Fuzzy Sets and Systems最新文献

It is well known that every bivariate copula induces a positive measure on the Borel σ-algebra on ${[0,1]}^2$, but there exist bivariate quasi-copulas that do not induce a signed measure on the same σ-algebra. In this paper we show that a signed measure induced by a bivariate quasi-copula can always be expressed as an infinite combination of measures induced by copulas. With this we are able to give the first characterization of measure-inducing quasi-copulas in the bivariate setting.

Extended multi-adjoint logic programming is a non-monotonic logic programming framework whose semantics is defined in terms of stable models. This paper will focus on the theoretical development of a syntactical sufficient condition for the existence and uniqueness of stable models in extended multi-adjoint logic programming, through the notion of stratification. Namely, we will detail a constructive method for the computation of the unique stable model of a given stratified extended multi-adjoint logic program. As a consequence, this study will be an interesting alternative to the semantical sufficient conditions for the existence and the uniqueness of stable models, given in the literature for multi-adjoint normal logic and extended multi-adjoint logic programs.

This article deals with a class of interval-valued multiobjective optimization problems (abbreviated as, IVMOP). We employ the notions of generalized Hukuhara (abbreviated as, gH) derivative and q-gH-Hessian to introduce the descent direction of the objective function of IVMOP at a noncritical point. Using this descent direction, we propose a new variant of Newton's method for solving IVMOP, employing an Armijo-like rule coupled with a backtracking technique to find the step length. Moreover, we establish that our proposed algorithm converges to a weak effective solution of IVMOP under certain suitable assumptions on the components of the objective function of IVMOP. A non-trivial example has been furnished to demonstrate the effectiveness of the proposed algorithm. To the best of our knowledge, this is the first time that a variant of Newton's method has been introduced to solve IVMOP, that does not involve the approach of scalarization of the objective function.

For L being a completely distributive lattice, we introduce a notion of L-coarse spaces, which can be regarded as a large-scale analogue of probabilistic uniform spaces. The main goal of this paper is to investigate the properties of L-coarse spaces that can induce L-valued coarse proximity spaces. First of all, we introduce a notion of L-valued coarse neighborhood systems, and show that the resulting category is isomorphic to that of L-valued coarse proximity spaces. Then we study the normality of coarsely connected L-coarse spaces and of asymptotically connected L-valued asymptotic resemblance spaces, and show that these two normality properties are coincident. More importantly, we show that a coarsely connected L-coarse space induces an L-valued coarse proximity if and only if it is coarsely normal. We conclude with noting that the previous result are also valid for asymptotically connected L-valued asymptotic resemblance spaces.

The (extended) homogeneity plays important, and often crucial role in economics, decision making and image processing. When studying the quasi-homogeneity equation, the multiplicative Cauchy equation on $[0,1]$ naturally appears. However, after a detailed analysis of its existing solutions it turned out that some solution of (extended) homogeneity equation was missing. The aim of the paper is to present a complete list of solutions of the multiplicative Cauchy equation and then to give the missing solution of quasi-homogeneity equation from the previous work. For a triangular norm T, we introduce a new concept of T-quasi-homogeneity and, for a strict t-norm T, we clarify the link between the quasi-homogeneity and the T-quasi-homogeneity.

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.