Fuzzy Sets and Systems

Overlap and grouping functions can be used to measure events in which we must consider either the maximum or the minimum lack of knowledge. The commutativity of overlap and grouping functions can be dropped out to introduce the notions of pseudo-...

Three basic issues of granular computing are construction or definition of granules, measures of granules, and computation or reasoning with granules. This paper reviews the main theories of granular computing and introduces the definition of ...

• Introduce the definition of spatial granules and explain its rationality.
• Define coarse-fine relation and all the granules can be hierarchicalized.
• Adopt a one-to-one mapping between the granules and the points.
• Discuss the ...

The enumeration of logical connectives and aggregation functions defined on a finite chain has been a hot topic in the literature for the last decades. Multiple advantages can be derived from knowing a general formula about their cardinality, for ...

In this paper, we investigate several classes of binary operations within the preordered framework. First, we give the definition of quasi-t-subnorm on preordered sets. Subsequently, we research two classes of quasi-t-subnorms by means of ...

Simplification logic, a logic for attribute implications, was originally defined for Boolean sets. It was extended to distributive fuzzy sets by using a complete dual Heyting algebra. In this paper, we weaken this restriction in the sense that we ...

This paper presents new properties of the so-called generalized derivatives of fuzzy and interval-valued functions, which consist of the gH, gH⁎, and g-derivatives of these functions. Several recent properties concerning the generalized ...

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 ...

This paper mainly considers the post-inverse matrix of a fuzzy relation matrix in terms of addition-min composition. A necessary and sufficient condition for the consistency of the inverse matrix problem is given by transforming the problem into ...

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 ...

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, ...

Consider ( Y , ρ ) as a complete metric space and S as the space of probability Borel measures on Y. Let dim ‾ B Ψ , Φ ( E ) be the general upper box dimension of the set E ⊂ Y. We begin by proving that the general packing dimension of the ...

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 ...

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 ...

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 ...

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 ...