Iranian journal of fuzzy systems
Volume:18 Issue: 6, Nov-Dec 2021

Positive homogeneity is represented as a constraint 0-homogeneity and generalized into z-homogeneity, called also z-end point linearity. Several special z-homogeneous aggregation functions are studied, in particular semicopulas, quasi-copulas, copulas, overlap functions, etc.

This paper studies the fixed-time synchronization problem of fuzzy stochastic cellular neural networks (FSCNNs) with discrete and distributed delay. Compared with the finite-time synchronization in the existing literature, the fixed-time synchronization of FSCNNs is studied for the first time, and the convergence time obtained does not depend on the upper bound of the initial value of the system. In addition, two kinds of control are designed, one is feedback control and the other is adaptive control. Besides, it is the first time to achieve fixed-time synchronization of FSCNNs via adaptive control. Finally, two numerical examples are also proposed to illustrate the practicability and validity of the results we proposed.

In this paper, the conception of centroid of $n$-dimensional fuzzy number is introduced viaregarding its membership function as the density function on its support set, and some properties of it are obtained. Compared with the mean of the multi dimensional fuzzy number, the centroid takes into account the overall relationship between the edge membership functions of the membership function of the multi dimensional fuzzy number. Therefore, it can approximate (characterize) the fuzzy number more objectively and reasonably than using the mean of the multi dimensional fuzzy number. The most important work of this paper is that for two special kinds of multi dimensional fuzzy numbers (fuzzy $n$-cell numbers and fuzzy $n$-ellipsoid numbers), we respectively give calculation formulas, which can be used conveniently in application since the formulas are based on a definite integral of the level set functions of the multi dimensional fuzzy number on the unit interval $[0,1]$, rather than the multiple integral of the membership function of the multi dimensional fuzzy number itself on its support set. Then, by using the calculation formulas, we obtain another special property of the centroid for fuzzy $n$-cell number and fuzzy $n$-ellipsoid number. Finally, as an example of application, by using the centroid of multi dimensional fuzzy number, we define a fuzzy order on $n$-dimensional fuzzy number space, which can be used to rank uncertain or imprecise multichannel digital information.

Several fuzzy topologies are defined and studied by different authors. In this article, we unify five of the most common fuzzy topologies existing in the literature, as well as the standard topology. This is done by introducing the notion of structural topology on objects in a category and proving that topologies on a set as well as fuzzy topologies on fuzzy sets and fuzzy topologies on fuzzy subsets are all structural topologies. We also introduce the notion of structural continuity and we show that the fuzzy continuity defined in the literature in all the above mentioned cases, as well as the standard continuity are structural.

In this paper, a new definition of a fuzzy k-pseudo metric is introduced and its induced fuzzifying structures are constructed, such as a fuzzifying neighborhood system, a fuzzifying topology, a fuzzifying closure operator, a fuzzifying uniformity. Besides, it is shown that there is a one-to-one correspondence between fuzzy k-pseudo metrics and nests of crisp k-pseudo metrics.

In real-world data deluge, due to insignificant information and high dimension, irrelevant and redundant attributes reduce the ability of experts both in predictive accuracy and speed, respectively. Attribute selection is the notion of selecting those attributes that are essential as well as enough to specify the target knowledge preferably. Fuzzy rough set-based approaches play a crucial role in selecting relevant and less redundant attributes from a high-dimensional dataset. Intuitionistic fuzzy set-based approaches can handle uncertainty as it gives an additional degree of freedom when compared to fuzzy approaches. So, it has a more flexible and practical ability to deal with vagueness and noise available in the information system. In this paper, we introduce two new robust approaches for attribute selection based on intuitionistic fuzzy rough set theory using the concepts of Different Classes ratio and Laplace Summation operator. Firstly, Different Classes ratio and Laplace Summation operator based lower andupper approximations are established based on intuitionistic fuzzy rough set concept. Moreover, we present algorithms and illustrative examples for a better understanding of our approaches. Finally, experimental analysis is performed on some real-valued datasets for attribute selection and classification accuracies.

In the design of recommender systems, it is believed that the set of reviews written by a user can somehow reveal his/her interests, and the content of an item can also be implied from its corresponding reviews. The present study attempts to model both the users and the items via extracting key information from the existing textual reviews. Based on this information, a fuzzy rule-based classifier is designed and tuned, which aims to predict whether a typical user will be interested in a typical item or not. For this purpose, the set of all reviews belonging to a user are mapped to a vector representing the user's interests. Similarly, the set of reviews written by different users over an item are merged and mapped to a vector representing the item. By conjoining these two vectors, a longer vector is obtained which will be used as the input of the classifier. To optimize the classifier, an adaptive approach is suggested and rule-weight learning is carried out, accordingly. The performance of the proposed fuzzy recommender system was evaluated on the Amazon dataset. Experimental results narrate from the promising classification ability of the proposed recommender system compared to state of the art.

Acceptance sampling plans (ASPs) offer inspection of a small set of items from a lot within a predefined plan to procure a certain output quality level with minimum cost in terms of time, effort, and damage to the inspected items. Although traditional ASPs use crisp plan parameters, quality characteristics of the incoming items or human evaluations about inspection process may contain uncertainties and may not always be defined as crisp values in real life problems. The fuzzy set theory (FST) is one of the most popular techniques to model these uncertainties by defining plan parameters as fuzzy numbers. Despite the advantages, traditional fuzzy sets are not flexible enough to model all kinds of uncertainties. For example, it has some disadvantages because of defining the status of any item based on defectiveness or non-defectiveness conditions and presuming the parts as non-defective whose defectiveness is not indeed determined. New extensions of FST can improve the quality of uncertainty modeling of ASPs. Intuitionistic Fuzzy Sets (IFSs) allow slackness for non-determination about the membership and give more sensitive modeling opportunity in human-related evaluations by the help of this ability. Since the inspection procedure of the ASPs depends on human-related judgements, IFSs have been used to define the defectiveness degree of the items in this study. ASPs based on interval-valued IFSs (IVIFSs) have also been designed and some characteristic functions of ASPs, such as acceptance probability ($P_a$), average sample number ($ASN$) and average total inspection ($ATI$) have been reformulated. Intuitionistic binomial and Poisson distributions have been defined to be able to formulate the ASPs. Additionally, the defectiveness of the items has been represented by using linguistic terms to overcome the difficulty of quantifying the verbal evaluation results as numerical measures. The $alpha$-cut technique has been combined with the linguistic approach to allow defining with multiple $alpha$ values for different product segments. Finally, some numerical examples have been presented to analyze the effectiveness of proposed ASPs and discuss the obtained results.

In general, agents always face an increasing need to focus on multiple aims efficiently under their operational processes. However, agents might take different activity levels to participate and might represent administrative areas of different scales. Therefore, this paper proposes a normalized index considering multi-criteria situations and supreme-utilities among fuzzy activity level (decision, strategy) vectors. Three existing notions of traditional game theory are reinterpreted in the framework of multi-criteria fuzzy transferable utility games. First, the normalized index could be represented as an alternative formulation in terms of excess functions. Second, an axiomatic result is proposed to present the rationality of this normalized index based on the reduced game and related consistency. Finally, two dynamic processes are introduced to illustrate that this normalized index could be reached by agents who start from an arbitrary efficient payoff vector and make successive adjustments.

The purpose of this paper is to study the stabilization problem for a class of uncertain chaotic systems against unknown dynamics and disturbances, based on fuzzy sliding mode controller approaches. To fulfill this aim, the first- and the second-orders sliding mode controllers and an adaptive variable universe fuzzy sliding mode controller are combined to a set of linguistic rules, to design some novel approaches for improving the performance of the control action and eliminating the chattering issue. The stability analysis of the closed-loop system is proved via the Lyapunov stability theorem, and also the convergence of the tracking error to zero in finite-time is guaranteed. The new proposed control laws contribute the control actions to outperform the conventional one in terms of chattering reduction and elimination, along with lessening in the reaching time. Moreover, some numerical simulations are provided to depict that the proposed control laws are not only robust with respect to uncertainties and external disturbances, which lead the system to the desired state, but also can significantly eliminate the chattering effect.

In this work, we present some useful results of discrete fractional calculus for ivf s. The composition rules for interval fractional operators are introduced, which are used to construct the general form of the solutions to nonlinear interval fractional difference equations. An illustrative example is provided in which the method of recursive iterations is applied to obtain explicit formulas for the solutions of linear interval fractional difference equations.

People's demand for the decision-making space of opinion expression is getting higher, and the methods to determine the threshold value of current consensus still remain elusive. To deal with large and diverse information of users and discuss deeply the threshold in social networks, we establish a new consistency model with a new preference structure. In this paper, the Pythagorean fuzzy numbers (PFNs) are introduced into social network group decision-making for the expression of decision-makers' preference (DMs) and the concepts definition of the distance measurements, consensus index, and threshold indifference curves, respectively. In addition, we establish a Pythagorean fuzzy group consensus model with minimum adjustment through determining the setting rule of threshold value before reaching the consensus. Finally, we use the proposed model to solve the selection of square cabin hospitals.

Fuzzy arithmetic performed with the product t-norm is the focus of this paper. The subject is handled from both practical and theoretical perspectives. Explicit formulas for product-sum and product-multiplication of triangular fuzzy numbers are obtained. These formulas can effectively replace the computational methods proposed so far. The issue that these operations are not shape preserving is solved by the presentation of appropriate approximations. Finally, the product arithmetic is compared in detail to the arithmetic performed with the boundary t-norms, namely the minimum and drastic sum.