Fuzzy Set Theory and Its Applications in Decision Making

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

Deadline for manuscript submissions: closed (31 March 2023) | Viewed by 19825

Special Issue Editor


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Guest Editor
School of Engineering, Catholic University of the North, Larrondo 1281, Coquimbo, Chile
Interests: multiple-criteria decision making (MCDM); fuzzy set theory; sustainability; supply chain management; strategic management
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Special Issue Information

Dear Colleagues,

Uncertainties are an inevitable part of decision making in today’s fast-growing world. These uncertainties can show themselves in the determination of criteria or related actions. Therefore, approaches that can help decision makers solve problems in the ambiguous environment are of great interest. Fuzzy set theory has become one of the reliable methods in this field due to its continuous development and flexibility in challenging uncertainty issues. It is widely used in solving various MCDM problems such as environmental sustainability, healthcare waste management, service quality, supply chains, etc. Many decision-making methods based on this theory have been developed or are being developed. In addition, the fuzzy theory has even been used in operations research, giving rise to fuzzy programming, and it has been integrated with OR techniques such as goal programming.

Furthermore, fuzzy-based decision support systems have been developed in various fields; for example, the evaluation of suppliers in the supply chain, disease diagnosis, appropriate treatment determination, etc. Despite the mentioned cases, there is still a vast space for implementing fuzzy set theory in developing MCDM methods and solving decision-making problems. Thus, this Special Issue aims to contribute to developing and implementing fuzzy set theory in multi-criteria decision making to solve problems under uncertain conditions. We also welcome the submission of articles that utilize this theory in the optimization field, such as fuzzy programming, integration of fuzzy theory and goal programming, etc.

Dr. Sarfaraz Hashemkhani Zolfani
Guest Editor

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Keywords

  • fuzzy Set Theory
  • decision Theory
  • Multiple Criteria Decision Making (MCDM)
  • uncertainty
  • soft computing
  • intelligent decision support systems
  • optimization
  • group decision making

Published Papers (10 papers)

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Research

25 pages, 3239 KiB  
Article
Fuzzy Logic and Decision Making Applied to Customer Service Optimization
by Gabriel Marín Díaz and Ramón Alberto Carrasco González
Axioms 2023, 12(5), 448; https://doi.org/10.3390/axioms12050448 - 30 Apr 2023
Cited by 5 | Viewed by 1828
Abstract
In the literature, the Information Technology Infrastructure Library (ITIL) methodology recommends determining the priority of incident resolution based on the impact and urgency of interactions. The RFID model, based on the parameters of Recency, Frequency, Importance and Duration in the resolution of incidents, [...] Read more.
In the literature, the Information Technology Infrastructure Library (ITIL) methodology recommends determining the priority of incident resolution based on the impact and urgency of interactions. The RFID model, based on the parameters of Recency, Frequency, Importance and Duration in the resolution of incidents, provides an individual assessment and a clustering of customers based on these factors. We can improve the traditional concept of waiting queues for customer service management by using a procedure that adds to the evaluation provided by RFID such additional factors as Impact, Urgency and Emotional character of each interaction. If we also include aspects such as Waiting Time and Contact Center Workload, we have a procedure that allows prioritizing interactions between the customer and the Contact Center dynamically and in real time. In this paper we propose to apply a model of unification of heterogeneous information in 2-tuple linguistic evaluations, to obtain a global evaluation of each interaction by applying the Analytic Hierarchy Process (AHP), and in this way be able to have a dynamic process of prioritization of interactions. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Its Applications in Decision Making)
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13 pages, 552 KiB  
Article
Linguistic Complex Fuzzy Sets
by Songsong Dai
Axioms 2023, 12(4), 328; https://doi.org/10.3390/axioms12040328 - 28 Mar 2023
Cited by 3 | Viewed by 918
Abstract
Complex fuzzy sets (CFSs) are a suitable tool to manage spatial directional information which includes distance and direction. However, spatial directional information is given by linguistic values. It is very awkward for the CFS to describe this type of spatial directional information. To [...] Read more.
Complex fuzzy sets (CFSs) are a suitable tool to manage spatial directional information which includes distance and direction. However, spatial directional information is given by linguistic values. It is very awkward for the CFS to describe this type of spatial directional information. To overcome this limitation, we first propose a novel concept called a linguistic complex fuzzy set (LCFS) to serve as an extension of the CFS. Then we put forward some basic operational laws for LCFSs. After that, we define three operators for LCFSs: the linguistic complex fuzzy weighted averaging (LCFWA) operator, the linguistic amplitude max (Amax) operator and the linguistic amplitude min (Amin) operator. In actual application, we use the LCFWA operator to deal with group decision making when the importance weights of experts are known. For the situation in which the weights of experts are unknown, we develop an Amax-Amin method for group decision making. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Its Applications in Decision Making)
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23 pages, 1277 KiB  
Article
Aczel–Alsina Hamy Mean Aggregation Operators in T-Spherical Fuzzy Multi-Criteria Decision-Making
by Haolun Wang, Tingjun Xu, Liangqing Feng, Tahir Mahmood and Kifayat Ullah
Axioms 2023, 12(2), 224; https://doi.org/10.3390/axioms12020224 - 20 Feb 2023
Cited by 4 | Viewed by 1634
Abstract
A T-spherical fuzzy set is a more powerful mathematical tool to handle uncertain and vague information than several fuzzy sets, such as fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, q-rung orthopair fuzzy set, and picture fuzzy set. The Aczel–Alsina t-norm and [...] Read more.
A T-spherical fuzzy set is a more powerful mathematical tool to handle uncertain and vague information than several fuzzy sets, such as fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, q-rung orthopair fuzzy set, and picture fuzzy set. The Aczel–Alsina t-norm and s-norm are significant mathematical operations with a high premium on affectability with parameter activity, which are extremely conducive to handling imprecise and undetermined data. On the other hand, the Hamy mean operator is able to catch the interconnection among multiple input data and achieve great results in the fusion process of evaluation information. Based on the above advantages, the purpose of this study is to propose some novel aggregation operators (AOs) integrated by the Hamy mean and Aczel–Alsina operations to settle T-spherical fuzzy multi-criteria decision-making (MCDM) issues. First, a series of T-spherical fuzzy Aczel–Alsina Hamy mean AOs are advanced, including the T-spherical fuzzy Aczel–Alsina Hamy mean (TSFAAHM) operator, T-spherical fuzzy Aczel–Alsina dual Hamy mean (TSFAADHM) operator, and their weighted forms, i.e., the T-spherical fuzzy Aczel–Alsina-weighted Hamy mean (TSFAAWHM) and T-spherical fuzzy Aczel–Alsina-weighted dual Hamy mean (TSFAAWDHM) operators. Moreover, some related properties are discussed. Then, a MCDM model based on the proposed AOs is built. Lastly, a numerical example is provided to show the applicability and feasibility of the developed AOs, and the effectiveness of this study is verified by the implementation of a parameters influence test and comparison with available methods. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Its Applications in Decision Making)
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20 pages, 1418 KiB  
Article
An Integrated Intuitionistic Fuzzy Closeness Coefficient-Based OCRA Method for Sustainable Urban Transportation Options Selection
by Arunodaya Raj Mishra, Pratibha Rani, Fausto Cavallaro, Ibrahim M. Hezam and Jyoti Lakshmi
Axioms 2023, 12(2), 144; https://doi.org/10.3390/axioms12020144 - 30 Jan 2023
Cited by 13 | Viewed by 1403
Abstract
Transportation systems play a key role in urban development by providing access for people to markets and education, employment, health care, recreation, and other key services. However, uncontrolled urban population and fast growth of vehicle mobility inevitably lead to unsustainable urban transportation systems [...] Read more.
Transportation systems play a key role in urban development by providing access for people to markets and education, employment, health care, recreation, and other key services. However, uncontrolled urban population and fast growth of vehicle mobility inevitably lead to unsustainable urban transportation systems in terms of economic, technical, social, and geographical aspects of sustainability. Thus, there is a need to select suitable sustainable urban transportation (SUT) alternatives, which can contributed to the technological advancement of a city and changes in societal necessities, mitigating the climate change impact from transport and transforming living habits, in the context of high urban population growth. Therefore, this paper aims to introduce an integrated multi-attribute decision analysis (MADA) framework for assessing and ranking the sustainable urban transportation (SUT) options under an intuitionistic fuzzy sets (IFSs) context. In this regard, firstly IF-distance measures and their properties are developed to obtain the criteria weight. Second, an IF-relative closeness coefficient-based model is presented to find the criteria weights. Third, the operational competitiveness rating (OCRA) model is introduced with the IF-score function-RS-based decision experts’ weighing model and the relative closeness coefficient-based criteria weight determination model under the IFSs environment. To exemplify the utility and effectiveness of the developed IF-relative closeness coefficient-based OCRA methodology, a case study ranking the different SUT bus options is presented from an intuitionistic fuzzy perspective. A comparison with different models is made to prove the superiority and solidity of the obtained outcome. Moreover, the comparative analysis outperforms the other extant MADA models, as it can provide more sound outcomes than others, and thus it is more suitable and efficient to elucidate uncertain information in handling practical MADA problems. In this study, we analyze and determine the most suitable and sustainable SUT by considering the economic, technical, environmental, and social dimensions of sustainability and also make a significant contribution to the current scientific knowledge by providing a novel decision support system from an uncertainty perspective. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Its Applications in Decision Making)
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19 pages, 368 KiB  
Article
TOPSIS Method Based on Hamacher Choquet-Integral Aggregation Operators for Atanassov-Intuitionistic Fuzzy Sets and Their Applications in Decision-Making
by Tahir Mahmood, Zeeshan Ali, Samruam Baupradist and Ronnason Chinram
Axioms 2022, 11(12), 715; https://doi.org/10.3390/axioms11120715 - 10 Dec 2022
Cited by 8 | Viewed by 1232
Abstract
The collection of Hamacher t-norms was created by Hamacher in 1970, which played a critical and significant role in computing aggregation operators. All aggregation operators that are derived based on Hamacher norms are very powerful and are beneficial because of the parameter [...] Read more.
The collection of Hamacher t-norms was created by Hamacher in 1970, which played a critical and significant role in computing aggregation operators. All aggregation operators that are derived based on Hamacher norms are very powerful and are beneficial because of the parameter 0ζ+. Choquet first posited the theory of the Choquet integral (CI) in 1953, which is used for evaluating awkward and unreliable information to address real-life problems. In this manuscript, we analyze several aggregation operators based on CI, aggregation operators, the Hamacher t-norm and t-conorm, and Atanassov intuitionistic fuzzy (A-IF) information. These are called A-IF Hamacher CI averaging (A-IFHCIA), A-IF Hamacher CI ordered averaging (A-IFHCIOA), A-IF Hamacher CI geometric (A-IFHCIG), and A-IF Hamacher CI ordered geometric (A-IFHCIOG) operators; herein, we identify their most beneficial and valuable results according to their main properties. Working continuously, we developed a multi-attribute decision-making (MADM) procedure for evaluating awkward and unreliable information, with the help of the TOPSIS technique for order performance by similarity to the ideal solution, and derive operators to enhance the worth and value of the present information. Finally, by comparing the pioneering information with some of the existing operators, we illustrate some examples for evaluating the real-life problems related to enterprises, wherein the owner of a company appointed four senior board members of the enterprise to decide what was the best Asian company in which to invest money, to show the supremacy and superiority of the invented approaches. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Its Applications in Decision Making)
25 pages, 728 KiB  
Article
Assessing Green Approaches and Digital Marketing Strategies for Twin Transition via Fermatean Fuzzy SWARA-COPRAS
by Selçuk Korucuk, Ahmet Aytekin, Fatih Ecer, Çağlar Karamaşa and Edmundas Kazimieras Zavadskas
Axioms 2022, 11(12), 709; https://doi.org/10.3390/axioms11120709 - 08 Dec 2022
Cited by 15 | Viewed by 2568
Abstract
Integrating green approaches and digital marketing strategies for Information and Communication Technologies (ICTs), which reduce environmental risks to desired levels by eliminating emissions and pollution, is considered one of the most promising solutions for logistics companies. The study strives to bring a practical [...] Read more.
Integrating green approaches and digital marketing strategies for Information and Communication Technologies (ICTs), which reduce environmental risks to desired levels by eliminating emissions and pollution, is considered one of the most promising solutions for logistics companies. The study strives to bring a practical and applicable solution to the decision problem involving the selection of indicators for green approaches and digital marketing strategies for ICTs in the logistics sector. An integrated Fermatean Fuzzy Step-wise Weight Assessment Ratio Analysis (FF–SWARA) and Fermatean Fuzzy Complex Proportional Assessment (FF–COPRAS) methodology is applied to evaluate green approaches and digital marketing strategies. Concerning the findings, the foremost criterion is “data management,” whereas the best strategy is “programmatic advertising.” To the best of the authors’ knowledge, there is no other study that both offers a strategy selection for the logistics industry and considers environmental protection, sustainability, digital transformation, energy costs, and social and economic factors. The study is a part of ongoing research on productivity, sustainability, the environment, digitization, recycling and estimating levels of waste reduction, as well as business practices, competitiveness and ensuring employee satisfaction and resource efficiency. Also, it investigates the similarities and dissimilarities in the green approach practices of business in logistics and determines the extent to which these practices could be reflected. It is expected to ensure a roadmap for green approach practices and to support sustainable and ecological awareness efforts for ICTs in the logistics sector. Logistics companies can select an integrated digital strategy based on green informatics that suits them using the decision model employed in this study, which can handle uncertainties effectively. In this regard, the study’s findings, which focus on reaching customers and the most precise target audience in digital applications for businesses, are critical for developing strategy, plan and process. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Its Applications in Decision Making)
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29 pages, 462 KiB  
Article
Trapezoidal Intuitionistic Fuzzy Power Heronian Aggregation Operator and Its Applications to Multiple-Attribute Group Decision-Making
by Jeevaraj Selvaraj, Prakash Gatiyala and Sarfaraz Hashemkhani Zolfani
Axioms 2022, 11(11), 588; https://doi.org/10.3390/axioms11110588 - 25 Oct 2022
Cited by 5 | Viewed by 1443
Abstract
Decision-making problems involve imprecise and incomplete information that can be modelled well using intuitionistic fuzzy numbers (IFNs). Various IFNs are available in the literature for modelling such problems. However, trapezoidal intuitionistic fuzzy numbers (TrIFNs) are widely used. It is mainly because of the [...] Read more.
Decision-making problems involve imprecise and incomplete information that can be modelled well using intuitionistic fuzzy numbers (IFNs). Various IFNs are available in the literature for modelling such problems. However, trapezoidal intuitionistic fuzzy numbers (TrIFNs) are widely used. It is mainly because of the flexibility in capturing the incompleteness that occurs in the data. Aggregation operators play a vital role in real-life decision-making problems (modelled under an intuitionistic fuzzy environment). Different aggregation operators are available in the literature for better decision-making. Various aggregation operators are introduced in the literature as a generalization to the conventional aggregation functions defined on the set of real numbers. Each aggregation operator has a specific purpose in solving the problems effectively. In recent years, the power average (PA) operator has been used to reduce the effect of biased data provided by decision-makers. Similarly, the Heronian mean (HM) operator has a property that considers the inter-relationship among various criteria available in the decision-making problem. In this paper, we have considered both the operators (HM, PA) to introduce a new aggregation operator (on the set of TrIFNs), which takes advantage of both properties of these operators. In this study, firstly, we propose the idea of a trapezoidal intuitionistic fuzzy power Heronian aggregation (TrIFPHA) operator and a trapezoidal intuitionistic fuzzy power weighted Heronian aggregation (TrIFPWHA) operator by combining the idea of the Heronian mean operator and power average operator in real numbers. Secondly, we study different mathematical properties of the proposed aggregation operators by establishing a few essential theorems. Thirdly, we discuss a group decision-making algorithm for solving problems modelled under a trapezoidal intuitionistic fuzzy environment. Finally, we show the applicability of the group decision-making algorithm by solving a numerical case problem, and we compare the proposed method’s results with existing methods. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Its Applications in Decision Making)
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17 pages, 908 KiB  
Article
An Interactive Consensus Model in Group Decision Making with Heterogeneous Hesitant Preference Relations
by Yongming Song
Axioms 2022, 11(10), 517; https://doi.org/10.3390/axioms11100517 - 29 Sep 2022
Cited by 1 | Viewed by 1285
Abstract
This paper proposes an interactive consensus reaching model in the group decision making for heterogeneous hesitant preference relations (i.e., hesitant fuzzy preference relations, hesitant multiplicative preference relations, hesitant fuzzy linguistic preference relations). First, the consistencies of three hesitant preference relations are defined, respectively. [...] Read more.
This paper proposes an interactive consensus reaching model in the group decision making for heterogeneous hesitant preference relations (i.e., hesitant fuzzy preference relations, hesitant multiplicative preference relations, hesitant fuzzy linguistic preference relations). First, the consistencies of three hesitant preference relations are defined, respectively. Then, based on their definitions, three optimization models are constructed to obtain the weight vector of alternatives, based on which an interactive consensus adjustment algorithm is established based on the direct consensus framework. This framework adopts feedback mechanism to facilitate the information correction of decision makers. After several rounds of adjustment, the decision results with satisfactory consensus level are achieved. Finally, the practicability and effectiveness of the model are illustrated through a case study of mine accident emergency decision making. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Its Applications in Decision Making)
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16 pages, 1885 KiB  
Article
Development of Integrated Linear Programming Fuzzy-Rough MCDM Model for Production Optimization
by Milan Dordevic, Rade Tešić, Srdjan Todorović, Miloš Jokić, Dillip Kumar Das, Željko Stević and Sabahudin Vrtagic
Axioms 2022, 11(10), 510; https://doi.org/10.3390/axioms11100510 - 27 Sep 2022
Cited by 5 | Viewed by 1638
Abstract
One of the most common tools for achieving optimization and adequate production process management is linear programming (LP) in various forms. However, there are specific cases of the application of linear programming when production optimization implies several potential solutions instead of one. Exactly [...] Read more.
One of the most common tools for achieving optimization and adequate production process management is linear programming (LP) in various forms. However, there are specific cases of the application of linear programming when production optimization implies several potential solutions instead of one. Exactly such a problem is solved in this paper, which integrates linear programming and a Multi-Criteria Decision-Making (MCDM) model. First, linear programming was applied to optimize production and several potential solutions lying on the line segment AB were obtained. A list of criteria was created and evaluated using the Improved Fuzzy Stepwise Weight Assessment Ratio Analysis (IMF SWARA). To obtain the final solution, a novel Rough compromise ranking of alternatives from distance to ideal solution (R-CRADIS) method was developed and verified through comparative analysis. The results show that the integration of linear programming and a Fuzzy-Rough MCDM model can be an exceptional solution for solving specific optimization problems. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Its Applications in Decision Making)
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22 pages, 1059 KiB  
Article
Evaluation of Cryptocurrencies for Investment Decisions in the Era of Industry 4.0: A Borda Count-Based Intuitionistic Fuzzy Set Extensions EDAS-MAIRCA-MARCOS Multi-Criteria Methodology
by Fatih Ecer, Adem Böyükaslan and Sarfaraz Hashemkhani Zolfani
Axioms 2022, 11(8), 404; https://doi.org/10.3390/axioms11080404 - 15 Aug 2022
Cited by 18 | Viewed by 4077
Abstract
Blockchain technologies, which form the basis of Industry 4.0, paved the way for cryptocurrencies to emerge as technological innovation in the technology age. Recently, investors worldwide have been interested in cryptocurrencies with increasing acceleration due to high earning expectations though they have no [...] Read more.
Blockchain technologies, which form the basis of Industry 4.0, paved the way for cryptocurrencies to emerge as technological innovation in the technology age. Recently, investors worldwide have been interested in cryptocurrencies with increasing acceleration due to high earning expectations though they have no backing and intrinsic value. As such, this paper seeks to identify the most proper cryptocurrencies from an investment standpoint in our technological era. Fifteen well-known cryptocurrencies with the highest market capitalization are evaluated as per sixteen factors. An intuitionistic fuzzy set-driven methodology incorporating Evaluation Based on Distance from Average Solution (EDAS), Multi-Attributive Ideal Real Comparative Analysis (MAIRCA, and Measurement of Alternatives and Ranking according to COmpromise Solution (MARCOS), which is the study’s prominent novelty, has been applied to provide a strong group decision vehicle for cryptocurrency selection. Notwithstanding, although the results obtained with the three approaches are highly consistent, investors would not like to doubt the instrument they will invest in. The Borda count is then applied to obtain a compromise for the rankings obtained from each approach. As per our findings, Ethereum, Tether, and Bitcoin are the most suitable cryptocurrencies, whereas reliable software, ease of inclusion in the wallet, and stability are the foremost factors to consider when investing in cryptocurrencies. The findings are further discussed in detail from a financial perspective. The proposed approach could be employed to select different investment instruments in future studies. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Its Applications in Decision Making)
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