Transactions on Fuzzy Sets and Systems
Volume:2 Issue: 1, Spring - Summer 2023

In this paper‎, ‎we extend the fuzzy similarity measure of‎ ‎two rankings to any finite number of rankings‎. ‎We provide a method to‎ ‎convert a measure for a finite number of rankings to a number that‎ ‎represents the number for two rankings‎. ‎We apply our results to the‎ ‎sustainability ranking of countries by the Environmental Performance Index‎ ‎(EPI)‎. ‎The $2020$ EPI provides a summary of the state of sustainability‎ ‎around the world‎. ‎It uses $32$ performance indicators across $11$‎ ‎categories‎. ‎These indicators provide a way to determine problems‎, ‎set‎ ‎targets‎, ‎track trends‎, ‎understand outcomes‎, ‎and identify best policy‎ ‎practices‎. ‎The EPI ranks $180$ countries on environmental health and‎ ‎ecosystem vitality‎. ‎The EPI provides a method in support of efforts to meet‎ ‎the targets of the UN Sustainable Development Goals‎. ‎The EPI determined‎ ‎that the Global West region ranked the highest‎. ‎The purpose of our project‎ ‎is to find the similarity of the $11$ rankings of the countries for eight‎ ‎different regions‎.

The proliferation of the web and social networks has made people more connected to their friends and neighbors than ever before‎. ‎The desire of individuals to relate to similar tastes and choices in a social network leads to the formation of clusters or virtual communities‎. ‎Such information can be useful for commercial‎, ‎educational or developmental purposes and therefore a large number of algorithms for detecting communities have been presented‎. ‎There are many algorithms for detecting communities on social networks‎. ‎In this paper‎, ‎using the label propagation algorithm and fuzzy Delphi method‎, ‎an improved method is presented that can identify communities more accurately and quickly than other similar methods‎. ‎Accordingly‎, ‎in the proposed algorithm‎, ‎instead of randomly selecting from the maximum labels of the neighboring nodes‎, ‎the label with the highest weight is chosen‎. ‎By doing this‎, ‎random selection is eliminated‎, ‎and stability and certainty in the outcomes of the algorithm are achieved‎.

This paper proposes an application of a Takagi-Sugeno fuzzy model to the prediction of complex mass transfer behavior in smart toilet bidet systems‎. ‎The model is constructed through the integration of fuzzy logic theory‎, ‎nonlinear autoregressive moving average exogenous input models‎, ‎neural networks‎, ‎and data clustering algorithms‎. ‎To develop the model for estimating the air quality of the smart toilet-bidet system‎, ‎many datasets are collected from a smart toilet bidet model equipped with an automatic odor/bacteria suction system using Sulfur hexafluoride ($SF_6$) gas‎. ‎Many case studies were carried out as a function of the suction flow rate‎, ‎suction angle‎, ‎the number of suction holes‎, ‎and suction hole size‎. ‎The inputs for training the fuzzy model are the size‎, ‎number‎, ‎and angles of suction holes‎, ‎whereas its output is the undesirable gas concentration‎. ‎The trained fuzzy model is tested using different datasets‎. ‎Modeling and testing results show the effectiveness of the fuzzy model in predicting the gas concentration of the toilet bowl‎. ‎The proposed fuzzy model is expected to be useful in the implementation of smart toilet bowl systems in the near future‎.

‎Student assessment is a very important process in education‎, ‎because it helps the instructor to determine student mistakes and to improve their performance by reforming his/her teaching plans‎. ‎A hybrid assessment method using qualitative grades for evaluating student mathematical skills is presented in this work‎. ‎The paper starts with the mathematical background which is necessary for the understanding of its contents‎. ‎This includes basic information about fuzzy‎, ‎neutrosophic and soft sets‎, ‎and about grey numbers‎. ‎It also includes a description of the use of the center of gravity ($COG$) defuzzification technique for assessing a student group's quality performance‎. ‎The $COG$ technique is compared with the classical method of calculating the $GPA$ index‎. ‎The hybrid assessment method‎, ‎which is based on all the previous concepts and processes‎, ‎is developed next and the article closes with the final conclusion and some recommendations for future research‎.

In this paper‎, ‎we investigate the filter theory of Intuitionistic Linear Algebra (IL-algebra‎, ‎in short) with emphasis on the lattice of filters of IL-algebras and relationship between filters and congruences on IL-algebras‎. ‎We characterize the filter generated by a subset and give some related properties‎. ‎The prime filter for IL-algebras is characterized and the prime filter theorem for IL-algebra is established‎. ‎We get that the lattice $(F(\textbf{L}),\subseteq )$ of filters of an IL-algebra $\textbf{L}$ is algebraic‎, ‎Brouwerian‎, ‎pseudocomplemented and endowed with the structure of Heyting algebra‎. ‎We prove that the lattice of congruences and that of filters of any IL-algebra are isomorphic‎.

With this paper the authors try to newly reflect on Zadeh's concept of a fuzzy set‎. ‎The departing point is the fact that not only fuzzy sets originate in Language‎, ‎but that they are just 'linguistic entities' genetically different from the concept of 'crisp sets' whose origin is either in a physical collection of objects‎, ‎or in a list of them‎.Thus‎, ‎a new definition of a fuzzy set is presented by means of two magnitudes‎: ‎A qualitative one‎, ‎a graph‎, ‎the basic magnitude‎, ‎and a quantitative one‎, ‎a scalar magnitude‎. ‎If the first reflects the language's relational ground of the fuzzy set‎, ‎the second‎ - ‎and thanks to 'measuring the meaning of words'‎ -, ‎reflects the (numerical) extensional state in which it currently appears‎.‎Since the second‎, ‎the scalar magnitude‎, ‎is essential for the applications‎, ‎it is also introduced the concept of a 'working fuzzy set' by taking into account the numerical function‎, ‎the meaning's measure or the membership function‎. ‎The working fuzzy set‎, ‎that enlarges the corresponding fuzzy set‎, ‎allows us to see the 'same fuzzy set' with different membership functions‎, ‎that is‎, ‎the same graph appearing in different extensional states‎. ‎Notice that a 'working crisp set' is but the same crisp set‎.

This work presents an approach to taxi demand forecasting and classification‎. ‎The proposed approach uses historical data from taxi rides and meteorological data‎. ‎The Kruskal-Wallis variable ranking method is used to identify the most relevant variables‎. ‎The selected variables are used as input to an evolving fuzzy system to perform the prediction‎. ‎Once the forecast is made‎, ‎the demand results are classified by value ranges‎. ‎Those ranges are also identified by colors that compose a heatmap‎, ‎displayed at each time interval‎. ‎In this work‎, ‎to perform the prediction‎, ‎four evolving systems are evaluated‎: ‎Autonomous Learning Multi-Model (ALMMo); evolving Multivariable Gaussian Fuzzy Modeling System (eMG); evolving Fuzzy with Multivariable Gaussian Participatory Learning and Recursive Maximum Correntropy eFCE and; evolving Neo-Fuzzy Neuron (eNFN)‎. ‎Computational experiments were carried out to evaluate the evolving systems in predicting Pick-Up and Drop-Off‎, ‎at intervals of 15 and 30 minutes‎, ‎for 86 zones in New York‎, ‎covering the period from 01/01/2018 to 31‎/ ‎10/2018‎. ‎The results obtained by the evolving systems are compared with each other and state of the art‎. ‎Among the evolving models‎, ‎ALMMo presented the best results compared to the state of the art and other evolving models‎. ‎Performance obtained by the evolving models suggests that the proposed approach is promising an alternative to forecasting and classifying passenger demand‎.

The class of De Morgan residuated lattices was introduced by L‎. ‎C‎. ‎Holdon (Kybernetika 54(3):443-475‎, ‎2018)‎, ‎recently‎, ‎many mathematicians have studied the theory of ideals or filters in De Morgan residuated lattices and some of them investigated the‎ ‎properties of De Morgan residuated lattices endowed with a topology‎. ‎In this paper‎, ‎we introduce the notion of semitopological De Morgan residuated lattice‎, ‎we present some examples and‎ ‎by considering the notion of upsets‎, ‎for any element $a$ of a De Morgan residuated lattice $L,$ there is a topology $\tau_{a}$ on $L$‎ ‎and we show that $L$ endowed with the topology‎ ‎$\tau_{a}$ is semitopological with respect to $\vee‎, ‎\wedge$ and $\odot,$ and right topological with respect to $\rightarrow.$‎ ‎Moreover‎, ‎in the general case of residuated lattices we prove that $L$ endowed with the topology‎ ‎$\tau_{a}$ is semitopological with respect to $\odot$ and right topological with respect to $\rightarrow.$‎ ‎Finally‎, ‎we obtain some of the topological‎ ‎aspects of this structure such as $L$ endowed with the topology‎ ‎$\tau_{a}$ is a $\mathbf{T_0}$-space‎, ‎but it is not a $\mathbf{T_1}$-space or Hausdorff space‎.

Economic and financial phenomena are highly complex and‎ ‎non-linear‎. ‎However‎, ‎surprisingly‎, ‎in many cases‎, ‎these phenomena‎ ‎are accurately described by linear models‎ -- ‎or‎, ‎sometimes‎, ‎by‎ ‎piecewise linear ones‎. ‎In this paper‎, ‎we show that fuzzy‎ ‎techniques can explain the unexpected efficiency of linear and‎ ‎piecewise linear models‎: ‎namely‎, ‎we show that a natural‎ ‎fuzzy-based precisiation of imprecise (``fuzzy'') expert knowledge‎ ‎often leads to linear and piecewise linear models‎.‎We show this by applying invariance ideas to analyze which membership functions‎, ‎which fuzzy ``and''-operations (t-norms)‎, ‎and which‎ ‎fuzzy implication operations are most appropriate for applications to economics and finance‎. ‎We also discuss which expert-motivated nonlinear models should be‎ ‎used to get a more accurate description of economic and financial‎ ‎phenomena‎: ‎specifically‎, ‎we show that a natural next step is to add cubic‎ ‎terms to the linear (and piece-wise linear) expressions‎, ‎and‎, ‎in general‎, ‎to consider polynomial (and piece-wise polynomial) dependencies‎.

‎Machines can model and improve the human mind’s capabilities through artificial intelligence‎. ‎One of the most popular tools of artificial intelligence is fuzzy sets‎, ‎which can capture and model the vagueness and impreciseness in human thoughts‎. ‎This paper‎, ‎first of all‎, ‎introduces the recent extensions of ordinary fuzzy sets and then presents a literature review on the integration of fuzzy sets with other artificial intelligence techniques such as automated reasoning‎, ‎autonomous agents‎, ‎multi-agent systems‎, ‎machine learning‎, ‎case-based reasoning‎, ‎deep learning‎, ‎information reasoning‎, ‎information representation‎, ‎natural language processing‎, ‎symbolic reasoning‎, ‎and neural networks‎. ‎Graphical illustrations of literature review results are presented for each of these integrated artificial intelligence techniques‎. ‎The results of a patent search on fuzzy artificial intelligence are also given‎.

‎This paper introduces the notion of the combined product of two‎ ‎$RL$-graphs‎ ‎while it is an‎ ‎$RL$-graph‎. ‎It is stated that the combined product has commutative properties‎, ‎i.e.‎, ‎$G\boxtimes H$‎ ‎and‎ ‎$H\boxtimes G$ are two isomorphic $RL$-graphs‎. ‎Moreover‎, ‎it is shown under a theorem that two isomorphic‎ ‎$RL$-graphs‎ ‎$G$‎ ‎and‎ ‎$G'$‎ ‎and‎ ‎two isomorphic‎ ‎$RL$-graphs‎ ‎$H$‎ ‎and‎ ‎$H'$‎ ‎have isomorphic combined products‎ ‎$G\boxtimes H$‎ ‎and‎ ‎$G'\boxtimes H'$‎. ‎Further‎, ‎it is investigated the relationships between these graphs and their operations by some notions such as strong‎ ‎$RL$-graph‎, ‎regular $RL$-graph‎, ‎and totally regular $RL$-graph‎. ‎Afterward‎, ‎it is displayed in a theorem that the combined product of two regular ($\alpha$-regular‎, ‎complete‎, ‎connected) $RL$-graphs is a regular ($\alpha$-regular‎, ‎complete‎, ‎connected) $RL$-graph‎. ‎It is also shown in theorems what properties certain types of‎ ‎$RL$-graphs combined will have‎. ‎Also‎, ‎these notions and theorems are clarified by some examples‎. ‎The combined product of two‎ ‎$RL$-graphs has many applications in various fields‎, ‎such as probability sciences‎, ‎urban planning‎, ‎etc‎. ‎In this article‎, ‎only two of these applications‎, ‎which determine the impact of effective factors on people's quality of life‎ ‎and‎ ‎factors effective in raising the production of a factory‎, ‎are stated and they are clarified by an example‎.

It has been shown in literature that in the two-dimensional case, the lattices of truth values considered are pairwise isomorphic, and so are the corresponding families of fuzzy sets. Therefore, each result for one of these types of fuzzy sets can be directly rewritten for each (isomorphic) type of fuzzy sets. In this paper, we show that there is a strong connection between weighted graphs and fuzzy graphs. We accomplish this by using lattice isomorphisms. Consequently, under certain conditions, results for one area can be carried over immediately to the other. Many situations in fuzzy graph theory do not depend on the weights of the vertices. The situation of providing weights for the vertices of a weighted graph is also considered. We also consider lattice homomorphisms with an illustration involving nonstandard analysis. In particular, we consider a nonstandard weighted graph, i.e., a graph where the weights of the edges are from a nonstandard interval.