Iranian Journal of Fuzzy Systems
https://ijfs.usb.ac.ir/
Iranian Journal of Fuzzy Systemsendaily1Wed, 01 Feb 2023 00:00:00 +0330Wed, 01 Feb 2023 00:00:00 +0330The analysis of a fractional network-based epidemic model with saturated treatment function and fuzzy transmission
https://ijfs.usb.ac.ir/article_7342.html
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 $\tilde{\mathcal{R}}_0&gt;\mathcal{R}_0$ that not only determines the existence of endemic equilibrium &nbsp;$\mathbf{E}_\ast$ 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.The Craig interpolation property for rational Gödel logic
https://ijfs.usb.ac.ir/article_7343.html
In this article, the Craig interpolation property for rational G&ouml;del logic is studied. Despite classical G&ouml;del logic, this property can be proved in this new extension of G&ouml;del logic. This new predicate version of G&ouml;del logic is similar to continuous logic and also, its semantics is extended similar to metric model theory with some differences.Generalization of rough fuzzy sets based on a fuzzy ideal
https://ijfs.usb.ac.ir/article_7344.html
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 &nbsp;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.On the global stabilization of perturbed nonlinear fuzzy control systems
https://ijfs.usb.ac.ir/article_7345.html
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 &nbsp;bounded by some known &nbsp;functions and in certain cases not necessarily smooth. We prove that the solution of the closed-loop system with a linear fuzzy controller convergeto &nbsp;a neighborhood of the origin. We use common quadratic Lyapunov function &nbsp;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.VIKOR-based group decision-making method for software quality assessment
https://ijfs.usb.ac.ir/article_7346.html
Software quality is an important research direction in software engineering domain,&nbsp; which is a multi-dimen-sional evaluation problem.&nbsp; The VIsekriterijumska optimizacija i KOmpromisno Resenje (VIKOR) technique is a comprehensive&nbsp; method for handing the multi-dimensional evaluation problems. The projection is commonly used to measure the closeness between two decision objects in decision science.&nbsp; However, two research questions are found in this work: (1) There is no specific concrete regret&nbsp; matrix in current VIKOR technique; (2) The existing projection measures are not&nbsp; always reasonable in interval-valued intuitionistic fuzzy setting. Two research gaps are filled&nbsp; 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.&nbsp; The decision procedures are also provided in this paper. A practical application to&nbsp; the software quality assessment is introduced.&nbsp; Some experimental comparisons are provided in order to illustrate the feasibility and practicability of introduced method.A picture fuzzy distance measure and its application to pattern recognition problems
https://ijfs.usb.ac.ir/article_7347.html
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.A parametric similarity measure between picture fuzzy sets and its applications in multi-attribute decision-making
https://ijfs.usb.ac.ir/article_7348.html
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 &nbsp;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 &nbsp;and counter-intuitive cases due to &nbsp;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 &nbsp;obtain &nbsp;the appropriate similarity measure by adjusting parameters $m_1, m_2$ and $m_3$. Moreover, we &nbsp;analyze some existing similarity measures from the perspective of mathematics and show that the proposed similarity measure is effective by &nbsp; numerical examples. In the end, we use the proposed similarity measure to solve the problems of multi-attribute decision-making. Through the &nbsp;comparison and analysis, we find that the proposed similarity measure is more effective &nbsp;than some existing similarity measures between picture fuzzy sets.New constructions of lattice-valued quasi-overlap functions
https://ijfs.usb.ac.ir/article_7349.html
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.Second Zagreb index for fuzzy graphs and its application in mathematical chemistry
https://ijfs.usb.ac.ir/article_7350.html
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 &nbsp;appropriateness of the index in QSPR research.Simplex algorithm for hesitant fuzzy linear programming problem with hesitant cost coefficient
https://ijfs.usb.ac.ir/article_7351.html
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 &nbsp;consider such problems.Especially, we study HFLP problems with hesitant cost coefficients. For this purpose,we propose the simplex &nbsp;method to solve the introduced optimization problems and draw a flowchart of the proposed &nbsp;method.Finally, by solving two illustrative examples with hesitant fuzzy information, we examine the applicability of the proposed method.Quintuple intuitionistic fuzzy implications reasoning algorithms and application
https://ijfs.usb.ac.ir/article_7352.html
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.Fuzzy implications satisfying the generalized hypothetical syllogism based on the Bandler-Kohout subproduct with semicopulas
https://ijfs.usb.ac.ir/article_7353.html
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 &nbsp;subproduct (BK-GHS) in order to measure the availability of fuzzy inference. &nbsp;This paper aims to study the (BK-GHS) property &nbsp; 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 &nbsp;$f$-, $g$-, 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.A new approach to solve intuitionistic fuzzy bi-matrix games involving multiple opinions
https://ijfs.usb.ac.ir/article_7354.html
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.Translate 20-1 February 2023
https://ijfs.usb.ac.ir/article_7355.html
(2105-6671) Some aspects on computation of scalar valued and fuzzy valued integrals over fuzzy domains
https://ijfs.usb.ac.ir/article_7245.html
In this note, we consider the problem of computing a scalar-valued, and also a fuzzy-valued integral over fuzzy spatial domains, which is useful, for instance, to calculate &nbsp;fuzzy areas described by a certain property, allowing the density function to be variable, or evaluate magnitudes in the case where the field function is fuzzily known.(2202-7225) On the first-order autonomous interval-valued difference equations under gH-difference
https://ijfs.usb.ac.ir/article_7246.html
The theory of interval-valued difference equations under gH-difference is an interesting topic, since it can be applied to study numerical solutions to interval-valued or fuzzy-valued differential equations. In this paper, we estimate the number of solutions to a class of first-order interval-valued difference equations under gH-difference, which reveals the complexity of the stability analysis in this area, as well as the difficulty for prediction and control problems. Then, based on the relative positions of initial values and equilibrium points, we provide sufficient conditions for the existence of convergent solutions. We also provide examples to illustrate the validity of our results.(2208-7557) On linearly ordered index sets for ordinal sums in the sense of A. H. Clifford yielding uninorms
https://ijfs.usb.ac.ir/article_7247.html
This paper focuses on the topic of ordinal sums of semigroups in the sense of A. H. Clifford -- a method for constructing a new semigroup from a given system of semigroups indexed by a linearly ordered index set. We completely describe the linearly ordered index set for an ordinal sum of semigroups yielding a uninorm.(2204-7370) Completeness of L-quasi-uniform convergence spaces
https://ijfs.usb.ac.ir/article_7260.html
The aim of this paper is to study the completeness of L-quasi-uniform convergence spaces and L-quasi-uniform spaces. Firstly, we describe L-quasi-uniform convergence spaces as enriched categories. Then we give two kinds of completeness of L-quasi-uniform convergence spaces and show that Lawvere completeness implies Cauchy completeness. Finally, we use the Cauchy completeness of L-quasi-uniform convergence spaces to define the Cauchy completeness of L-quasi-uniform spaces, and show that Cauchy completeness is equivalent to Lawvere completeness in L-quasi-uniform spaces.(2203-7262) Conditional distributivity of continuous triangular norms over 2-uninorms
https://ijfs.usb.ac.ir/article_7261.html
Conditional distributivity of aggregation functions, which has received wide attention from the researchers, is vital for many different fields, for example, integration theory, utility theory and so on. This article is mainly devoted to dealing with the conditional distributivity of continuous t-norms over 2-uninorms. As the first step for investigating the conditional distributivity of 2-uninorms, we give the complete characterization of all pairs $(T,\mathcal{H})$ {fulfilling} this property. Compared to the case of distributivity of continuous t-norms over 2-uniorms, which leads to the 2-uninorm must be idempotent, the results obtained in this paper demonstrate that conditional distributivity and &nbsp;distributivity on this topic, are not equivalent.(2111-7058) A controller design and analysis using asymmetry triangular cloud models
https://ijfs.usb.ac.ir/article_7267.html
The cloud model is one of the mathematical tools that realize the transformation of quantitative information from qualitative data. Therefore, cloud model theory is widely used in computer science, reliability estimation, nonlinear function approximation, controller design, etc. In general, cloud controller design is known to use Gaussian membership clouds. However, it is computationally expensive because membership cloud computing is a nonlinear operation, and it has a disadvantage that it is difficult to decompose the structure of the controller. This paper proposes a new asymmetric triangular cloud model consisting of linear operations instead of Gaussian functions and, on this basis, develops a controller design method to approximate the output of the controlled plant to the desired value. Furthermore, it is demonstrated that the proposed controller is capable of stability analysis even if the mathematical model of the plant is not given, and it is validated by simulation of electrode up and down control of ultra-high power electric arc furnace and stabilization control of inverted pendulum.(2108-6866) The distributivity characterization of idempotent null-uninorms over two special aggregation operators
https://ijfs.usb.ac.ir/article_7281.html
Recently, Zhao et al. \cite{Zhao-2021-25} characterized the distributivity equations of null-uninorms with continuous and Archimedean underlying operators over overlap or grouping functions. Moreover, Liu et al. \cite{Liu-2020-25} studied the distributive laws of continuous t-norms over overlap functions. In this paper, we proceed with the distributivity characterization of idempotent null-uninorms over overlap or grouping functions. In order to do that, we introduce a class of weak overlap and grouping functions with weak coefficients, and obtain the full characterizations of overlap and grouping functions by considering the different values of underlying uninorms' associated functions of idempotent null-uninorms on the interval endpoints and comparing them with the weak coefficients. Obviously, idempotent null-uninorms generalize idempotent uninorms. Thus, the obtained results also generalize the distributivity of idempotent uninorms proposed as future work in \cite{Liu-2020-25}.(2107-6811) A dual probabilistic linguistic MARCOS approach based on generalized Dombi operator for decision-making
https://ijfs.usb.ac.ir/article_7290.html
Dual probabilistic linguistic term sets (DPLTSs) are more powerful compare to probabilistic linguistic term sets, probabilistic hesitant fuzzy sets, hesitant fuzzy sets and intuitionistic fuzzy sets for the reason that they deal with both belongingness grades and non-belongingness grades along with their respective probabilities. On the other hand, the generalized Dombi operators have higher flexibility due to inclusion of two parameters. MARCOS (Measurements alternatives and ranking according to compromise solution) technique was developed by utilizing the utility degrees of options using the ideal and anti-ideal solutions. Here, we combine the merits of generalized Dombi operator and MARCOS and propose a DPL-MARCOS approach under dual probabilistic linguistic setting. In this methodology, the concepts of consistency and similarity between the experts are used to calculate their weights of subjective and objective types, respectively. For aggregating experts' preferences, we propose dual probabilistic linguistic- generalized Dombi weighted averaging aggregation operator. A biomass feedstock selection problem is furnished to show the applicability of our technique. We have considered coconut shell, coffee husk and sugarcane baggage as alternatives. The result shows that coffee husk is the most suitable option. The sensitivity assessment of parameter values reveals that our technique is stable. The comparative study proves that our model is more significant and realistic compare to the existing ones.(2109-6921) Proper process selection during flight schedule disruption using a fuzzy multi-criteria decision-making expert system
https://ijfs.usb.ac.ir/article_7296.html
The aviation industry is a complicated, sensitive, and challenging phenomenon. &nbsp;One of the major issues in the operation of streamlined processes in this industry is the management of proper decisions during the disruption of flight schedules. Such disruptions commonly reduce customer satisfaction and the profitability of the airlines. Since there are multiple reasons for the disruption of the flight schedules along with the different possible decisions, a correct decision is very difficult to make requiring the opinions of the specialist staff. In this research, an expert model using a &ldquo;fuzzy multi-criteria decision-making&rdquo; method is proposed to provide a correct decision during the disruption of the flight schedules. The results show that the most important factors that make disruption of flight schedules are arrival delays and technical failure of the airline fleet. Besides, the most important possible decisions are the announcement of the delay and canceling of the flight. Thanks to utilizing the fuzzy analytical network process, the outcomes of the proposed expert model are in good alignment with the opinions of the specialist staff. The fuzzy analytical network process determines the values of 0.5124 and 0.2621 for the magnitude of the arrival delay and technical defect respectively. This method also determines the values of 0.7042 and 0.2076 for flight delay and flight canceling as the two most important possible decisions.(2204-7365) Some aggregation operators for IVI-octahedron sets and their application to MCDGM
https://ijfs.usb.ac.ir/article_7297.html
In this paper, in order to apply the concept of IVI-octahedron sets to MCDGM problems, we define some aggregation operators via IVI-octahedron sets and obtain some their properties. We &nbsp;define some aggregation operators via IVI-octahedron sets and obtain some their properties. &nbsp;We present a MCGDM method with linguistic variables in IVI-octahedron set environment. Finally, we give a numerical examples &nbsp;for MCGDM problems.(2205-7384) Restricted equivalence functions induced from fuzzy implication functions
https://ijfs.usb.ac.ir/article_7304.html
Restricted equivalence function, as an effective tool for the theoretical research and practical applications of fuzzy sets and systems along with fuzzy logic, has been continuously considered by scholars since it was proposed. In particular, recently, Bustince, Campi\'{o}n, De Miguel et al. (H. Bustince, M.J. Campi\'{o}n, L. De Miguel, E. Indur\'{a}in, Strong negations and restricted equivalence functions revisited: An analytical and topological approach, Fuzzy Sets and Systems (2021), https://doi.org/10.1016/j.fss.2021.10.013.) investigated it using analytical and topological approach and proposed an open problem to ask whether the binary function $F(x,y)=T(I(x,y),I(y,x))$ obtained from a t-norm $T$ and a fuzzy implication function $I$ is a restricted equivalence function or not. In this paper, we pay attention to this problem and give positive answer of it. Specifically, first, we consider the binary functions obtained from overlap functions and fuzzy implication functions by following the construction way of $F$ and get the necessary and sufficient condition that makes such obtained $F$ to be a restricted equivalence function. Second, we introduce the so-called $\heartsuit$-functions, which are binary functions on unit closed interval with few additional axioms and obtain the necessary and sufficient condition that ensures the binary function constructed via any non-decreasing $\heartsuit$-function and fuzzy implication function as the way of $F$ to be a restricted equivalence function. Finally, we give the necessary and sufficient condition that makes $F$ to be a restricted equivalence function.(2206-7441) Designing a sustainable development model for agricultural sector under critical circumstances (COVID-19 Pandemic): A fuzzy approach
https://ijfs.usb.ac.ir/article_7305.html
The COVID-19 pandemic has affected health, economic, and social factors and harmed the distribution and sales of agricultural products. It has become a crucial factor in agricultural development. The purpose of the present study is to design a sustainable development model in the agricultural sector under circuital circumstances (i.e., the COVID-19 pandemic). To achieve this goal of used a combined methodology of grounded theory, the Fuzzy Delphi Method (FDM), the Fuzzy decision-making trial and evaluation laboratory (FDEMATEL) method, and the Fuzzy decision-making trial and evaluation laboratory-based analytic network process (FDANP) method. The criteria of higher importance were identified using grounded theory and FDM. Then, the fuzzy DEMATEL method was carried out to identify internal relationships, effects, and dependencies of the main criteria. Finally, the weight of the main criteria of the model has been calculated with the Fuzzy DANP method. According to the results of the Fuzzy DEMATEL method, Critical circumstances (COVID-19), environmental factors, educational factors, health factors, and economic factors had the highest effects. The &ldquo;critical circumstances&rdquo; criterion (COVID-19) had the largest effect and strongest relationship with the other criteria. On the other hand, the results of the Fuzzy DANP method show that environmental factors (MC7), social factors (MC2), critical circumstances (COVID-19) (MC5), health factors (MC1), entrepreneurial factors (MC8), are the most important criteria of the sustainable development model of the agricultural sector under critical circumstances. Therefore, to move on the path of sustainable development in the agricultural sector, one should focus on the factors that have a higher influence and importance.(2206-7472) On existence and stability results to fuzzy Caputo fractional differential inclusions driven by fuzzy mixed quasivariational inequalities
https://ijfs.usb.ac.ir/article_7313.html
In this paper, we consider a generalized fuzzy differential system (GFDS) consisting of a fuzzy Caputo fractional differential inclusion &nbsp; &nbsp;combined with a fuzzy mixed quasivariational inequality. The GFDS has been known as a framework of fuzzy fractional differential quasivariational inequalities involving Caputo fractional derivatives. First, we verify the existence of solutions for the fuzzy mixed quasivariational inequality by using the Kakutani-Fan-Glicksberg fixed point theorem. Then, the existence of mild solutions for the GFDS is also obtained under some mild conditions. Finally, the upper semicontinuity of the solution mapping to the GFDS provided in the case of the perturbed &nbsp; &nbsp;parameters is discussed.(2205-7400) Weighted K-nearest neighbors classification based on Whale optimization algorithm
https://ijfs.usb.ac.ir/article_7314.html
K-Nearest Neighbors (KNN) is a classification algorithm based on supervised machine learning, which works according to a voting system. The performance of the KNN algorithm depends on different factors, such as unbalanced distribution of classes, the scalability problem, and considering equal values for all training samples. Regarding the importance of the KNN algorithm, different improved versions of this algorithm are introduced, such as fuzzy KNN, weighted KNN, and KNN with variable neighbors. In this paper, a weighted KNN based on Whale Optimization Algorithm is proposed for the objective of increasing the level of detection accuracy. The proposed algorithm devotes a weight to each training sample of every feature by employing the WOA to explore the optimized weight matrix. The algorithm is implemented and experimented on five standard datasets. The evaluation results prove that the proposed algorithm performs better than both weighted KNN based on the Genetic Algorithm (GA) and the classic KNN algorithm.(2108-6875) Fuzzy accompanied approximation space under fuzzy relation
https://ijfs.usb.ac.ir/article_7358.html
If there is a fuzzy relation $\widetilde{R}$ between two spaces $U$ and $V$, the fuzzy approximations in both spaces based on $\widetilde{R}$ are widely studied, and they basically reflect only the influence from one space to another. In this paper, on each space of $U$ and $V$, two new fuzzy relations are derived from $\widetilde{R}$, a positive low-value relation and a conservative high-value relation, to reflect the interaction and feedback between the two spaces. So, the fuzzy approximations based on them can reflect the combination of the action and the reaction from one space to another. Therefore, two spaces $U$ and $V$ are closely accompanied, and $(U, V, \widetilde{R})$ is a whole, so it is called a fuzzy accompanied approximation space (FAAS). In a FAAS, the properties of the fuzzy approximation models on each space are studied, the relationships between fuzzy approximation models of two spaces are researched, and examples to show how the approximation operator models in the FAAS to solve practical problems from multiple perspectives are also illustrated. More importantly, when the fuzzy relation $\widetilde{R}$ is a binary relation $R$ or the two spaces are the same, the special cases of FAAS are investigated and some important new models and new results are obtained, which add new ideas and methods to the current research.(2207-7533) The general algebraic solution of fuzzy linear systems based on a block representation of {1}-inverses
https://ijfs.usb.ac.ir/article_7364.html
A new method for solving a fuzzy linear system (FLS), AX&tilde;=Y&tilde;, where the coefficient matrix A is an arbitrary real matrix is obtained. A necessary and sufficient condition for the R-consistency of the associated system of linear equations is obtained, related to its representative solutions. &nbsp;Moreover, the general form of representative solutions of such linear systems is presented. The straightforward method for solving m&times;n FLS based on an arbitrary {1}-inverse of A is introduced. This method is illustrated by interesting examples.(2204-7351) A new extension of a triangular norm on a subinterval [0, ∝] via an Interior operator to the underlying entire bounded lattice
https://ijfs.usb.ac.ir/article_7373.html
As a proper generalization of the ordinal sum t-norm construction on bounded lattices proposed in [E. A\c{s}{\i}c{\i}, R. Mesiar, New constructions of triangular norms and triangular conorms on an arbitrary bounded lattice, International Journal of General Systems, 49(2) (2020), 143-160], the present paper studies a new extension of a triangular norm on a subinterval [0,&prop;] via an interior operator to the underlying entire bounded lattice, where the necessary and sufficient conditions under which the constructed operation is again a t-norm are given. By comparing the graphic structures of two t-norms on a common bounded lattice which are constructed in different ways, it is shown that the new method in this paper is essentially different from the ones existing in the literature. As an end, this new construction is generalized to construct ordinal sums of finitely many t-norms by recursion on bounded lattices. The dual results for ordinal sum construction of t-conorms via closure operators on bounded lattices are also presented.