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Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking and...
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Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking and Their Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (30 October 2024) | Viewed by 11164

Special Issue Editors

Prof. Dr. Ta-Chung Chu

E-Mail Website
Guest Editor
Department of Industrial Management and Information, Southern Taiwan University of Science and Technology, Tainan City 710301, Taiwan
Interests: fuzzy MCDM; fuzzy number ranking and their applications
Prof. Dr. Wei-Chang Yeh

E-Mail Website
Guest Editor
Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu, Taiwan
Interests: network reliability; scheduling problem; cloud computing management; SSO and soft computing; data mining
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fuzzy multiple criteria decision making (MCDM) and multiple attribute decision making (MADM), which are usually used interchangeably in the literature, are useful tools for modelling and resolving complex decision-making problems with imprecise and ambiguous data in an uncertain environment. In the past decade, numerous fuzzy MCDM techniques and their hybrid methods, among them AHP/fuzzy AHP, ANP/fuzzy ANP, ELECTRE/fuzzy ELECTRE, PROMETHEE/fuzzy PROMETHEE, MODM/fuzzy MODM, optimization methods/fuzzy optimization methods, TOPSIS/fuzzy TOPSIS, DEMATEL/fuzzy DEMATEL, VIKOR/fuzzy VIKOR, etc., have been extensively investigated. In most fuzzy MCDM techniques and their hybrid methods, ratings of alternatives versus criteria and criteria weights are usually assessed in linguistic terms represented by fuzzy numbers such as type-1, type-2, intuitionistic, bipolar, hesitant, Pythagorean, etc. Therefore, methods for the computing of words, aggregating of fuzzy numbers, and ranking of fuzzy numbers are needed to complete the fuzzy MCDM and hybrid models to resolve the problems. The guest editor would like to provide a platform to present the latest advances in the aspects of fuzzy MCDM techniques, hybrid methods, computing of words, aggregating of fuzzy numbers, fuzzy number ranking, and their various applications. This Special Issue is devoted to state-of-the-art research on the above topics. The goal is to help to foster the development and practice of fuzzy MCDM techniques to resolve management, business, engineering, or societal problems in an uncertain environment. Any theoretical, empirical, and experimental works related to the above (or other relevant) topics associated with solution methods and/or applications are welcome.

We hope that this initiative will be attractive to researchers specialized in the above-mentioned topics. Contributions may be submitted on a continuous basis before the deadline. After a peer-review process, submissions will be selected for publication based on their quality and relevance.

Prof. Dr. Ta-Chung Chu
Prof. Dr. Wei-Chang Yeh
Guest Editors

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 submissions that pass pre-check are 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. Axioms 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 2400 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 MCDM
  • hybrid methods
  • fuzzy modeling
  • fuzzy numbers
  • ranking
  • computing with words

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Published Papers (10 papers)

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Research

11 pages, 305 KiB  
Article
A Framework for I*-Statistical Convergence of Fuzzy Numbers
by Tanushri, Ayaz Ahmad and Ayhan Esi
Axioms 2024, 13(9), 639; https://doi.org/10.3390/axioms13090639 - 18 Sep 2024
Viewed by 442
Abstract
In this study, we investigate the concept of I*-statistical convergence for sequences of fuzzy numbers. We establish several theorems that provide a comprehensive understanding of this notion, including the uniqueness of limits, the relationship between I*-statistical convergence and classical [...] Read more.
In this study, we investigate the concept of I*-statistical convergence for sequences of fuzzy numbers. We establish several theorems that provide a comprehensive understanding of this notion, including the uniqueness of limits, the relationship between I*-statistical convergence and classical convergence, and the algebraic properties of I*-statistically convergent sequences. We also introduce the concept of I*-statistical pre-Cauchy and I*-statistical Cauchy sequences and explore its connection to I*-statistical convergence. Our results show that every I*-statistically convergent sequence is I*-statistically pre-Cauchy, but the converse is not necessarily true. Furthermore, we provide a sufficient condition for an I*-statistically pre-Cauchy sequence to be I*-statistically convergent, which involves the concept of I*−liminf. Full article
(This article belongs to the Special Issue Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking and Their Applications)
14 pages, 293 KiB  
Article
Extensions of Orders to a Power Set vs. Scores of Hesitant Fuzzy Elements: Points in Common of Two Parallel Theories
by Esteban Induráin, Ana Munárriz and M. Sergio Sara
Axioms 2024, 13(8), 549; https://doi.org/10.3390/axioms13080549 - 13 Aug 2024
Viewed by 759
Abstract
We deal with two apparently disparate theories. One of them studies extensions of orderings from a set to its power set. The other one defines suitable scores on hesitant fuzzy elements. We show that both theories have the same mathematical substrate. Thus, important [...] Read more.
We deal with two apparently disparate theories. One of them studies extensions of orderings from a set to its power set. The other one defines suitable scores on hesitant fuzzy elements. We show that both theories have the same mathematical substrate. Thus, important possibility/impossibility results concerning criteria for extensions can be transferred to new results on scores. And conversely, conditions imposed a priori on scores can give rise to new extension criteria. This enhances and enriches both theories. We show examples of translations of classical results on extensions in the context of scores. Also, we state new results concerning the impossibility of finding a utility function representing some kind of extension order if some restrictions are imposed on the utility function considered as a score. Full article
(This article belongs to the Special Issue Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking and Their Applications)
25 pages, 2134 KiB  
Article
Modelling Up-and-Down Moves of Binomial Option Pricing with Intuitionistic Fuzzy Numbers
by Jorge de Andrés-Sánchez
Axioms 2024, 13(8), 503; https://doi.org/10.3390/axioms13080503 - 26 Jul 2024
Viewed by 508
Abstract
Since the early 21st century, within fuzzy mathematics, there has been a stream of research in the field of option pricing that introduces vagueness in the parameters governing the movement of the underlying asset price through fuzzy numbers (FNs). This approach is commonly [...] Read more.
Since the early 21st century, within fuzzy mathematics, there has been a stream of research in the field of option pricing that introduces vagueness in the parameters governing the movement of the underlying asset price through fuzzy numbers (FNs). This approach is commonly known as fuzzy random option pricing (FROP). In discrete time, most contributions use the binomial groundwork with up-and-down moves proposed by Cox, Ross, and Rubinstein (CRR), which introduces epistemic uncertainty associated with volatility through FNs. Thus, the present work falls within this stream of literature and contributes to the literature in three ways. First, analytical developments allow for the introduction of uncertainty with intuitionistic fuzzy numbers (IFNs), which are a generalization of FNs. Therefore, we can introduce bipolar uncertainty in parameter modelling. Second, a methodology is proposed that allows for adjusting the volatility with which the option is valued through an IFN. This approach is based on the existing developments in the literature on adjusting statistical parameters with possibility distributions via historical data. Third, we introduce into the debate on fuzzy random binomial option pricing the analytical framework that should be used in modelling upwards and downwards moves. In this sense, binomial modelling is usually employed to value path-dependent options that cannot be directly evaluated with the Black–Scholes–Merton (BSM) model. Thus, one way to assess the suitability of binomial moves for valuing a particular option is to approximate the results of the BSM in a European option with the same characteristics as the option of interest. In this study, we compared the moves proposed by Renddleman and Bartter (RB) with CRR. We have observed that, depending on the moneyness degree of the option and, without a doubt, on options traded at the money, RB modelling offers greater convergence to BSM prices than does CRR modelling. Full article
(This article belongs to the Special Issue Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking and Their Applications)
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12 pages, 597 KiB  
Article
Fuzzy Testing Model Built on Confidence Interval of Process Capability Index CPMK
by Wei Lo, Tsun-Hung Huang, Kuen-Suan Chen, Chun-Min Yu and Chun-Ming Yang
Axioms 2024, 13(6), 379; https://doi.org/10.3390/axioms13060379 - 4 Jun 2024
Viewed by 532
Abstract
A variety of process capability indices are applied to the quantitative measurement of the potential and performance of processes in manufacturing. As it is easy to understand the formulae of these indices, this method is easy to apply. Furthermore, a process capability index [...] Read more.
A variety of process capability indices are applied to the quantitative measurement of the potential and performance of processes in manufacturing. As it is easy to understand the formulae of these indices, this method is easy to apply. Furthermore, a process capability index is frequently utilized by a manufacturer to gauge the quality of a process. This index can be utilized by not only an internal process engineer to assess the quality of the process but also as a communication tool for an external sales department. When the manufacturing process deviates from the target value T, the process capability index CPMK can be quickly detected, which is conducive to the promotion of smart manufacturing. Therefore, this study applied the index CPMK as an evaluation tool for process quality. As noted by some studies, process capability indices have unknown parameters and therefore must be estimated from sample data. Additionally, numerous studies have addressed that it is essential for companies to establish a rapid response mechanism, as they wish to make decisions quickly when using a small sample size. Considering the small sample size, this study proposed a 100 (1 − α)% confidence interval for the process capability index CPMK based on suggestions from previous studies. Subsequently, this study built a fuzzy testing model on the 100 (1 − α)% confidence interval for the process capability index CPMK. This fuzzy testing model can help enterprises make decisions rapidly with a small sample size, meeting their expectation of having a rapid response mechanism. Full article
(This article belongs to the Special Issue Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking and Their Applications)
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13 pages, 793 KiB  
Article
Fuzzy Decision-Making and Resource Management Model of Performance Evaluation Indices
by Kuen-Suan Chen, Tsung-Hua Hsieh, Chia-Pao Chang, Kai-Chao Yao and Tsun-Hung Huang
Axioms 2024, 13(3), 198; https://doi.org/10.3390/axioms13030198 - 15 Mar 2024
Viewed by 1152
Abstract
The Performance Evaluation Matrix (PEM) is an excellent decision-making tool for assessment and resource management. Satisfaction Index and Importance Index are two important evaluation indicators of construction and PEM. Managers can decide whether the service item needs to be improved based on the [...] Read more.
The Performance Evaluation Matrix (PEM) is an excellent decision-making tool for assessment and resource management. Satisfaction Index and Importance Index are two important evaluation indicators of construction and PEM. Managers can decide whether the service item needs to be improved based on the Satisfaction Index of the service item. When resources are limited, managers can determine the priority of improving the service item based on the Importance Index. In order to avoid the risk of misjudgment caused by sample errors and meet the needs of enterprises’ rapid decision-making, this study proposed a fuzzy test built on the confidence intervals of the above two key indicators to decide whether essential service items should be improved and determine the priority of improvement. Since the fuzzy test was relatively complex, this study further came up with fuzzy evaluation values and fuzzy evaluation critical values of service items following fuzzy testing rules. Besides, evaluation rules were established to facilitate industrial applications. This approach can be completed with any common word processing software, so it is relatively convenient in application and easy to manage. Finally, an application example was presented in this paper to explain the applicability of the proposed approach. Full article
(This article belongs to the Special Issue Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking and Their Applications)
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23 pages, 1449 KiB  
Article
An Emotionally Intuitive Fuzzy TODIM Methodology for Decision Making Based on Online Reviews: Insights from Movie Rankings
by Qi Wang, Xuzhu Zheng and Si Fu
Axioms 2023, 12(10), 972; https://doi.org/10.3390/axioms12100972 - 16 Oct 2023
Cited by 1 | Viewed by 1255
Abstract
With the burgeoning growth of the internet, online evaluation systems have become increasingly pivotal in shaping consumer decision making. In this context, this study introduces an intuitionistic fuzzy TODIM (an acronym in Portuguese for interactive and multicriteria decision making) methodology to rank products [...] Read more.
With the burgeoning growth of the internet, online evaluation systems have become increasingly pivotal in shaping consumer decision making. In this context, this study introduces an intuitionistic fuzzy TODIM (an acronym in Portuguese for interactive and multicriteria decision making) methodology to rank products based on online reviews. Our approach aims to enhance user decision making efficiency and address the prevalent issue of information overload. Initially, we devised a product attribute emotion quantification framework within the confines of the intuitionistic fuzzy paradigm. This allows for the transformation of online reviews into exact functional outputs via our advanced intuitionistic fuzzy scoring mechanism and its associated precise function. Following this, we take into account the inherent correlation among product attributes, leading to the development of an attribute-associated intuitionistic fuzzy model. This model further ascertains the dominance degree of alternative products. Moreover, by integrating the risk aversion factor, we can derive a hierarchical structure for alternative products, aiding in the prioritization process. Finally, this paper validates the proposed method using movie sequencing as a case study. The results show that the proposed method, which takes into account the emotional tendencies of different attributes in a movie and the different preferences of viewers in the attribute weighting and movie selection process, is more reasonable than methods proposed in previous studies. Full article
(This article belongs to the Special Issue Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking and Their Applications)
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21 pages, 760 KiB  
Article
Decision Rules for Renewable Energy Utilization Using Rough Set Theory
by Chuying Huang, Chun-Che Huang, Din-Nan Chen and Yuju Wang
Axioms 2023, 12(9), 811; https://doi.org/10.3390/axioms12090811 - 23 Aug 2023
Cited by 1 | Viewed by 1220
Abstract
Rough Set (RS) theory is used for data analysis and decision making where decision-making rules can be derived through attribute reduction and feature selection. Energy shortage is an issue for governments, and solar energy systems have become an important source of renewable energy. [...] Read more.
Rough Set (RS) theory is used for data analysis and decision making where decision-making rules can be derived through attribute reduction and feature selection. Energy shortage is an issue for governments, and solar energy systems have become an important source of renewable energy. Rough sets may be used to summarize and compare rule sets for different periods. In this study, the analysis of rules is an element of decision support that allows organizations to make better informed decisions. However, changes to decision rules require adjustment and analysis, and analysis is inhibited by changes in rules. With this consideration, a solution approach is proposed. The results show that not only can decision costs be reduced, but policymakers can also make it easier for the public to understand the incentives of green energy programs and the use of solar panels. The application process is simplified for the implementation of sustainable energy policies. Full article
(This article belongs to the Special Issue Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking and Their Applications)
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23 pages, 343 KiB  
Article
Sugeno Integral Based on Overlap Function and Its Application to Fuzzy Quantifiers and Multi-Attribute Decision-Making
by Xiaoyan Mao, Chaolu Temuer and Huijie Zhou
Axioms 2023, 12(8), 734; https://doi.org/10.3390/axioms12080734 - 27 Jul 2023
Viewed by 994
Abstract
The overlap function is an important class of aggregation function that is closely related to the continuous triangular norm. It has important applications in information fusion, image processing, information classification, intelligent decision-making, etc. The usual multi-attribute decision-making (MADM) is to select the decision [...] Read more.
The overlap function is an important class of aggregation function that is closely related to the continuous triangular norm. It has important applications in information fusion, image processing, information classification, intelligent decision-making, etc. The usual multi-attribute decision-making (MADM) is to select the decision object that performs well on all attributes (indicators), which is quite demanding. The MADM based on fuzzy quantifiers is to select the decision object that performs well on a certain proportion or quantification (such as most, many, more than half, etc.) of attributes. Therefore, it is necessary to study how to express and calculate fuzzy quantifiers such as most, many, etc. In this paper, the Sugeno integral based on the overlap function (called the O-Sugeno integral) is used as a new information fusion tool, and some related properties are studied. Then, the truth value of a linguistic quantified proposition can be estimated by using the O-Sugeno integral, and the O-Sugeno integral semantics of fuzzy quantifiers is proposed. Finally, the MADM method based on the O-Sugeno integral semantics of fuzzy quantifiers is proposed and the feasibility of our method is verified by several illustrative examples such as the logistics park location problem. Full article
(This article belongs to the Special Issue Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking and Their Applications)
34 pages, 1767 KiB  
Article
Ranking Startups Using DEMATEL-ANP-Based Fuzzy PROMETHEE II
by Huyen Trang Nguyen and Ta-Chung Chu
Axioms 2023, 12(6), 528; https://doi.org/10.3390/axioms12060528 - 28 May 2023
Cited by 3 | Viewed by 1359
Abstract
In entrepreneurship management, the evaluation and selection of startups for acceleration programs, especially technology-based startups, are crucial. This process involves considering numerical and qualitative criteria such as sales, prior startup experience, demand validation, and product maturity. To effectively rank startups based on the [...] Read more.
In entrepreneurship management, the evaluation and selection of startups for acceleration programs, especially technology-based startups, are crucial. This process involves considering numerical and qualitative criteria such as sales, prior startup experience, demand validation, and product maturity. To effectively rank startups based on the varying importance of these criteria, a fuzzy multi-criteria decision-making (MCDM) approach is needed. Although MCDM methods have been successful in handling complex problems, their application in startup selection and evaluating criteria interrelationships from the accelerator perspective is underexplored. To address this gap, a hybrid DEMATEL-ANP-based fuzzy PROMETHEE II model is proposed in this study, facilitating startup ranking and examining interrelationships among factors. The resulting preference values are fuzzy numbers, necessitating a fuzzy ranking method for decision-making. An extension of ranking fuzzy numbers using a spread area-based relative maximizing and minimizing set is suggested to enhance the flexibility of existing ranking MCDM methods. Algorithms, formulas, and a comparative analysis validate the proposed method, while a numerical experiment verifies the viability of the hybrid model. The final ranking of four startup projects is A4<A1<A3<A2 which indicates that startup project A2 has the highest comprehensive potential, followed by startup project A3. Full article
(This article belongs to the Special Issue Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking and Their Applications)
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17 pages, 3610 KiB  
Article
A New Perspective for Multivariate Time Series Decision Making through a Nested Computational Approach Using Type-2 Fuzzy Integration
by Martha Ramirez and Patricia Melin
Axioms 2023, 12(4), 385; https://doi.org/10.3390/axioms12040385 - 17 Apr 2023
Cited by 3 | Viewed by 1544
Abstract
The integration of key indicators from the results of the analysis of time series represents a constant challenge within organizations; this could be mainly due to the need to establish the belonging of each indicator within a process, geographic region or category. This [...] Read more.
The integration of key indicators from the results of the analysis of time series represents a constant challenge within organizations; this could be mainly due to the need to establish the belonging of each indicator within a process, geographic region or category. This paper thus illustrates how both primary and secondary indicators are relevant for decision making, and why they need to be integrated by making new final fuzzy indicators. Thus, our proposal consists of a type-2 fuzzy integration of multivariate time series, such as OECD country risk classification, inflation, population and gross national income (GNI) by using multiple type-1 fuzzy inference systems to perform time series classification tasks. Our contribution consists of the proposal to integrate multiple nested type-1 fuzzy inference systems using a type-2 fuzzy integration. Simulation results show the advantages of using the proposed method for the fuzzy classification of multiple time series. This is done in order so the user can have tools that allow them to understand the environment and generate comparative analyses of multiple information sources, and finally use it during the process prior to decision making considering the main advantage of modeling the inherent uncertainty. Full article
(This article belongs to the Special Issue Advances in Fuzzy MCDM, Hybrid Methods, Fuzzy Number Ranking and Their Applications)
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