r. mesiar

We investigate the linear objective function optimization problem constrained by a new system of fuzzy relationequations, utilizing the minimum t-norm for fuzzy compositions. Our findings reveal that the feasible region ischaracterized as a finite union of closed convex cells. We provide necessary and sufficient conditions to determinethe problem’s feasibility. To streamline optimization, seven novel rules are proposed, on which an algorithm is basedto achieve a global optimum. Notably, a specific instance of our problem is shown to be equivalent to the well-knownminimal vertex cover problem. The efficacy of our algorithm is demonstrated through a concrete example.

In this article, we go on to discuss the structure of uninorms on bounded lattices. We suggest two techniques to yield  uninorms with some constraints on the identity element by applying that the t-norms and t-conorms are always present on the considered bounded lattices. These techniques ensure new approaches for getting idempotent uninorms on bounded lattices when regarding infimum t-norm and supremum t-conorm. Furthermore, we display the distinctness between our new construction techniques and the published ones.

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.

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.

We discuss ordinal sums as one of powerful tools in the aggregation theory serving, depending on the context, both as a construction method and as a representation, respectively. Up to recalling of several classical results dealing with ordinal sums, in particular dealing, e.g.,  with continuous t-norms, copulas, or recent results, e.g., concerning uninorms with continuous underlying functions, we present also several new results, such as the uniqueness of the link between t-norms or t-conorms, and related Archimedean components, problems dealing with the cardinality of the considered index sets in ordinal sums, or infinite ordinal sums of aggregation functions covering by one type of ordinal sums both t-norms and t-conorms ordinal sums.

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.

We generalize set-based extended functions, recently introduced by Mesiar et al., into 2-set-based extended functions. In both cases, an efficient reduction of repeated  data to be fused is considered which prepares a sound background for big data processing. We discuss and study several types of 2-set-based extended functions, in particular,  2-set-based extended aggregation functions, including t-norms, t-conorms, uninorms, nullnorms and OWA operators.

In this work, we study the joint distribution function as well as the copula of (X-Z,Y) where the random vector (X, Y, Z)  is characterized by a copula C_{X,Y,Z}. We use this copula to analyze a measurement error model. Some theoretical results, several examples as well as a simulation study are proposed for illustration.

Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defined on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods for constructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for the clarity. Finally, we show that our construction methods can be generalized by induction to a modified ordinal sum for triangular norms and triangular conorms on an arbitrary bounded lattice, respectively.

This study discusses some variants of Ordered WeightedAveraging (OWA) operators and related information aggregation methods. Indetail, we define the Extended Ordered Weighted Sum (EOWS) operator and theExtended Ordered Weighted Averaging (EOWA) operator, which are applied inscientometrics evaluation where the preference is over finitely manyrepresentative works. As contrast, we also define the Infinite OrderedWeighted Sum (InOWS) operator and the Infinite Ordered Weighted Averaging(InOWA) operator, which are more suitable for the correspondingscientometrics evaluation where all of works of scholars are considered. Wealso define the family of Infinite Gaussian maxitive OWA weights functionand the family of Infinite Gaussian OWA weights function, and discuss someof their mathematical properties. Some illustrative examples, comparisonsand figures are provided to better expound their applicability inscientometrics evaluation.