Iranian Journal of Fuzzy Systems
https://ijfs.usb.ac.ir/
Iranian Journal of Fuzzy Systemsendaily1Fri, 01 Dec 2023 00:00:00 +0330Fri, 01 Dec 2023 00:00:00 +0330Interval-valued q-rung orthopair fuzzy integrals and their application in multi-criteria group decision making
https://ijfs.usb.ac.ir/article_7627.html
The generalized interval-valued orthopair fuzzy sets provide an extension of Yager&rsquo;s generalized orthopair fuzzy sets, where membership and non-membership degrees are subsets of closed interval [0, 1]. Due to the uncertainty and ambiguity of real life, it is more superior for decision makers to provide their judgments by intervals rather than crisp numbers. Moreover, in the era of huge scale and rapid updating of information, individual weights have been quietly diluted, and the integration of information one by one is time-consuming and complicated. In recent years, some&nbsp; cholars have conducted research on the calculus of generalized orthopair fuzzy sets, but no research has further revealed the intrinsic connection between the integrals of generalized interval-valued orthopair fuzzy sets and traditional aggregation operators, which is very important in applications such as large group decision making. In order to fill this theoretical gap, this paper aims to study the integrals of generalized interval-valued orthopair fuzzy functions. In detail, we define the indefinite integral starting from the inverse operations of the interval-valued q-rung orthopair fuzzy functions&nbsp; (IVq-ROFFs)&rsquo; derivatives, and some fundamental properties with rigorous mathematical proofs are also discussed. To be more&nbsp; practical, we continue to develop definite integrals for both simplified and generalized IVq-ROFFs. Besides, we give the corresponding Newton-Leibniz formula through limit procedure, which shows the calculation relationship between the&nbsp; indefinite and definite integrals of the IVq-ROFFs. After obtaining the basic calculus results under generalized interval-valued orthopair fuzzy circumstance, we further reveal the inherent link between the integrals of generalized IVq-ROFFs and the traditional discrete aggregation operators. Finally, the practicability and feasibility of the proposed definite&nbsp; integral models are illustrated by an example of public health emergency group decision-making, and sensitivity analysis and comparison are also carried out.&nbsp;Divisible associative aggregation operations on finite chains
https://ijfs.usb.ac.ir/article_7756.html
There exist several versions of discrete counterpart of continuity in the framework of finite chains, e.g., the smoothness, the divisibility, intermediate-value property and the 1-Lipschitz property. In this paper, we first discuss the relationships among the smoothness, divisibility, intermediate-value property and 1-Lipschitz property. Second, we present complete characterizations of divisible associative aggregation operations on finite chains.Fuzzy approximation of a fractional Lorenz system and a fractional financial crisis
https://ijfs.usb.ac.ir/article_7628.html
Our aim in this paper is to study the fuzzy stability of a fractional Lorenz system in the sense of the Caputo-Fabrizio derivative and a fractional financial crisis in the sense of }&minus;Hilfer derivative. Defining a new type of fuzzy control function that has a dynamic situation helps us to investigate new stability results for these mathematical models.New intuitionistic fuzzy operations, operators and topological structures
https://ijfs.usb.ac.ir/article_7629.html
Two new intuitionistic fuzzy operations (union and intersection) are defined. Based on them, two new topological operators (of a closure and of an interior types) are introduced. Some properties of these obects are studied. Based on them, four new intuitionistic fuzzy topological structures are introduced and some of their properties are discussed. Integral forms of both new intuitionistic fuzzy operations and of both intuitionistic fuzzy operators are given.&nbsp;Unsupervised feature selection: A fuzzy multi-criteria decision-making approach
https://ijfs.usb.ac.ir/article_7630.html
Feature selection (FS) has shown remarkable performance in decreasing the dimensionality of high-dimensional datasets by selecting a good subset of features. Labeling high-dimensional data can be expensive and time-consuming as labeled samples are not always available. Therefore, providing effective unsupervised FS methods is essential in machine learning. This article provides a fuzzy multi-criteria decision-making method for unsupervised FS in which an ensemble of unsupervised FS rankers is utilized to evaluate the features. These methods are aggregated based on a fuzzy TOPSIS method. This is the first time a fuzzy multi-criteria decision-making approach has been used for an FS problem. Multiple comparisons are made to show the optimality and effectiveness of the proposed strategy against multiple competing FS methods. Our approach regarding two classification metrics, F-score and accuracy, appears superior to comparable&nbsp; strategies. Also, it is performing so swiftly.&nbsp;&nbsp;Completions of ⊤-quasi-Cauchy spaces
https://ijfs.usb.ac.ir/article_7631.html
In the category of ⊤-quasi-Cauchy spaces, completeness and completion can be studied in a non-symmetric framework encompassing ⊤-quasi-uniform (limit) spaces. Based on constructions by E.E. Reed in the category of Cauchy spaces and, recently, by L. Reid and G. Richardson in the category of ⊤-Cauchy spaces, we give a family of completions for a non-complete ⊤-quasi Cauchy space. As particular instances we study pretopological and topological completions of ⊤-quasi-Cauchy spaces.Analyzing of process capability indices under uncertain information and hesitancy by using Pythagorean fuzzy sets
https://ijfs.usb.ac.ir/article_7632.html
Process capability analysis (PCA) is a completely effective statistical tool for ability of a process to meet predetermined specification limits (SLs). Unfortunately, especially the real case problems include many uncertainties, it is one of the critical necessities to define the parameters of PCIs by using crisp numbers. So, the results obtained may be incorrect, if the PCIs are calculated without taking into account the uncertainty. To overcome this problem, the fuzzy set theory (FST) has been successfully used to design of PCA. We also know that fuzzy set extensions have an important role in modelling the case that include uncertainty, incomplete and inconsistent information and they are more powerful than traditional FST to model uncertainty. Defining of main parameters of PCIs such as SLs, mean (&micro;) and variance (&sigma;2) by using the flexible of fuzzy set extensions rather than precise values due to uncertainty, time, cost, inspectors hesitancy and the results based on fuzzy sets for PCIs contain more, flexible and&nbsp; sensitive information. In this study, two of well-known PCIs called Cp and Cpk have been re-designed at the first time by using one of fuzzy set extensions named Pythagorean fuzzy sets (PFSs). Defining PCIs with more than one membership function instead of an only one membership function is enabling to evaluate the process more&nbsp; broadly more flexibility. For this aim, the main parameters of PCIs have been defined&nbsp; and analyzed by using PFSs. Finally, four new PCIs based on PFSs such as Csp, Cspk, Cfp and Cfpk have been derived. The proposed new PCIs based on PFSs have been also applied on manufacturing process and capability for gears have been analyzed. It is shown that the flexibility of the PFSs on PCIs enables the PCA to give more realistic,&nbsp; more sensitive, and more comprehensive results.&nbsp;&nbsp;Equivalent axioms of M-fuzzifying convex matroids
https://ijfs.usb.ac.ir/article_7633.html
In this paper, our aim is to present some characterizations of M-fuzzifying convex matroids. First we discuss the relation between M-fuzzifying convex matroids and M-fuzzy families of dependent sets. Secondly, we give characterizations of M-fuzzifying convex matroids by M-fuzzifying rank functions. Finally we discuss the relation between two concept of M-fuzzifying hull (closure) operators.Methods for obtaining uninorms on some special classes of bounded lattices
https://ijfs.usb.ac.ir/article_7660.html
In this article, we go on to discuss the structure of uninorms on bounded lattices. We suggest two techniques to yield&nbsp; uninorms with some constraints on the identity element by applying that the t-norms and t-conorms are always present on the considered bounded lattices. These techniques ensure new approaches for getting idempotent uninorms on bounded lattices when regarding infimum t-norm and supremum t-conorm. Furthermore, we display the distinctness between our new construction techniques and the published ones.&nbsp;Radical of filters on hoops
https://ijfs.usb.ac.ir/article_7661.html
In this paper, by using the notion of prime filter, we show representation theorem of hoops and we prove that every nontrivial &or;-hoop is a subdirect product of hoop-chains. In the following, by using the concept of maximal filter of hoops, we introduce radical of hoops. Then some equivalence definitions of it and some related properties are investigated. Then by using this notion, we introduce the concepts of r-filters and p-filters on hoops and the relation between them and other filters of hoops are investigated. Finally, by using p-filters on hoops, we define new open sets on hoop that could be used to construct a Zarisky topology.&nbsp;A study of BL-algebras by UC-filters
https://ijfs.usb.ac.ir/article_7668.html
In this article, with the aim of further investigating BL-algebras, the concepts of Unity Co-annihilator-filters (UC-filters) is introduced and discussed. Also, for the faster study of UC-filters in BL-algebras, some equivalent conditions are obtained, and (with some examples) it is shown that these filters have differences. In addition, we consider several additional&nbsp; conditions imposed on UC-filters and prime filters and establish links between them. So, we get relationships between&nbsp; these types of filters and prime filters in BL-algebras. Finally, the form of all UC-saturated &or;-closed subsets of a G- algebras (by the concept of UC-saturated &or;-closed subsets) is stated.Solving fully linear programming problem based on Z-numbers
https://ijfs.usb.ac.ir/article_7669.html
Generally exploring the exact solution of linear programming problems in which all variables and parameters are&nbsp; Z-numbers, is either not possible or difficult. Therefore, a few numerical methods to find the numerical solutions do act an&nbsp; important role in these problems. In this paper, we concentrate on introducing a new numerical method to solve such&nbsp; problems based on the ranking function. After proving the necessary theories, for more illustrations and the correctness&nbsp; of the topic, some theoretical and practical examples are also provided. Finally, the results obtained from the proposed&nbsp; method have been compared with some existing methods.Subcategories of the category of stratified $(L,M)$-semiuniform convergence tower spaces
https://ijfs.usb.ac.ir/article_7735.html
In this paper, we propose the concepts of stratified (L,M)-semiuniform convergence spaces and stratified (L,M)-semiuniform limit tower spaces. It is shown that (1) the category S(L,M)-SUC of stratified (L,M)-semiuniform convergence spaces can be embedded in the category S(L,M)- SUCT of stratified (L,M)-semiuniform convergence tower spaces as a bireflective subcategory; (2) the full subcategory of S(L,M)-SUCT, consisting of stratified (L,M)-semiuniform limit tower spaces is strongly Cartesian closed; (3) the category S(L,M)-FT of stratified (L,M)-filter tower spaces can be embedded in the category S(L,M)-SUCT as a simultaneously bireflective and bicoreflective subcategory.(2208-7564) Idempotent semi-t-operators on bounded lattices
https://ijfs.usb.ac.ir/article_7507.html
As a generalization of nullnorms, semi-t-operators are interesting both in theory and practical applications. In this paper, we investigate some properties of idempotent semi-t-operators on bounded lattices. Furthermore, we propose two construction methods of idempotent semi-t-operators on bounded lattices containing only two different elements which are incomparable with a but comparable with b. These methods are the generalization of several known ones in the literature.(2108-6889) Adaptive non-singular fast terminal sliding mode control and synchronization of a chaotic system via interval type-2 fuzzy inference system with proportionate controller
https://ijfs.usb.ac.ir/article_7625.html
This paper introduces a novel adaptive nonsingular fast terminal sliding mode approach that benefits from an interval type-2 fuzzy logic estimator and a gain for control and synchronization of chaotic systems in the presence of uncertainty. The nonsingular fast terminal sliding mode controller is developed to increase the convergence rate and remove the singularity problem of the system. Using the proposed method, the finite-time convergence has been ensured. To eliminate the chattering phenomenon in the conventional sliding mode controller, the discontinuous sign function is estimated using an interval type-2 fuzzy inference system (FIS) based on the center of sets type reduction followed by defuzzification. By adding the proportionate gain to the interval type-2 FIS, the robustness and speed of the controller system is enhanced. An appropriate Lyapunov function is utilized to ensure the closed-loop stability of the control system. The performance of the controller is evaluated for a nonlinear time-varying second-order magnetic space-craft chaotic system with different initial conditions in the presence of uncertainty. The simulation results show the efficacy of the proposed approach for the tracking control problems. The time and frequency domain analysis of the control signal demonstrates that the chattering phenomenon is successfully diminished(2205-7386) Identification of cement rotary kiln using type 2 Takagi-Sugeno neuro-fuzzy system considering the effect of different noisy condition
https://ijfs.usb.ac.ir/article_7653.html
A Cement rotary kiln is the main part of the cement production process, which has always attracted many researchers&rsquo; attention. However, this complex nonlinear system has not been modeled efficiently, which can make an appropriate performance, especially in noisy condition. In this work, the type 2 Takagi-Sugeno neuro-fuzzy system (T2TSNFS) is used to identify the cement rotary kiln, and the gradient descent (GD) algorithm is applied for tuning the parameters of antecedent and consequent parts of fuzzy rules. In addition, the optimal inputs of the system are selected by the genetic algorithm (GA) to achieve less complexity in the fuzzy system. The data relating to the Saveh White Cement (SWC) factory is used in the simulations. The Results demonstrate that the proposed identifier has an appropriate performance in noisy conditions. Furthermore, in this work, T2TSNFS is evaluated in noisy conditions, which had not been worked out before in related research works. Also, T2TSNFS and type 1 Takagi-Sugeno neuro-fuzzy system (T1TSNFS) are compared. The simulations show that T2TSNFS has more proper performance when the standard deviation of noise increases.(2201-7210) A bilevel linear programming model with interval type-2 triangular fuzzy numbers
https://ijfs.usb.ac.ir/article_7675.html
In the real world, the parameters of a problem may not be the crisp values. The fuzzy theory among the theories in which uncertainty plays a crucial role. Type-2 fuzzy sets generalize fuzzy sets. We consider a special type of such sets here.In this paper, we consider two issues. First, we review the method proposed by Javanmard and Mishmast Nehi for solving an interval type-2 triangular fuzzy linear programming problem, and improve it.Then, we express a bilevel linear programming problem, that, to the best of our knowledge, has not been investigated so far.We consider the bilevel linear programming problem with uncertainty where all the coefficients in the problem are interval type-2 triangular fuzzy numbers.We convert an interval type-2 triangular fuzzy bilevel linear programming problem into an interval bilevel linear programming problem using Grzegorzewski's nearest interval approximation method.Finally, we obtain five problems, and by solving them, we achieve the solution of interval type-2 triangular fuzzy bilevel linear programming problem as an interval type-2 triangular fuzzy number.( 2301-7844 ) Characterizing three classes of idempotent uninorms on a bounded lattice
https://ijfs.usb.ac.ir/article_7685.html
This study presents characterizations of three classes of idempotent uninorms on a bounded lattice by the orders of their associated meet-semilattices. The first one is the class of internal uninorms, the second one is the class of idempotent uninorms defined on a lattice in which all elements are comparable with the corresponding neutral element and the third one is the class of idempotent uninorms defined on a lattice in which a single point is incomparablewith the corresponding neutral element.(2207-7510) Grouping fuzzy granular structures based on k-means and fuzzy c-means clustering algorithms in information granulation
https://ijfs.usb.ac.ir/article_7689.html
Fuzzy information granulation theory is based on the way humans granulate and reason about information, and it is essential to the remarkable ability of people to act logically in ambiguous and uncertain situations. In the study of fuzzy information granulation, instead of discussing single fuzzy granules, it is common to consider a fuzzy granular structure arising from a set of fuzzy information granules. Different approaches and perspectives may generate different fuzzy granular structures in the same universe by dividing the object into a number of meaningful fuzzy information granules. However, a specific task usually requires only a selection of representative fuzzy granular structures. Therefore, the main aim of this paper is to group fuzzy granular structures efficiently and accurately. To this end, we first introduce the distances between two fuzzy granular structures and illustrate the relevant properties. Subsequently, k-means and fuzzy c-means clustering algorithms are designed for clustering fuzzy granular structures, and their convergence is demonstrated. In this way, similar fuzzy granular structures can be grouped into the same class. In addition, two evaluation indicators, dispersion and separation, are constructed to evaluate the effect of clustering fuzzy granular structures. Experiments on 12 publicly available datasets demonstrate the feasibility and effectiveness of the proposed algorithms.(2210-7713) Immediate consequences operator through ordered weighted average operators
https://ijfs.usb.ac.ir/article_7696.html
The immediate consequences operator has been a widely studied and used operator for defining the semantics of a &nbsp;logic program. For instance, it has been considered in the fuzzy case for handling datasets with &nbsp;imperfect, imprecise or vague information.The natural generalization of this operator to the mentioned fuzzy framework is based on the supremum operator, which preserves the strict nature of the universal quantifier.As a consequence, errors in the data, which are usual in the uncertainty environment of the considered dataset, can cause loss of information. This is the main reason why this paper makes different generalizations of this operator by using weighted aggregation operators and &nbsp;introducing interesting results.(2302-7881) Finite-time stability results for fuzzy fractional stochastic delay system under Granular differentiability concept
https://ijfs.usb.ac.ir/article_7719.html
In present manuscript, we investigate a new type of fuzzy fractional stochastic delay system (FFSDS), in which the derivative is defined by Granular differentiability. We first transform the considered system into an equivalent integral system with the aid of fuzzy Laplace transformation and its inverse involving Mittag-Leffler function. Subsequently, existence and uniqueness results of the solutions for FFSDS are derived by applying Carath\'{e}odory approximation, under non-Lipschitz conditions, and contradiction method, respectively. \textcolor{black}{In addition, we establish the finite-time stability of the system by utilizing the generalized Gr\"{o}nwall delay inequality. Finally, the obtained conclusions are expound via an example.(2210-7692) Ranking intuitionistic fuzzy numbers by relative preference relation
https://ijfs.usb.ac.ir/article_7721.html
Ranking fuzzy numbers(FNs) was a critical issue in fuzzy computing field. Generally, triangular FNs, trapezoidal FNs, and even interval-valued FNs(IVFNs) were often expressed in ranking. However, ranking intuitionistic FNs(IFNs) were less mentioned due to the complicated components in membership functions. Herein, we will develop fuzzy binary relation that is an extended fuzzy preference relation(EFPR) to express the preference degree of two IFNs, and then the relation is improved to be a relative preference relation(RPR) used to rank a set of IFNs. Since EFPR on IFNs is a total ordering relation, RPR will be also a total ordering relation. Based on belonging and non-belonging components of membership functions in IFNs, using EFPR being also fuzzy preference relation(FPR) is suitable to compare FNs on pairwise, but time complexity on fuzzy operation of comparison computing is complicated. Hence, RPR is developed to avoid comparing on pairwise. Through yielding RPR values for a set of IFNs, IFNs are effectively and efficiently ranked to utilize related decision-making problems.(2303-7961) The g-sum of two posets and its application to construct idempotent uninorms
https://ijfs.usb.ac.ir/article_7833.html
In this study, a new method, called g-sum, is presented to join two posets together that generalizes the linear sum oftwo posets. Idempotent uninorms on a bounded chain are in one-to-one correspondence with special linear orders on itand g-sum can be used to construct such special linear orders.&nbsp;(2302-7893) Improving the genetic algorithm in fuzzy cluster analysis for numerical data and its applications
https://ijfs.usb.ac.ir/article_7834.html
This study proposes an automatic genetic algorithm in fuzzy cluster analysis for numerical data. In this algorithm, anew measure called the FB index is used as the objective function of the genetic algorithm. In addition, the algorithmnot only determines the appropriate number of groups but also improves the steps of traditional genetic algorithmas crossover, mutation and selection operators. The proposed algorithm is shown the step by step throughout thenumerical example, and can perform fast by the established Matlab procedure. The result from experiments show thesuperiority of the proposed algorithm when it overcomes the existing algorithms. Moreover, it has been applied inrecognizing the image data, and building the fuzzy time series model. These show the potential of this study for manyreal applications of the different fields.(2302-7899) Characterizations for the alpha-cross-migrativity of continuous t-conorms over generated implications
https://ijfs.usb.ac.ir/article_7838.html
The &alpha;-cross-migrativity can be regarded as weaker form of the commuting equation. It has been extensively investigatedbetween some aggregation functions including t-norms, overlap functions, uninorms, and semi-t-operators. Recently,Fang [10] has proposed the &alpha;-cross-migrativity of t-conorms over fuzzy implications. This paper continues to considerthis research topic and mainly focuses on the fuzzy implications generated by additive (resp. multiplicative) generatorsof continuous Archimedean t-norms and t-conorms. Full characterizations for the &alpha;-cross-migrativity of continuoust-conorms over (f, g)-, k-, h- and (&theta;, t)-generated implications are obtained. Moreover, some supporting examples forsolutions are given.(2208-7606) A Robust Fuzzy Clustering Model for Fuzzy Data Based on an Adaptive Weighted L1-Norm
https://ijfs.usb.ac.ir/article_7839.html
The imprecision related to measurements can be managed in terms of fuzzy features, which are characterized by twocomponents: Center and spread. Outliers affect the outcome of the clustering models. In trying to overcome thisproblem, this paper proposes a fuzzy clustering model for L-R fuzzy data, which is based on a dissimilarity measurebetween each pair of fuzzy data defined as an adaptive weighted sum of the L1-norms of the centers and the spreads.The proposed method is robust based on the metric and weighting approaches. It estimates the weight of a given fuzzyfeature on a given fuzzy cluster by considering the relevance of that feature to the cluster; if outlier fuzzy features arepresent in the dataset, it tends to assign them weights close to 0.To deeply investigate the capability of our model, i.e., alleviating undesirable effects of outlier fuzzy data, we providea wide simulation study. We consider the ability to classify correctly and the ability to recover the true prototypes,both in the presence of outliers. The comparison made with other existing robust methods indicates that the proposedmethodology is more robust to the presence of outliers than other methods. Moreover, the performance of our methoddecreases more slowly than others when the percentage of outliers increases. An application of the suggested methodto a real-world categorical dataset is also provided.( 2304-8012 ) Intuitionistic fuzzy type basic uncertain information
https://ijfs.usb.ac.ir/article_7840.html
Recently, a new paradigm for uncertain information has been proposed that can effectively handle various types ofuncertainty in decision-making problems. This approach utilizes a certainty degree, which is represented by a realnumber indicating the level of certainty associated with input values. However, just like intuitionistic fuzzy informationcan handle more problems that cannot be well modeled by fuzzy information, the certainty degree in basic uncertaininformation can also be intuitionistic fuzzy granule, which allows it to handle more uncertainty involved decision makingsituations. In this paper, we introduce the concept of intuitionistic fuzzy type basic uncertain information and explainits parameters. We also define a weighted arithmetic mean for aggregating this type of information and discuss differentapproaches for allocating induced weights based on trust preferred preference from four perspectives: (i) preference forhigher certainty degrees; (ii) aversion to higher levels of uncertainty; (iii) preference for greater differences in certaintydegrees; and (iv) preference for intuitionistic fuzzy certainties. Additionally, we explore trichotomic rules-based decisionmaking using intuitionistic fuzzy type basic uncertain information. Finally, we present an objective-subjective evaluationnumerical example utilizing these methods.(2302-7915) An adaptive image encryption scheme guided by fuzzy models
https://ijfs.usb.ac.ir/article_7876.html
A new image encryption scheme using the advanced encryption standard (AES), a chaotic map, a genetic operator, and a fuzzy inference system is proposed in this paper. In this work, plain images were used as input, and the required security level was achieved. Security criteria were computed after running a proposed encryption process. Then an adaptive fuzzy system decided whether to repeat the encryption process, terminate it, or run the next stage based on the achieved results and user demand. The SHA-512 hash function was employed to increase key sensitivity. Security analysis was conducted to evaluate the security of the proposed scheme, which showed it had high security and all the criteria necessary for a good and eﬀicient encryption algorithm were met. Simulation results and the comparison of similar works showed the proposed encryptor had a pseudo-noise output and was strongly dependent upon the changing key and plain image.