Hua-Wen Liu

Distributivity and conditional distributivity of a uninorm with continuous underlying operators over a continuous t-conorm

This paper deals with the distributivity and conditional distributivity of uninorms with continuous underlying operators over continuous triangular conorms. In particular, the involved triangular conorm is either maximum operator or an ordinal sum with only one summand in which the corresponding triangular conorm is strict. From the obtained results, it is deduced that distributivity and conditional distributivity are equivalent. Moreover, we obtain the full characterization of some cases of this class of uninorms of which either the underlying triangular norm or triangular conorm is strict.

On ordinal sum implications

Abstract A new class of fuzzy implications, called ordinal sum implications, is introduced by means of the ordinal sum of a family of given implications, which is similar to the ordinal sum of t -norms (or t -conorms). Basic properties of ordinal sum implications are discussed. It is shown that the ordinal sum implication is really a new class, which is different from the known ( S , N ) -, R -, QL - and Yager’s f - and g -implications.

Migrativity property for uninorms

The α-migrative uninorms over a fixed uninorm with different neutral elements are presented. All cases when both uninorms lay in any one of the most usual classes of uninorms are analyzed, characterizing all solutions of the migrativity equation for some possible combinations. The solutions obtained generalize the results where both uninorms have the same neutral elements.

The distributivity equations for semi t-operators over uninorms

Recently the distributivity equation was discussed in families of certain operations (e.g. triangular norms, conorms, uninorms and nullnorms (or called t-operators)). In this paper we describe the solutions of distributivity for semi t-operators over uninorms. Previous results about distributivity for nullnorms over uninorms can be obtained as a corollary.

Solutions to the functional equation I(x,y)=I(x,I(x,y)) for three types of fuzzy implications derived from uninorms

This paper investigates an iterative Boolean-like law with fuzzy implications derived from uninorms. More precisely, we characterize the solutions to the functional equation I(x,y)=I(x,I(x,y)) that involve RU-, (U,N)- and QLU-implications generated by the most usual classes of uninorms.

On migrativity property for uninorms

Recently, ( α , U 0 ) -migrative uninorms U were introduced and discussed, where U and U 0 are two uninorms with neutral element e. In this paper, we will further study ( α , U 2 ) -migrative uninorms U 1 , where U 1 and U 2 are two uninorms with different neutral elements e 1 and e 2 , respectively. All cases when the uninorm U 1 and U 2 are in different families out of the most usual classes of uninorms are analyzed, characterizing all solutions of the migrativity equation for some possible combinations of U 1 and U 2 .

On the conditional distributivity of nullnorms over uninorms

Conditional distributivity of nullnorm over uninorm with continuous operators is discussed.The structure of uninorms with idempotent operators is discussed. The problem of conditional distributivity for different two aggregation operators plays an important role in many different fields such as utility theory and integration theory. This paper deals with the conditional distributivity of a continuous nullnorm with respect to a uninorm with the continuous underlying t-norm and t-conorm.

Migrative Property for Nullnorms

The α-migrativity is an important property of a binary operation, and many authors discussed this property for various operators. In this paper, the migrative property for nullnorms is investigated. All solutions of the migrativity equation for all possible combinations of nullnorms are analyzed and characterized.

Migrativity property for uninorms and semi t-operators

In this paper, the notions of α-migrative uninorms over semi t-operators and α-migrative semi t-operators over uninorms are introduced and investigated. All solutions of the migrativity equations for all possible combinations of semi t-operators and uninorms are characterized.

Discrete aggregation operators with annihilator

Abstract Mas et al. have investigated a special kind of commutative and associative aggregation operators with annihilator on the unit interval [ 0 , 1 ] , which includes S-uninorms, S-nullnorms, T-uninorms, T-nullnorms, bi-uninorms and bi-nullnorms. This paper is devoted to extending this kind of operators from the unit interval [ 0 , 1 ] to a finite chain. A characterization of this kind of operators on a finite chain is given, including some examples. This class of operators can be viewed as a generalization of both uninorms and nullnorms on a finite chain.