Iranian journal of fuzzy systems
Volume:19 Issue: 5, Sep-Oct 2022

The Max-Mean Dispersion Problem comprises selecting a subset of elements from a set while maximising the average of a measure of dispersion. We usually compute this measure of dispersion based on some distance metric between the elements of the candidate set. However, in real-world applications, this measure of dispersion could be ill-defined or vague. For example, consider the problem of building a team to execute some kinds of project. We can see the dispersion between the members of the team as the team chemistry, so the coach is interested in maximising this chemistry. In this example, it would be very difficult to compute exactly a dispersion measure for each candidate. This is due to the lack of information about how well the candidates worked together in the past. To cope with imprecise or vague information, in this paper, we propose three mixed integer linear programming models based on possibility, necessity, and credibility measures. To the best of our knowledge, this is the first approach which explicitly considers this type of uncertainty in this optimisation problem.

This article discusses the comments made by some scientists that multidimensional interval arithmetic (MIA) is the same as constraint interval arithmetic (CIA) and multidimensional fuzzy arithmetic (MFA) is the same as constraint fuzzy arithmetic (CFA). Both types of arithmetic are briefly presented and then the difference in their dimensions, calculation methods, differences in the obtained results and the way they are used in complex calculations are shown. The answer to the question posed is presented in the conclusions.

In this note, pointwise best-possible (lower and upper) bounds on the set of copulas with a given value of the Gini's gamma coefficient are established. It is shown that, unlike the best-possible bounds on the set of copulas with a given value of other known measures such as Kendall's tau, Spearman's rho or Blomqvist's beta, the bounds found are not necessarily copulas, but proper quasi-copulas.

This paper deals with the issues of the finite-time synchronization (FTS) for a class of fractional-order fuzzy Cohen-Grossberg neural networks (FOFCGNNs) with time delay. Based on the finite-time stability theory,  fractional-order Razumikhin theorem and applying fractional-order differential inequalities and other inequality techniques, a few new and effective criteria formulated by testable algebraic inequalities are derived to ensure the FTS for the concerned models via designing a discontinuous control strategy. Finally, two numerical simulations examples are furnished to demonstrate the feasibility and effectiveness of the derived theoreticalresults.

Fuzzy arithmetic with standard methods such as the extension principle and$alpha $-cut lead to restricted possibilities for solving fuzzy equations.The procedures to find a solution to a fuzzy equality with these methodsrequire strong assumptions and high computation costs. Among severalapproaches dealing with this restrictions this paper focuses on theTransmission Average (TA) fuzzy arithmetic. The shape preservation ofthe TA arithmetic operations on L-R fuzzy numbers is proven. Theseproperties together with some other algebraic properties investigatedin the paper are applied to solve fuzzy polynomial equations as well as systems of linear fuzzy equations in general form. Several examples in the paper present the advantages of TA arithmetic in solving fuzzy equations.  It is shown that the results in this paper support the fact that TA arithmetic is an easy to implement approach in fuzzy modeling.

Cyber security is a hot topic in recent years and one of the main performances in the decision-making is the choice of cyber security service providers (CSSPs). For enterprises and government units, the selection of appropriate NSSPs needs to be measured and evaluated from multiple perspectives, which is obviously a multiple attribute decision making (MADM) or multiple attribute group decision making (MAGDM). In this paper, the traditional MABAC method is improved by using the prospect theory, and the evaluation information is collected and sorted by using PULTS. The improved PUL-PT-MABAC method can not only deal with the uncertainty well, but also fully consider the influence of the psychological state of decision maker (DM) on the decision result. More importantly, we apply the improved PUL-PT-MABAC model to the selection of NSSPs and prove the reliability of this proposed method by taking advantage of comparative analysis with three existed methods. These results show that the model can deal with practical problems, and has good practicability and science.

In this paper, the concepts of L-enclosed L-order space, L-order L-concave space, L-internal L-order space and L-order L-convex filter are introduced. The main results are:(1) the categories of L-order L-convex spaces, L-enclosed L-order spaces, L-order L-concave spaces and L-internal L-order spaces are isomorphic; (2) the category of L-order convergence spaces based on L-order L-convex filters is topological; (3) there is a Galois correspondence between the category of L-order convergence spaces and that of L-order L-convex spaces.

Design of an adaptive supervisory fuzzy sliding mode control for a planar cable-driven parallel robot is aided in this paper. The fuzzy logic controller is proposed to generate the switching control signal without occurring the chattering problem. For this purpose, an adaptive mechanism is suggested for online tuning of the output gain of the fuzzy sliding mode controller. Moreover, for better tracking, a supervisory control system is considered for online tuning of the PID sliding surface gains. The Grasshopper Optimization Algorithm is suggested for optimization of the membership functions selected for the fuzzy sliding surface. The stability proof of the closed-loop system is derived by using the Lyapunov stability theorem. Simulation results are reported to show the merits of the proposed controller on reduced chatter, and system robustness against parameter uncertainty, load disturbance, and nonlinearities.

We study suitable diagonal conditions for $top$-uniform limit spaces. A dual diagonal condition is shown to be a suitable axiom for uniform regularity. We characterize this regularity concept by closures of $L$-sets. We apply all these diagonal axioms and prove an extension theorem for uniformly continuous mappings defined on a dense subspace.

Most of chronic liver diseases without suitable treatment will lead to cirrhosis of the liver, eventually progressing to liver cancer. Thus, early diagnosis is very important in detecting the liver diseases and suggesting the treatment at the right time. A useful model that effectively predicts the patient's liver fibrosis has great importance in reducing the load on doctors, especially in lower-level hospitals. In this paper, a new model combining semi-supervised learning method and fuzzy min max neural network with selective fuzzy rule set rendering is proposed. Cirrhosis level is evaluated by APRI and FIB-4. The proposed method is experimented on data sets from machine learning databases, including UCI and CS. Apart from that, our method is also implemented on the liver data set collected from the hospitals of Thai Nguyen province. The comparison among our proposed method and other related ones is also given. The obtained results show that our proposed model has better performance than compared methods in terms of execution time and the number of rules.

In a clustering task, choosing a proper clustering algorithm and obtaining qualified clusters are crucial issues. Sometimes, a clustering algorithm is chosen based on the data distribution, but data distributions are not known beforehand in real world problems. In this case, we hesitate which clustering algorithm to choose. In this paper, this hesitation is modeled by a hesitant fuzzy multi criteria decision making problem {small (HFMCDM)} in which some clustering algorithms play the role of experts. Here, we consider fuzzy {footnotesize C}-means {small (FCM)} and agglomerative clustering algorithms as representative of two popular categories of clustering algorithms partitioning and hierarchical clustering methods, respectively.Then, we propose a new clustering procedure based on hesitant fuzzy decision making approaches {small (HFC)} to decide which of the {small FCM} family or hierarchical clustering algorithms is suitable for our data. This procedure ascertains a good clustering algorithm using neutrosophic {small FCM} ({small NFCM}) through a two phases process. The {small HFC} procedure not only makes a true decision about applying partitioning clustering algorithms, but also improves the performance of {small FCM} and evolutionary kernel intuitionistic fuzzy c-means clustering algorithm ({small EKIFCM}) with construction hesitant fuzzy partition {small (HFP)} conveniently. Experimental results show that the clustering procedure is applicable and practical. According to {small HFC} procedure, it should be mentioned that it is possible to replace the other clustering algorithms that belong to any partitioning and hierarchical clustering methods. Also, we can consider other categories of clustering algorithms.

In this work, we introduce some categories of triangular norms in which truth values belong to the real unit interval, where arrows are a generalization of automorphisms. We investigate the existence of products, coproducts, equalizers and  coequalizers in these categories. Moreover, we show that Theorems 2.29, 2.30 in cite{Yousefi_Mashinchi_Mesiar_2021} are false by providing counterexamples.