzy Soft Set Based Decision Making Procedure for the Valuation of Assets
Symmetry 2017, 9(11), 253; https://doi.org/10.3390/sym9110253
Received: 22 September 2017 / Revised: 23 October 2017 / Accepted: 23 October 2017 / Published: 27 October 2017
Cited by 5 | PDF Full-text (1381 KB) | HTML Full-text | XML Full-text
Abstract
Zadeh’s fuzzy set theory for imprecise or vague data has been followed by other successful models, inclusive of Molodtsov’s soft set theory and hybrid models like fuzzy soft sets. Their success has been backed up by applications to many branches like engineering, medicine,
[...] Read more.
Zadeh’s fuzzy set theory for imprecise or vague data has been followed by other successful models, inclusive of Molodtsov’s soft set theory and hybrid models like fuzzy soft sets. Their success has been backed up by applications to many branches like engineering, medicine, or finance. In continuation of this effort, the purpose of this paper is to put forward a versatile methodology for the valuation of goods, particularly the assessment of real state properties. In order to reach this target, we develop the concept of (partial) valuation fuzzy soft set and introduce the novel problem of data filling in partial valuation fuzzy soft sets. The use of fuzzy soft sets allows us to quantify the qualitative attributes involved in an assessment context. As a result, we illustrate the effectiveness and validity of our valuation methodology with a real case study that uses data from the Spanish real estate market. The main contribution of this paper is the implementation of a novel methodology, which allows us to assess a large variety of assets where data are heterogeneous. Our technique permits to avoid the appraiser’s subjectivity (exhibited by practitioners in housing valuation) and the well-known disadvantages of some alternative methods (such as linear multiple regression). Full article
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Open AccessFeature PaperArticle A Comparative Study of Some Soft Rough Sets
Symmetry 2017, 9(11), 252; https://doi.org/10.3390/sym9110252
Received: 22 September 2017 / Revised: 23 October 2017 / Accepted: 24 October 2017 / Published: 27 October 2017
Cited by 2 | PDF Full-text (475 KB) | HTML Full-text | XML Full-text
Abstract
Through the combination of different types of sets such as fuzzy sets, soft sets and rough sets, abundant hybrid models have been presented in order to take advantage of each other and handle uncertainties. A comparative study of relationships and interconnections of some
[...] Read more.
Through the combination of different types of sets such as fuzzy sets, soft sets and rough sets, abundant hybrid models have been presented in order to take advantage of each other and handle uncertainties. A comparative study of relationships and interconnections of some existing hybrid models has been carried out. Some foundational properties of modified soft rough sets (MSR sets) are analyzed. It is pointed out that MSR approximation operators are some kinds of Pawlak approximation operators, whereas approximation operators of Z-soft rough fuzzy sets are equivalent to approximation operators of rough fuzzy sets. The relationships among F-soft rough fuzzy sets, M-soft rough fuzzy sets and Z-soft rough fuzzy sets are surveyed. A new model called soft rough soft sets has been provided as the generalization of F-soft rough sets, and its application in group decision-making has been studied. Various soft rough sets models show great potential as a tool to solve decision-making problems, and a depth study of the connections among these models contributes to the flexible application of soft rough sets based decision-making approaches. Full article
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Open AccessArticle A Method for Fuzzy Soft Sets in Decision-Making Based on an Ideal Solution
Symmetry 2017, 9(10), 246; https://doi.org/10.3390/sym9100246
Received: 25 September 2017 / Revised: 17 October 2017 / Accepted: 18 October 2017 / Published: 23 October 2017
Cited by 7 | PDF Full-text (398 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, a decision model based on a fuzzy soft set and ideal solution approaches is proposed. This new decision-making method uses the divide-and-conquer algorithm, and it is different from the existing algorithm (the choice value based approach and the comparison score
[...] Read more.
In this paper, a decision model based on a fuzzy soft set and ideal solution approaches is proposed. This new decision-making method uses the divide-and-conquer algorithm, and it is different from the existing algorithm (the choice value based approach and the comparison score based approach). The ideal solution is generated according to each attribute (pros or cons of the attributes, with or without constraints) of the fuzzy soft sets. Finally, the weighted Hamming distance is used to compute all possible alternatives and get the final result. The core of the decision process is the design phase, the existing decision models based on soft sets mostly neglect the analysis of attributes and decision objectives. This algorithm emphasizes the correct expression of the purpose of the decision maker and the analysis of attributes, as well as the explicit decision function. Additionally, this paper shows the fact that the rank reversal phenomenon occurs in the comparison score algorithm, and an example is provided to illustrate the rank reversal phenomenon. Experiments indicate that the decision model proposed in this paper is efficient and will be useful for practical problems. In addition, as a general model, it can be extended to a wider range of fields, such as classifications, optimization problems, etc. Full article
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Open AccessArticle Fuzzy Logic-Based Model That Incorporates Personality Traits for Heterogeneous Pedestrians
Symmetry 2017, 9(10), 239; https://doi.org/10.3390/sym9100239
Received: 15 September 2017 / Revised: 7 October 2017 / Accepted: 13 October 2017 / Published: 20 October 2017
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Abstract
Most models designed to simulate pedestrian dynamical behavior are based on the assumption that human decision-making can be described using precise values. This study proposes a new pedestrian model that incorporates fuzzy logic theory into a multi-agent system to address cognitive behavior that
[...] Read more.
Most models designed to simulate pedestrian dynamical behavior are based on the assumption that human decision-making can be described using precise values. This study proposes a new pedestrian model that incorporates fuzzy logic theory into a multi-agent system to address cognitive behavior that introduces uncertainty and imprecision during decision-making. We present a concept of decision preferences to represent the intrinsic control factors of decision-making. To realize the different decision preferences of heterogeneous pedestrians, the Five-Factor (OCEAN) personality model is introduced to model the psychological characteristics of individuals. Then, a fuzzy logic-based approach is adopted for mapping the relationships between the personality traits and the decision preferences. Finally, we have developed an application using our model to simulate pedestrian dynamical behavior in several normal or non-panic scenarios, including a single-exit room, a hallway with obstacles, and a narrowing passage. The effectiveness of the proposed model is validated with a user study. The results show that the proposed model can generate more reasonable and heterogeneous behavior in the simulation and indicate that individual personality has a noticeable effect on pedestrian dynamical behavior. Full article
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Open AccessFeature PaperArticle Managing Non-Homogeneous Information and Experts’ Psychological Behavior in Group Emergency Decision Making
Symmetry 2017, 9(10), 234; https://doi.org/10.3390/sym9100234
Received: 25 September 2017 / Revised: 11 October 2017 / Accepted: 13 October 2017 / Published: 18 October 2017
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Abstract
After an emergency event (EE) happens, emergency decision making (EDM) is a common and effective way to deal with the emergency situation, which plays an important role in mitigating its level of harm. In the real world, it is a big challenge for
[...] Read more.
After an emergency event (EE) happens, emergency decision making (EDM) is a common and effective way to deal with the emergency situation, which plays an important role in mitigating its level of harm. In the real world, it is a big challenge for an individual emergency manager (EM) to make a proper and comprehensive decision for coping with an EE. Consequently, many practical EDM problems drive group emergency decision making (GEDM) problems whose main limitations are related to the lack of flexibility in knowledge elicitation, disagreements in the group and the consideration of experts’ psychological behavior in the decision process. Hence, this paper proposes a novel GEDM approach that allows more flexibility for preference elicitation under uncertainty, provides a consensus process to avoid disagreements and considers experts’ psychological behavior by using the fuzzy TODIM method based on prospect theory. Eventually, a group decision support system (GDSS) is developed to support the whole GEDM process defined in the proposed method demonstrating its novelty, validity and feasibility. Full article
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Open AccessArticle Decomposition and Intersection of Two Fuzzy Numbers for Fuzzy Preference Relations
Symmetry 2017, 9(10), 228; https://doi.org/10.3390/sym9100228
Received: 11 September 2017 / Revised: 7 October 2017 / Accepted: 9 October 2017 / Published: 14 October 2017
Cited by 2 | PDF Full-text (1588 KB) | HTML Full-text | XML Full-text
Abstract
In fuzzy decision problems, the ordering of fuzzy numbers is the basic problem. The fuzzy preference relation is the reasonable representation of preference relations by a fuzzy membership function. This paper studies Nakamura’s and Kołodziejczyk’s preference relations. Eight cases, each representing different levels
[...] Read more.
In fuzzy decision problems, the ordering of fuzzy numbers is the basic problem. The fuzzy preference relation is the reasonable representation of preference relations by a fuzzy membership function. This paper studies Nakamura’s and Kołodziejczyk’s preference relations. Eight cases, each representing different levels of overlap between two triangular fuzzy numbers are considered. We analyze the ranking behaviors of all possible combinations of the decomposition and intersection of two fuzzy numbers through eight extensive test cases. The results indicate that decomposition and intersection can affect the fuzzy preference relations, and thereby the final ranking of fuzzy numbers. Full article
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Open AccessArticle Asymmetries in the Maintenance Performance of Spanish Industries before and after the Recession
Symmetry 2017, 9(8), 166; https://doi.org/10.3390/sym9080166
Received: 26 June 2017 / Revised: 10 August 2017 / Accepted: 16 August 2017 / Published: 20 August 2017
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Abstract
Abstract: Until the last few decades, maintenance has not been considered of special importance by organisations. Thus, the number of studies that assess maintenance performance in a country is still very small, despite the relevance this area has to the level of national
[...] Read more.
Abstract: Until the last few decades, maintenance has not been considered of special importance by organisations. Thus, the number of studies that assess maintenance performance in a country is still very small, despite the relevance this area has to the level of national competitiveness. This article describes a multicriteria model integrating the fuzzy analytic hierarchy process (FAHP) with multi-attribute utility theory (MAUT) to assess the maintenance performance of large, medium and small enterprises in Spain, before and after the recession, as well as the asymmetries in the state of maintenance between different activity sectors. The weightings are converted to utility functions which allow the final utility of an alternative to be calculated via a Multi-Attribute Utility Function. From the Spanish maintenance data for different industrial sectors in 2005 and 2010, 2400 discrete probability distributions have been produced. Finally, a Monte Carlo simulation is applied for the estimation of the uncertainty. The results show that the economic crisis experienced by Spain since 2008 has negatively affected the level of maintenance applied, rather than it being considered an area that could deliver cost reductions and improvements in productivity and quality to organisations. Full article
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Open AccessArticle Multi-objective Fuzzy Bi-matrix Game Model: A Multicriteria Non-Linear Programming Approach
Symmetry 2017, 9(8), 159; https://doi.org/10.3390/sym9080159
Received: 13 July 2017 / Revised: 8 August 2017 / Accepted: 11 August 2017 / Published: 15 August 2017
Cited by 1 | PDF Full-text (276 KB) | HTML Full-text | XML Full-text
Abstract
A multi-objective bi-matrix game model based on fuzzy goals is established in this paper. It is shown that the equilibrium solution of such a game model problem can be translated into the optimal solution of a multi-objective, non-linear programming problem. Finally, the results
[...] Read more.
A multi-objective bi-matrix game model based on fuzzy goals is established in this paper. It is shown that the equilibrium solution of such a game model problem can be translated into the optimal solution of a multi-objective, non-linear programming problem. Finally, the results of this paper are demonstrated through a numerical example. Full article
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Open AccessArticle Selecting Project Delivery Systems Based on Simplified Neutrosophic Linguistic Preference Relations
Symmetry 2017, 9(8), 151; https://doi.org/10.3390/sym9080151
Received: 14 July 2017 / Revised: 29 July 2017 / Accepted: 3 August 2017 / Published: 9 August 2017
Cited by 14 | PDF Full-text (348 KB) | HTML Full-text | XML Full-text
Abstract
Project delivery system selection is an essential part of project management. In the process of choosing appropriate transaction model, many factors should be under consideration, such as the capability and experience of proprietors, project implementation risk, and so on. How to make their
[...] Read more.
Project delivery system selection is an essential part of project management. In the process of choosing appropriate transaction model, many factors should be under consideration, such as the capability and experience of proprietors, project implementation risk, and so on. How to make their comprehensive evaluations and select the optimal delivery system? This paper proposes a decision-making approach based on an extended linguistic preference structure: simplified neutrosophic linguistic preference relations (SNLPRs). The basic elements in SNLPRs are simplified neutrosophic linguistic numbers (SNLNs). First, several distance measures of SNLNs are introduced. A distance-based consistency index is provided to measure the consistency degree of a simplified neutrosophic linguistic preference relation (SNLPR). When the SNLPR is not acceptably consistent, a consistency-improving automatic iterative algorithm may be used. Afterwards, a decision-making method with SNLPRs is developed. The example of its application in project delivery systems’ selection is offered, and a comparison analysis is given in the end as well. Full article
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Open AccessArticle Group Decision-Making for Hesitant Fuzzy Sets Based on Characteristic Objects Method
Symmetry 2017, 9(8), 136; https://doi.org/10.3390/sym9080136
Received: 28 June 2017 / Revised: 15 July 2017 / Accepted: 25 July 2017 / Published: 29 July 2017
Cited by 20 | PDF Full-text (2576 KB) | HTML Full-text | XML Full-text
Abstract
There are many real-life problems that, because of the need to involve a wide domain of knowledge, are beyond a single expert. This is especially true for complex problems. Therefore, it is usually necessary to allocate more than one expert to a decision
[...] Read more.
There are many real-life problems that, because of the need to involve a wide domain of knowledge, are beyond a single expert. This is especially true for complex problems. Therefore, it is usually necessary to allocate more than one expert to a decision process. In such situations, we can observe an increasing importance of uncertainty. In this paper, the Multi-Criteria Decision-Making (MCDM) method called the Characteristic Objects Method (COMET) is extended to solve problems for Multi-Criteria Group Decision-Making (MCGDM) in a hesitant fuzzy environment. It is a completely new idea for solving problems of group decision-making under uncertainty. In this approach, we use L-R-type Generalized Fuzzy Numbers (GFNs) to get the degree of hesitancy for an alternative under a certain criterion. Therefore, the classical COMET method was adapted to work with GFNs in group decision-making problems. The proposed extension is presented in detail, along with the necessary background information. Finally, an illustrative numerical example is provided to elaborate the proposed method with respect to the support of a decision process. The presented extension of the COMET method, as opposed to others’ group decision-making methods, is completely free of the rank reversal phenomenon, which is identified as one of the most important MCDM challenges. Full article
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Open AccessArticle A Novel Single-Valued Neutrosophic Set Similarity Measure and Its Application in Multicriteria Decision-Making
Symmetry 2017, 9(8), 127; https://doi.org/10.3390/sym9080127
Received: 13 June 2017 / Revised: 9 July 2017 / Accepted: 17 July 2017 / Published: 25 July 2017
Cited by 7 | PDF Full-text (810 KB) | HTML Full-text | XML Full-text
Abstract
The single-valued neutrosophic set is a subclass of neutrosophic set, and has been proposed in recent years. An important application for single-valued neutrosophic sets is to solve multicriteria decision-making problems. The key to using neutrosophic sets in decision-making applications is to make a
[...] Read more.
The single-valued neutrosophic set is a subclass of neutrosophic set, and has been proposed in recent years. An important application for single-valued neutrosophic sets is to solve multicriteria decision-making problems. The key to using neutrosophic sets in decision-making applications is to make a similarity measure between single-valued neutrosophic sets. In this paper, a new method to measure the similarity between single-valued neutrosophic sets using Dempster–Shafer evidence theory is proposed, and it is applied in multicriteria decision-making. Finally, some examples are given to show the reasonable and effective use of the proposed method. Full article
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Open AccessArticle Discrete Optimization with Fuzzy Constraints
Symmetry 2017, 9(6), 87; https://doi.org/10.3390/sym9060087
Received: 8 May 2017 / Revised: 5 June 2017 / Accepted: 13 June 2017 / Published: 16 June 2017
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Abstract
The primary benefit of fuzzy systems theory is to approximate system behavior where analytic functions or numerical relations do not exist. In this paper, heuristic fuzzy rules were used with the intention of improving the performance of optimization models, introducing experiential rules acquired
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The primary benefit of fuzzy systems theory is to approximate system behavior where analytic functions or numerical relations do not exist. In this paper, heuristic fuzzy rules were used with the intention of improving the performance of optimization models, introducing experiential rules acquired from experts and utilizing recommendations. The aim of this paper was to define soft constraints using an adaptive network-based fuzzy inference system (ANFIS). This newly-developed soft constraint was applied to discrete optimization for obtaining optimal solutions. Even though the computational model is based on advanced computational technologies including fuzzy logic, neural networks and discrete optimization, it can be used to solve real-world problems of great interest for design engineers. The proposed computational model was used to find the minimum weight solutions for simply-supported laterally-restrained beams. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making) Printed Edition available
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Open AccessArticle Some Single-Valued Neutrosophic Dombi Weighted Aggregation Operators for Multiple Attribute Decision-Making
Symmetry 2017, 9(6), 82; https://doi.org/10.3390/sym9060082
Received: 2 May 2017 / Revised: 30 May 2017 / Accepted: 30 May 2017 / Published: 2 June 2017
Cited by 16 | PDF Full-text (395 KB) | HTML Full-text | XML Full-text
Abstract
The Dombi operations of T-norm and T-conorm introduced by Dombi can have the advantage of good flexibility with the operational parameter. In existing studies, however, the Dombi operations have so far not yet been used for neutrosophic sets. To propose new aggregation operators
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The Dombi operations of T-norm and T-conorm introduced by Dombi can have the advantage of good flexibility with the operational parameter. In existing studies, however, the Dombi operations have so far not yet been used for neutrosophic sets. To propose new aggregation operators for neutrosophic sets by the extension of the Dombi operations, this paper firstly presents the Dombi operations of single-valued neutrosophic numbers (SVNNs) based on the operations of the Dombi T-norm and T-conorm, and then proposes the single-valued neutrosophic Dombi weighted arithmetic average (SVNDWAA) operator and the single-valued neutrosophic Dombi weighted geometric average (SVNDWGA) operator to deal with the aggregation of SVNNs and investigates their properties. Because the SVNDWAA and SVNDWGA operators have the advantage of good flexibility with the operational parameter, we develop a multiple attribute decision-making (MADM) method based on the SVNWAA or SVNWGA operator under a SVNN environment. Finally, an illustrative example about the selection problem of investment alternatives is given to demonstrate the application and feasibility of the developed approach. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making) Printed Edition available
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Open AccessArticle Multiple Attribute Decision-Making Method Using Correlation Coefficients of Normal Neutrosophic Sets
Symmetry 2017, 9(6), 80; https://doi.org/10.3390/sym9060080
Received: 29 April 2017 / Revised: 20 May 2017 / Accepted: 25 May 2017 / Published: 26 May 2017
Cited by 12 | PDF Full-text (260 KB) | HTML Full-text | XML Full-text
Abstract
The normal distribution is a usual one of various distributions in the real world. A normal neutrosophic set (NNS) is composed of both a normal fuzzy number and a neutrosophic number, which a significant tool for describing the incompleteness, indeterminacy, and inconsistency of
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The normal distribution is a usual one of various distributions in the real world. A normal neutrosophic set (NNS) is composed of both a normal fuzzy number and a neutrosophic number, which a significant tool for describing the incompleteness, indeterminacy, and inconsistency of the decision-making information. In this paper, we propose two correlation coefficients between NNSs based on the score functions of normal neutrosophic numbers (NNNs) (basic elements in NNSs) and investigate their properties. Then, we develop a multiple attribute decision-making (MADM) method with NNSs under normal neutrosophic environments, where, by correlation coefficient values between each alternative (each evaluated NNS) and the ideal alternative (the ideal NNS), the ranking order of alternatives and the best one are given in the normal neutrosophic decision-making process. Finally, an illustrative example about the selection problem of investment alternatives is provided to demonstrate the application and feasibility of the developed decision-making method. Compared to the existing MADM approaches based on aggregation operators of NNNs, the proposed MADM method based on the correlation coefficients of NNSs shows the advantage of its simple decision-making process. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making) Printed Edition available
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