Fuzzy Sets and Systems最新文献

The main work of this paper is to extend deterministic two-dimensional on-line tessellation automata (D2OTAs) to the fuzzy setting. We call these new automata models deterministic fuzzy two-dimensional on-line tessellation automata (DF2OTAs) and focus on some of their properties. Concretely, we firstly give the definitions of DF2OTAs and the fuzzy picture languages recognized by them. Next, the closure properties of the collection of fuzzy picture languages recognized by DF2OTAs are concentrated on under some familiar operations. The decomposition theorem, the representation theorem and the Pumping lemma, which are studied in the theory of fuzzy string automata and the related languages, are also considered scrupulously in the framework of DF2OTAs and their languages. Then, we put forward the concepts of transition-accessible DF2OTAs and state-accessible DF2OTAs, and conclude that transition-accessible DF2OTAs are special state-accessible DF2OTAs and DF2OTAs are equivalent to state-accessible DF2OTAs. Finally, state reduction relations on state-accessible DF2OTAs are defined to study the problem of the state reduction of DF2OTAs. Given a state-accessible DF2OTA $A$, in order to construct the factor DF2OTA of $A$ with respect to a state reduction relation on $A$ such that this factor one is equivalent to $A$ and possesses a fewer states, we design a polynomial-time algorithm to compute the largest state reduction relation and then construct the corresponding factor automaton.

We aim at representing the recently introduced conditional aggregation-based Choquet integral as a standard Choquet integral on a hyperset. The representation is one of transformations considered by R.R. Yager and R. Mesiar in 2015. Thus we study the properties of the conditional aggregation-based Choquet integral using well-known facts about the standard Choquet integral. In particular, we obtain several formulas for its computation. We also provide the representation of the conditional aggregation-based Choquet integral in terms of the Möbius transform.

In this paper, we explore the concept of local contrast of a fuzzy relation, which can be perceived as a measure for distinguishing the degrees of membership of elements within a defined region of an image. We introduce four distinct methods for constructing fuzzy local contrast: one uses a similarity measure, the second relies on the aggregation of similarity, the third is based on the aggregation of restricted equivalence, and the fourth utilizes the notion of equivalence. We further divide the constructions using similarity measures into two categories based on the two known definitions of similarity: distance-based similarity and aggregation function-based similarity. These construction methods also incorporate fuzzy implications and negations. Aggregation functions, which can be manipulated to enhance the effectiveness of the constructed fuzzy local contrast, play a significant role in most of our proposed constructions. For each construction method, several examples of fuzzy local contrasts are provided. The usefulness of the new fuzzy local contrasts is examined by applying them in image processing for salient region detection.

The paper investigates the dynamic memory event-triggered reachable set (DMETRS) estimation problem for a class of switched Takagi-Sugeno fuzzy systems (ST-SFSs). A switching fuzzy dynamic memory event-triggered (SFDMET) mechanism is developed with a memory element inserted, which provides a lower communication frequency. Under the SFDMET rule, the controllers and switching command are constructed to force the reachable set estimation of the ST-SFSs. The reachable set estimation region is relevant to the SFDMET rule. In the end, the effectiveness of the proposed DMETRS estimation approach is validated through a room air regulating system.

This paper is concerned with the stability and stabilization problems for T-S fuzzy systems with two additive time-varying delays. Firstly, a novel Lyapounov-Krasovskii functional (LKF) is constructed by delay-product-type functional method together with the state vector augmentation. In order to handle time-delay square terms introduced into the derivative of LKF, an extended binary quadratic function negative-determination lemma is proposed. A less conservative delay-dependent stability condition is developed since not only some new bounding technologies are employed to deal with integral terms, but also the proposed lemma is employed to dispose nonlinear time-delay terms in derivative of constructed function. Then, the corresponding controller design method for closed-loop delayed fuzzy system is derived based on parallel distributed compensation scheme. Finally, four numerical examples are given to illustrate the superiority and effectiveness of the proposed criteria.

Given a target class T of an OWL 2 ontology, positive (and possibly negative) examples of T, we address the problem of learning, viz. inducing, from the examples, fuzzy class inclusion rules that aim to describe conditions for being an individual classified as an instance of the class T.

To do so, we present PN-OWL which is a two-stage learning algorithm consisting of a P-stage and an N-stage. In the P-stage, the algorithm learns fuzzy class inclusion rules (the P-rules). These rules aim to cover as many positive examples as possible, increasing recall, without compromising too much precision. In the N-stage, the algorithm learns fuzzy class inclusion rules (the N-rules), that try to rule out as many false positives, covered by the rules learnt at the P-stage, as possible. Roughly, the P-rules tell why an individual should be classified as an instance of T, while the N-rules tell why it should not.

PN-OWL then aggregates the P-rules and the N-rules by combining them via an aggregation function to allow for a final decision on whether an individual is an instance of T or not.

We also illustrate the effectiveness of PN-OWL through extensive experimentation.

Since fuzzy discrete-event systems (FDESs) modeled by fuzzy automata were put forward, extensive research on FDESs has been successfully conducted from different perspectives. Recently, the safe codiagnosability of decentralized FDESs was introduced and an approach of constructing the safe codiagnoser to verify the safe codiagnosability was proposed. However, the complexity of constructing the safe codiagnoser of decentralized FDESs is exponential. In this paper, we present a polynomial verification. Firstly, the recognizer and the safe coverifier are constructed to recognize the prohibited strings in the illegal language and carry out safe diagnosis of decentralized FDESs, respectively. Then the necessary and sufficient condition for safe codiagnosability of decentralized FDESs is presented. In particular, an algorithm for verifying the safe codiagnosability of decentralized FDESs is proposed based on the safe coverifier. Notably, both complexities of constructing the safe coverifier and verifying the safe codiagnosability are polynomial in the numbers of fuzzy events and fuzzy states of FDESs. Finally, two examples are provided to illustrate the proposed algorithm and the derived results.

Random Permutation Set is a newly proposed method for handling uncertainty, which considers the order of the elements in evidence. However, how to fuse RPSs efficiently is still an open issue. To solve this problem, the space composed of order code is defined. Then the mutual mappings between this space and permutation event space are also presented. Finally, the new orthogonal sum is proposed. Compared with the existing left orthogonal sum, the new orthogonal sum can obtain more accurate results with lower entropy and deal with extreme situations. Numerical examples are used to illustrate the superiority of the new orthogonal sum.

While fuzzy logic connectives were seen as generalisations of classical logic connectives, their utility has extended beyond their intended use and context. One interesting avenue of exploration that began almost 4 decades ago is to obtain metrics from fuzzy logic connectives. Not only was this a fertile approach for obtaining metrics with myriad properties but such studies have also thrown up some interesting insights. In this work, we present a state-of-the-art survey of the different works detailing the multitude of operators used to obtain these distance functions, the host of properties they satisfy, the novel contexts in which they have been employed, and the insightful commentary that they have provided on the underlying structures.

Recently, monometrics - distance functions compatible with the underlying order - have attracted scrutiny for their utility in the fields of rationalisation of ranking rules, penalty-based aggregation, and binary classification. In this work, adding to the survey, we examine if and when the existing distance functions yield a monometric. Further, by employing monotonic fuzzy logic connectives and fuzzy negations, we offer a construction of distance functions that always yield monometrics and helps us in providing a characterisation of symmetric monometrics on the unit interval. Our work showcases a close relationship between monometrics and fuzzy implications.

Fuzzy inference systems have been widely investigated from different perspectives, including their logical correctness. It is not surprising that the logical correctness led mostly to the questions on the preservation of modus ponens. Indeed, whenever such a system processes an input equivalent to one of the rule antecedents, it is natural to expect the modus ponens to be preserved and the inferred output to be identical to the respective rule consequent. This leads to the related systems of fuzzy relational equations where the antecedent and consequent fuzzy sets are known values, the inference is represented either by the direct product related to the compositional rule of inference or by the Bandler-Kohout subproduct, and the fuzzy relation that represents the fuzzy rule base is the unknown element in the equations. The most important question is whether such systems are solvable, i.e., whether there even exists a fuzzy relation that models the given fuzzy rule base in such a way that the modus ponens is preserved.

Partiality allows dealing with partially defined truth values which allows to deal with situations, where we cannot define the truth value for a given predicate. The partial logics have been recently extended to partial fuzzy logics and the partial fuzzy set theory has been developed. Partial fuzzy sets then may have undefined membership degrees for some values from the given universe.

This background leads naturally to the problem of solvability of partial fuzzy relational equations, which are equations with partial fuzzy sets in the role of antecedents and consequents and with partial fuzzy relation as the model of the given fuzzy rule base. Such a setting led to a recent publication that uncovers the solvability and even the shape of the solutions. In this contribution, we revisit the problem and consider a specific case that allows partiality only in the input. In other words, antecedents, as well as consequents expressing the knowledge, are fully defined. Thus, the model of the fuzzy rules is one of the standard and fully defined relations. We investigate what happens if the input differs from one of the antecedents only by a few undefined values. This mimics the situation when a description of an observed object misses a few values in its feature vector. We show that under specific conditions, we still may preserve the modified modus ponens, i.e., that the inferred output is identical with the fully defined consequent of the respective rule.