The concept of aggregation has been usually associated with that of aggregation functions, assuming that any aggregation process can be represented by a function. Recently, computable aggregations have been introduced considering that the core of the aggregation processes is the program that enables...

The need of establishing a consensus ranking from the preferences expressed by different voters arises in several contexts. The method proposed by Kemeny to this purpose is famously known due to its numerous fulfilled properties and intuitive interpretation, as it minimizes the number of pairwise comparisons...

In this contribution, we analyse in details the recently introduced definition of migrative t-conorms [see Fuzzy implications: alpha migrativity and generalised laws of importation, M. Baczyński, B. Jayaram, R. Mesiar, 2020]. We also focus on some general functional equations, which might be obtained...

In this paper, we revisit the definition of a convolution of aggregation functions and we will examine the convolution of collection integrals defined on a finite space. Also, we introduce the concept of a convolution and of a lower convolution for monotone measures and examine properties of these convolutions...

Positive homogeneity of aggregation functions is one of important properties reflecting the ratio scales in decision making. We recall, introduce and discuss some generalizations of this property, including k-homogeneity, quasi-homogeneity and endpoint linearity.

Inspired by the basic fuzzy connectives min (t-norm TM) and max (t-conorm SM), we introduce and study outliers-based extended aggregation functions. Simply said, A is an (a, b)-outliers-based extended aggregation function if for each arity n ≥ a + b, its output values depend on the number a minimal and...

Discrete OWA operators introduced by Yager (1988) have been widely used and their theoretical as well as application aspects have been studied since their introduction. Some generalizations to continuous case have already been proposed. In this contribution we extend the approach by Jin et al. (2020).

Discrete copulas are useful tools in statistics to represent the joint distribution of discrete random vectors. Furthermore, they are fascinating mathematical objects that admit a representation as a convex polytope. In this work, we analyze the set of extreme points of convex polytopes of discrete copulas....

Classification relies on the rules expressed by domain experts, or on the labeled attribute explaining the output classes. However, such information is not always available. In this work, we explore classification according to aggregation functions of mixed behaviour by the variability in ordinal sums...

In this paper, we study an application of qualitative possibility theory to decision making under uncertainty. The word “qualitative” means that uncertainty is modeled using comparative possibility distributions on a universal set Ω. Such a possibility distribution defines how likely each elementary...

Cluster analysis aims at grouping objects represented by some feature vectors and as such revealing insight into subset structures among the considered objects. However, in many cases, the observations are subject to experimental errors and/or uncertainty. In such a case, a popular way is to summarize...

Fuzzy relations that are not T -transitive have not merited as much scrutiny as their T - transitive counterparts. Recently monometrics on a given betweenness set, or a B-set, has garnered a lot of attention, especially for their role in decision making and penalty based data aggregation. In this work,...

Recently many works have proposed different ways of obtaining orders from associative fuzzy logic operations. While the order ⊑ investigated by Karaçal and Kesicioğlu [10] was modified in [6] to obtain orders on uninorms, this order relation was based on the sub-domains of the arguments. Recently in...

In this paper, 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. Then, we investigate the relation between introduced methods and present methods given in Theorem...

Recently, the notation of the order induced by uninorms (t-norms, nullnorms) has been studied widely. In this paper, we study on the direct product of uninorms on bounded lattices. Also, we define an order induced by uninorms which are a direct product of two uninorms on bounded lattices. Also, we investigate...

Starting with three bivariate copulas and some auxiliary univariate functions, we determine a construction method of trivariate copulas, which generalizes a class of copulas previously introduced by M. Úbeda-Flores (2005). Specifically, we provide a characterization of this class of 3–copulas and we...

At present, in the field of aggregation of various input values, attention is focused on the construction of aggregation functions using other functions that can affect the resulting aggregated value. This resulting value should characterize the properties of the individual input values as accurately...

Revising the definitions of fuzzy relational erosion and dilation introduced by N. Madrid et al. (L-fuzzy relational mathematical morphology based on adjoint triples. Inf. Sci. 474, 75–89, 2019), we define the structured versions of these operators and study their basic properties. Our principal interest...

Recently there have been many works studying orders obtained from fuzzy logic connectives, using the relation proposed in [12]. However, almost all of these works have dealt only with associative operations. In this work, we investigate the conditions under which the above relation leads to a partial...

We introduce inf-lattices, sup-lattices and convexity algebras and we define closure or interior operators and congruences in these algebraic structures. We prove that any inf-lattice can be represented as a quotient of a power set lattice with respect to a congruence. Moreover we consider closure operators...

Following the extensively studied line of research of proposing new construction methods of fuzzy implication functions, recently a construction method based on a quadratic polynomial function and a given fuzzy implication function was proposed. The importance of this method relies on the fact that some...