Fuzzy Sets, Fuzzy Logic and Their Applications

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity

Analysis of luxury resort hotels by using the Fuzzy Analytic Hierarchy Process and the Fuzzy Delphi Method

Experience Economy is an accelerator switching the experience process of consumption into eternal memory, perfecting value and promoting positive after-buying intention. This research uses the Fuzzy Delphi Method (FDM) and Fuzzy Analytic Hierarchy Process (FAHP) to construct a system of evaluation criteria focused on understanding the luxury resort hotels (LRHs) industry in Taiwan and Macao. One finding of this study is that objective hotels in these two territories exhibit different hotel operating characteristic (the unity LRHs mode in Taiwan vs involving casino LRHs in Macao) and customer markets. These Macanese LRHs define them as international operations, in contrast the Taiwanese position themselves as domestic businesses. The other finding is that Taiwan based evaluation criteria on consumer-orientation and operation and management, while Macao stressed evaluation based on operation and management to manage LRHs industry

Refractured Well Selection for Multicriteria Group Decision Making by Integrating Fuzzy AHP with Fuzzy TOPSIS Based on Interval-Typed Fuzzy Numbers

Multicriteria group decision making (MCGDM) research has rapidly been developed and become a hot topic for solving complex decision problems. Because of incomplete or non-obtainable information, the refractured well-selection problem often exists in complex and vague conditions that the relative importance of the criteria and the impacts of the alternatives on these criteria are difficult to determine precisely. This paper presents a new model for MCGDM by integrating fuzzy analytic hierarchy process (AHP) with fuzzy TOPSIS based on interval-typed fuzzy numbers, to help group decision makers for well-selection during refracturing treatment. The fuzzy AHP is used to analyze the structure of the selection problem and to determine weights of the criteria with triangular fuzzy numbers, and fuzzy TOPSIS with interval-typed triangular fuzzy numbers is proposed to determine final ranking for all the alternatives. Furthermore, the algorithm allows finding the best alternatives. The feasibility of the proposed methodology is also demonstrated by the application of refractured well-selection problem and the method will provide a more effective decision-making tool for MCGDM problems

The Category of Matroids

The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful; there is a functor to the category of geometric lattices, that is nearly full; there are various adjunctions and free constructions on subcategories, inducing a simplification monad; there are two orthogonal factorization systems; some, but not many, combinatorial constructions from matroid theory are functorial.Comment: 31 pages, 10 diagrams, 28 reference

CO2 emission based GDP prediction using intuitionistic fuzzy transfer learning

The industrialization has been the primary cause of the economic boom in almost all countries. However, this happened at the cost of the environment, as industrialization also caused carbon emissions to increase exponentially. According to the established literature, Gross Domestic Product (GDP) is related to carbon emissions (CO2) which could be optimally employed to precisely estimate a country's GDP. However, the scarcity of data is a significant bottleneck that could be handled using transfer learning (TL) which uses previously learned information to resolve new tasks, more specifically, related tasks. Notably, TL is highly vulnerable to performance degradation due to the deficiency of suitable information and hesitancy in decision-making. Therefore, this paper proposes ‘Intuitionistic Fuzzy Transfer Learning (IFTL)’, which is trained to use CO2 emission data of developed nations and is tested for its prediction of GDP in a developing nation. IFTL exploits the concepts of intuitionistic fuzzy sets (IFSs) and a newly introduced function called the modified Hausdorff distance function. The proposed IFTL is investigated to demonstrate its actual capabilities for TL in modeling hesitancy. To further emphasize the role of hesitancy modelled with IFSs, we propose an ordinary fuzzy set (FS) based transfer learning. The prediction accuracy of the IFTL is further compared with widely used machine learning approaches, extreme learning machines, support vector regression, and generalized regression neural networks. It is observed that IFTL capably ensured significant improvements in the prediction accuracy over other existing approaches whenever training and testing data have huge data distribution differences. Moreover, the proposed IFTL is deterministic in nature and presents a novel way for mathematically computing the intuitionistic hesitation degree.© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).fi=vertaisarvioitu|en=peerReviewed

IVTURS: A linguistic fuzzy rule-based classification system based on a new interval-valued fuzzy reasoning method with tuning and rule selection

Interval-valued fuzzy sets have been shown to be a useful tool for dealing with the ignorance related to the definition of the linguistic labels. Specifically, they have been successfully applied to solve classification problems, performing simple modifications on the fuzzy reasoning method to work with this representation and making the classification based on a single number. In this paper we present IVTURS, a new linguistic fuzzy rule-based classification method based on a new completely interval-valued fuzzy reasoning method. This inference process uses interval-valued restricted equivalence functions to increase the relevance of the rules in which the equivalence of the interval membership degrees of the patterns and the ideal membership degrees is greater, which is a desirable behaviour. Furthermore, their parametrized construction allows the computation of the optimal function for each variable to be performed, which could involve a potential improvement in the system’s behaviour. Additionally, we combine this tuning of the equivalence with rule selection in order to decrease the complexity of the system. In this paper we name our method IVTURS-FARC, since we use the FARC-HD method to accomplish the fuzzy rule learning process. The experimental study is developed in three steps in order to ascertain the quality of our new proposal. First, we determine both the essential role that interval-valued fuzzy sets play in the method and the need for the rule selection process. Next, we show the improvements achieved by IVTURS-FARC with respect to the tuning of the degree of ignorance when it is applied in both an isolated way and when combined with the tuning of the equivalence. Finally, the significance of IVTURS-FARC is further depicted by means of a comparison by which it is proved to outperform the results of FARC-HD and FURIA, which are two high performing fuzzy classification algorithms.This work was supported in part by the Spanish Ministry of Science and Technology under projects TIN2011-28488 and TIN2010-15055 and the Andalusian Research Plan P10-TIC-6858 and P11-TIC-7765

A survey of the classification of fuzzy subgroups of some finite groups

In this lecture we survey the classification of fuzzy subgroups of finite groups as studied byProf. B.B Makamba and V. Murali. We present the impact of the research on our postgraduate students. The classification is focusing on finite abelian p-groups and dihedral groups, giving a mixture of abelian and non-abelian groups. We show some highlights and what still needs to be done in the classification of fuzzy subgroups. We also touch on what other researchers have achieved in the classification of fuzzy subgroups and how our work is related to theirs. We begin with a historical background of fuzzy logic.Inaugural Lecture Address by Prof. Babington Makamba- A survey of the classification of fuzzy subgroups of some finite groups

EWMA STATISTICS AND FUZZY LOGIC IN FUNCTION OF NETWORK ANOMALY DETECTION

Anomaly detection is used to monitor and capture traffic anomalies in network systems. Many anomalies manifest in changes in the intensity of network events. Because of the ability of EWMA control chart to monitor the rate of occurrences of events based on their intensity, this statistic is appropriate for implementation in control limits based algorithms. The performance of standard EWMA algorithm can be made more effective combining the logic of adaptive threshold algorithm and adequate application of fuzzy theory. This paper analyzes the theoretical possibility of applying EWMA statistics and fuzzy logic to detect network anomalies. Different aspects of fuzzy rules are discussed as well as different membership functions, trying to find the most adequate choice. It is shown that the introduction of fuzzy logic in standard EWMA algorithm for anomaly detection opens the possibility of previous warning from a network attack. Besides, fuzzy logic enables precise determination of degree of the risk