Iranian journal of fuzzy systems
Volume:20 Issue: 1, Jan-Feb 2023

For understanding the influence of malware attacking on complex heterogeneous networks, this work studies a fractional network-based SIRS epidemic model with fuzzy transmission and saturated treatment function. Firstly, we apply the next-generation method to obtain the basic reproductive ratio $\mathcal{R}_0$, that is an important threshold value in the investigation of asymptotic behavior of the proposed epidemic model. The obtained theoretical results indicates that the value $\mathcal{R}_0$ significantly depends on the topology structure of the underlying network and the malware load. In addition, we give a threshold value $\tilde{\mathcal{R}}_0>\mathcal{R}_0$ that not only determines the existence of endemic equilibrium  $\mathbf{E}_\ast$ but also ensures the clean of malware programs on the network. At last, the sensitivity analysis of the threshold value $\mathcal{R}_0$ and some graphical simulations are presented to illustrate for the theoretical results.

In this article, the Craig interpolation property for rational Gödel logic is studied. Despite classical Gödel logic, this property can be proved in this new extension of Gödel logic. This new predicate version of Gödel logic is similar to continuous logic and also, its semantics is extended similar to metric model theory with some differences.

Since Pawlak defined the notion of rough sets in 1982, many authors made wide research studying rough sets in the ordinary case and the fuzzy case. This paper introduced a new style of rough fuzzy sets based on %arbitrary fuzzy relation $R$ and a fuzzy ideal $\ell$ on a universal finite set $X$. New lower and new upper fuzzy sets are introduced, and consequently, fuzzy interior and  fuzzy closure operators of a rough fuzzy set are discussed. These definitions, if $\ell$ is restricted to $\ell^{\circ} = \{\overline{0}\}$, imply the fuzzification of previous definitions given in the ordinary case, and moreover in the crisp case, we get exactly these previous definitions. The new style gives us a better accuracy value of roughness than the previous styles. Rough fuzzy connectedness is introduced as a sample of applications on the recent style of roughness.

In this paper, we deal with the global practical exponential stabilization of a class of perturbed Takagi-Sugeno fuzzy control systems. The terms of perturbations are supposed uniformly  bounded by some known  functions and in certain cases not necessarily smooth. We prove that the solution of the closed-loop system with a linear fuzzy controller convergeto  a neighborhood of the origin. We use common quadratic Lyapunov function  and parallel distributed compensation controller techniques to study the asymptotic behavior of the solutions of fuzzy system. Numerical simulations are given to validate the proposed approach.

Software quality is an important research direction in software engineering domain,  which is a multi-dimen-sional evaluation problem.  The VIsekriterijumska optimizacija i KOmpromisno Resenje (VIKOR) technique is a comprehensive  method for handing the multi-dimensional evaluation problems. The projection is commonly used to measure the closeness between two decision objects in decision science.  However, two research questions are found in this work: (1) There is no specific concrete regret  matrix in current VIKOR technique; (2) The existing projection measures are not  always reasonable in interval-valued intuitionistic fuzzy setting. Two research gaps are filled  systematically in this paper: (1) A specific concrete regret matrix is provided in this extended VIKOR-based group decision-making method; (2) A new normalized projection measure is provided in order to measure the closeness between two decision matrices.  The decision procedures are also provided in this paper. A practical application to  the software quality assessment is introduced.  Some experimental comparisons are provided in order to illustrate the feasibility and practicability of introduced method.

The picture fuzzy sets are very useful in those uncertain problems which could not be solved by fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets, fermatean fuzzy sets, and q-rung orthopair fuzzy sets. For example, medical diagnosis, personnel selection, human voting, etc. All of these problems require answers of the type no, yes, abstain, and refusal. To compare two picture fuzzy sets, the distance measures play an important role. There are a lot of studies about the distance measures of picture fuzzy sets available in the literature. However, all of these distance measures lead to unreasonable results in most of the problems. So, we in this paper suggest a new distance measure for picture fuzzy sets that is more effective than all of the available distance measures. We also demonstrate its utility in classification and diagnostic problems and contrast its performance with the available ones.

Picture fuzzy set is an extension of intuitionistic fuzzy set, which can deal with inconsistent and uncertain information more accurately. Similarity measure, as an important  mathematical tool to evaluate the degree of similarity between picture fuzzy sets, has been widely used to deal with multi-attribute decision-making problems. But there are unreasonable  and counter-intuitive cases due to  a few undesirable properties. In order to handle these unreasonable cases, this paper proposes a parametric similarity measure based on three parameters $m_1, m_2$ and $m_3$, in which decision makers with different decision styles can  obtain  the appropriate similarity measure by adjusting parameters $m_1, m_2$ and $m_3$. Moreover, we  analyze some existing similarity measures from the perspective of mathematics and show that the proposed similarity measure is effective by   numerical examples. In the end, we use the proposed similarity measure to solve the problems of multi-attribute decision-making. Through the  comparison and analysis, we find that the proposed similarity measure is more effective  than some existing similarity measures between picture fuzzy sets.

In this paper, we first investigate some properties of lattice-valued quasi-overlap functions, which includes the relation between quasi-overlap functions and three kinds of aggregation functions and the Lipschitz property. Then we provide two new construction methods for lattice-valued quasi-overlap functions. One applies t-conorms and negations, the other involves quasi-overlap functions and implications. Examples are presented and some analytical properties are studied as well.

The Zagreb index (ZI) of a crisp graph and also for a fuzzy graph (FG) is a very much useful tool in network theory, spectral graph theory, molecular chemistry and several fields of chemistry and mathematics. The second ZI is studied for FGs here. Bounds of this index are calculated for several FGs: path, star, cycle, complete FG, partial fuzzy subgraph, etc. For isomorphic FGs, it is shown that the value of this index is same. Bounds of this index for the Cartesian product, composition, join and union of two FGs are established. At the end of this article, an application of the index in mathematical chemistry is studied. For this, octane isomers are considered and analyzed the correlation between this index with some physico-chemical properties of octane isomers. This index's correlation coefficient ($r$) with acentric factor and entropy is determined for the linear curve fittings. Using the value of $r$, one can conclude that this index can help estimate the acentric factor and entropy with significant accuracy. Also, these outcomes declare the  appropriateness of the index in QSPR research.

In the real world, in most cases, such as industry, management, and even in daily life, we encounter optimization and decision-making problems that require the opinions of experts and masters on the problem to be able to make the best decision. In these cases, it is necessary to use an optimization problem with hesitant fuzzy parameters.There are few studies on hesitant fuzzy linear programming (HFLP) problems. Therefore,in this paper, we  consider such problems.Especially, we study HFLP problems with hesitant cost coefficients. For this purpose,we propose the simplex  method to solve the introduced optimization problems and draw a flowchart of the proposed  method.Finally, by solving two illustrative examples with hesitant fuzzy information, we examine the applicability of the proposed method.

Atanassov's intuitionistic fuzzy sets have succussed in the application of decision making, data mining, artificial intelligence, image processing, and so on. In these applications, intuitionistic fuzzy reasoning plays a crucial role. To improve the quality of intuitionistic fuzzy reasoning, this paper presents a quintuple intuitionistic fuzzy implication principle (QIIP) to resolve intuitionistic fuzzymodus ponens (IFMP) and intuitionistic fuzzy modus tollens (IFMT) problems. The QIIP algorithms of IFMP and IFMT problems for intuitionistic R-implication, S-implication, and several fuzzy implications are represented. Moreover, we investigate the recovery property and continuity of QIIP algorithms for IFMP and IFMT.Finally, an application example for medical diagnosis is implemented to illustrate our proposed approaches.

Generalized hypothetical syllogism (GHS) plays a very important role in fuzzy inference.Therefore, it is valuable to investigate the GHS based on the Bandler-Kohout  subproduct (BK-GHS) in order to measure the availability of fuzzy inference.  This paper aims to study the (BK-GHS) property   of some well-known fuzzy implications including (S, N)-, QL-, $f$-, $g$-, probabilistic and probabilistic S-implications in detail. We use the method of automorphism transformation to investigate (S, N)- and QL-implications and make better use of some essential properties about  $f$-, $g$-, probabilistic and probabilistic S-implications to make them satisfy (BK-GHS) with semicopulas. With these results, (BK-GHS) can be more effectively applied in practice.

In the competitive business world, the whole thing is in a state of flux. It is not possible to know the exact outcomes of the strategies adopted by a company. Companies are always unsure of the customer's responses regarding their strategies, and the judgment of the decision-makers is correct to some extent but not always exact. To avoid erroneous estimations, the companies generally preferred the opinion of more than one expert. It is highly understood that no two experts will describe the similar payoffs for a mix of strategies used. Therefore, the payoff matrices, given by a group of experts, provide more information to select the best strategies for the companies. This paper presents an approach to solving bimatrix game problems with multiple experts in an intuitionistic fuzzy environment. Further, the applicability and superiority of the proposed method have been shown with the help of a real-life numerical example.