Iranian journal of fuzzy systems
Volume:20 Issue: 5, Sep-Oct 2023

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 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.

A Cement rotary kiln is the main part of the cement production process, which has always attracted many researchers’ 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.

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.

The immediate consequences operator has been a widely studied and used operator for defining the semantics of a  logic program. For instance, it has been considered in the fuzzy case for handling datasets with  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  introducing interesting results.

This research suggests a novel controller capable of achieving satisfactory tracking control performance for a class of multiple-input multiple-output (MIMO) systems. It aims to approximate an impracticable ideal controller to design directly due to insufficient knowledge about the plant or lack of data. The primary control unit is a function-link fuzzy cerebellar model articulation controller (FLFCMAC), applying the technique for order of preference by similarity to the ideal solution (TOPSIS) to eliminate less dominant rules in the fuzzy inference engine. A Function-link network (FLN) is added to this controller to enhance the tracking performance. Moreover, an interval type-2 fuzzy logic controller (IT2FLC) is proposed to improve the closed-loop system performance. Due to the caterpillar robot’s highly nonlinear dynamics and undesirable factors such as external disturbance and parametric uncertainties, online tuning laws are offered. In other words, the control system is designed to be robust. A Lyapunov stability approach is presented to show the stability of the controlled nonlinear plant. Furthermore, the adaptation laws are derived through this approach. Finally, numerical simulations are employed to validate the effectiveness and robustness of the controller for the caterpillar robot and the inverted double pendulum.

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 incomparable
with the corresponding neutral element.

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.

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.

This study introduces the Choquet integral of fuzzifying functions with respect to a fuzzy measure. To express various phenomena or ambiguous values in many applications may not be enough to show them as a function, in which case a fuzzifying function can be applied to achieve better expressions or flexibility for given function values. To apply Choquet integrals of fuzzifying functions, we consider Choquet integrals of interval-valued functions as an operator which are α-level functions of fuzzifying functions. In this study, we investigate some properties of Choquet integral of fuzzifying functions and present their applications. As part of this, a series of relevant examples and their subsequent applications are provided, along with the fuzzification of two integrands: a probability density function (PDF) and a utility function.

In this study, a new method, called g-sum, is presented to join two posets together that generalizes the linear sum of two posets. Idempotent uninorms on a bounded chain are in one-to-one correspondence with special linear orders on it and g-sum can be used to construct such special linear orders.

This study proposes an automatic genetic algorithm in fuzzy cluster analysis for numerical data. In this algorithm, a new measure called the FB index is used as the objective function of the genetic algorithm. In addition, the algorithm not only determines the appropriate number of groups but also improves the steps of traditional genetic algorithm as crossover, mutation and selection operators. The proposed algorithm is shown the step by step throughout the numerical example, and can perform fast by the established Matlab procedure. The result from experiments show the superiority of the proposed algorithm when it overcomes the existing algorithms. Moreover, it has been applied in recognizing the image data, and building the fuzzy time series model. These show the potential of this study for many real applications of the different fields.

Recently, a new paradigm for uncertain information has been proposed that can effectively handle various types of uncertainty in decision-making problems. This approach utilizes a certainty degree, which is represented by a real number indicating the level of certainty associated with input values. However, just like intuitionistic fuzzy information can handle more problems that cannot be well modeled by fuzzy information, the certainty degree in basic uncertain information can also be intuitionistic fuzzy granule, which allows it to handle more uncertainty involved decision making situations. In this paper, we introduce the concept of intuitionistic fuzzy type basic uncertain information and explain its parameters. We also define a weighted arithmetic mean for aggregating this type of information and discuss different approaches for allocating induced weights based on trust preferred preference from four perspectives: (i) preference for higher certainty degrees; (ii) aversion to higher levels of uncertainty; (iii) preference for greater differences in certainty degrees; and (iv) preference for intuitionistic fuzzy certainties. Additionally, we explore trichotomic rules-based decision making using intuitionistic fuzzy type basic uncertain information. Finally, we present an objective-subjective evaluation numerical example utilizing these methods.