On the distributivity equation for uni-nullnorms

summary:A uni-nullnorm is a special case of 2-uninorms obtained by letting a uninorm and a nullnorm share the same underlying t-conorm. This paper is mainly devoted to solving the distributivity equation between uni-nullnorms with continuous Archimedean underlying t-norms and t-conorms and some binary operators, such as, continuous t-norms, continuous t-conorms, uninorms, and nullnorms. The new results differ from the previous ones about the distributivity in the class of 2-uninorms, which have not yet been fully characterized

NEW APPROACH TO INFORMATION AGGREGATION

In this paper new types of aggregation operators, namely absorbing-norms and parametric type of operator families called distance-based or evolutionary operators are introduced. Absorbing- norms are commutative, associative binary operators having an absorbing element from the uni! interval. A detailed discussion of properties and structure of these operators is given in the paper. Two types of distance-based operators are defined. The maximum and minimum distance operators with respect to e have the value of the element, which is farther, or nearer to e, respectively, where e is an arbitrary element of the unit interval [0,1]. The special cases e = O and e = 1lead to the max and min operators. The new operators are evolutionary types in the sense that if e is increasing starting from zero till e = 1 the min operator is developing into the max operator, while on the other side the max is transformed into the min operator. It is shown that the evolutionary operators can be constructed by means of min and max operators, which are also special cases of the operators. The maximum distance operators are special operators called uninorms and the minimum distance ones are absorbing-norms

An extension of the ordering based on nullnorms

summary:In this paper, we generally study an order induced by nullnorms on bounded lattices. We investigate monotonicity property of nullnorms on bounded lattices with respect to the $F$-partial order. Also, we introduce the set of incomparable elements with respect to the F-partial order for any nullnorm on a bounded lattice. Finally, we investigate the relationship between the order induced by a nullnorm and the distributivity property for nullnorms

On the reinforcement of uninorms and absorbing norms

DUKE_HCERES2020Aggregation operators Reinforcement ... We propose a n-ary extension of absorbing norms, defined with the help of generative functions, and its relationship with additive generating functions of uninorms. In this paper, we also present new aggregation operators, namely the k-uninorms and k-absorbing norms. These operators are a generalization of usual uninorms and absorbing norms for which a set combination of inputs is introduced. Their main ability is to provide reinforcement for contradictory inputs, as nullnorms and as opposed to uninorms. On the other hand it still provides full reinforcement for agreeing inputs, as uninorms and as opposed to nullnorms. Numerous examples are given in order to illustrate the behavior of the proposed operators

Distributivity between extended nullnorms and uninorms on fuzzy truth values

This paper mainly investigates the distributive laws between extended nullnorms and uninorms on fuzzy truth values under the condition that the nullnorm is conditionally distributive over the uninorm. It presents the distributive laws between the extended nullnorm and t-conorm, and the left and right distributive laws between the extended generalization nullnorm and uninorm, where a generalization nullnorm is an operator from the class of aggregation operators with absorbing element that generalizes a nullnorm.Comment: 2

Fitting aggregation operators to data

Theoretical advances in modelling aggregation of information produced a wide range of aggregation operators, applicable to almost every practical problem. The most important classes of aggregation operators include triangular norms, uninorms, generalised means and OWA operators.With such a variety, an important practical problem has emerged: how to fit the parameters/ weights of these families of aggregation operators to observed data? How to estimate quantitatively whether a given class of operators is suitable as a model in a given practical setting? Aggregation operators are rather special classes of functions, and thus they require specialised regression techniques, which would enforce important theoretical properties, like commutativity or associativity. My presentation will address this issue in detail, and will discuss various regression methods applicable specifically to t-norms, uninorms and generalised means. I will also demonstrate software implementing these regression techniques, which would allow practitioners to paste their data and obtain optimal parameters of the chosen family of operators.<br /

Absorbent tuples of aggregation operators

We generalize the notion of an absorbent element of aggregation operators. Our construction involves tuples of values that decide the result of aggregation. Absorbent tuples are useful to model situations in which certain decision makers may decide the outcome irrespective of the opinion of the others. We examine the most important classes of aggregation operators in respect to their absorbent tuples, and also construct new aggregation operators with predefined sets of absorbent tuples.<br /

Migrativity properties of 2-uninorms over semi-t-operators

summary:In this paper, we analyze and characterize all solutions about $\alpha$-migrativity properties of the five subclasses of 2-uninorms, i. e. $C^{k}$, $C^{0}_{k}$, $C^{1}_{k}$, $C^{0}_{1}$, $C^{1}_{0}$, over semi-t-operators. We give the sufficient and necessary conditions that make these $\alpha$-migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for $G\in C^{k}$, the $\alpha$-migrativity of $G$ over a semi-t-operator $F_{\mu,\nu}$ is closely related to the $\alpha$-section of $F_{\mu,\nu}$ or the ordinal sum representation of t-norm and t-conorm corresponding to $F_{\mu,\nu}$. But for the other four categories, the $\alpha$-migrativity over a semi-t-operator $F_{\mu,\nu}$ is fully determined by the $\alpha$-section of $F_{\mu,\nu}$