Constructing Choquet integral-based operators that generalize weighted means and OWA operators

Llamazares, Bonifacio

doi:10.1016/j.inffus.2014.06.003

Cited by 48 publications

(84 citation statements)

References 29 publications

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“…Choquet integral can also be represented by using a decreasing sequences of values (see, for instance, Torra [16] and Llamazares [8]):…”

Section: Choquet Integralmentioning

confidence: 99%

“…160-161], Torra and Narukawa [5, pp. 150-151], Roy [6], Yager and Alajlan [7], Llamazares [8] and references therein). This fact has prompted the emergence of specific functions to deal with this class of problems.…”

Section: Introductionmentioning

confidence: 99%

“…For its part, WOWA operators have good properties given that they are Choquet integral-based operators with respect to normalized capacities (see Torra [16]). However, in some cases, their behavior is unsuitable to model certain problems (see Llamazares [9,8]). …”

Section: Introductionmentioning

confidence: 99%

“…Semi-uninorm based ordered weighted averaging operators (SUOWA) were introduced by Llamazares [8] as an alternative to the previous functions. They are also defined as Choquet integral-based operators associated with normalized capacities that are defined in terms of two weight distributions (one for the weighted mean part, the other for the OWA operator part) and "assembled" by semi-uninorms.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, in the case of using idempotent semi-uninorms, they present some interesting additional properties (see Llamazares [8]). …”

Section: Introductionmentioning

confidence: 99%

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SUOWA operators: Constructing semi-uninorms and analyzing specific cases

Llamazares

2016

Fuzzy Sets and Systems

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SUOWA operators are a new family of aggregation functions that simultaneously generalize weighted means and OWA operators. Semi-uninorms, which are an extension of uninorms by dispensing with the symmetry and associativity properties, play a fundamental role in their definition. In this paper we show several procedures to construct semi-uninorms. The first one allows us to obtain continuous semi-uninorms by using ordinal sums of aggregation operators while the second one is based on a combination of several given semi-uninorms. We also pay special attention to the smallest and the largest idempotent semi-uninorms and we point out some advantages of SUOWA operators over WOWA operators.

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“…Choquet integral can also be represented by using a decreasing sequences of values (see, for instance, Torra [16] and Llamazares [8]):…”

Section: Choquet Integralmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In addition, in the case of using idempotent semi-uninorms, they present some interesting additional properties (see Llamazares [8]). …”

Section: Introductionmentioning

confidence: 99%

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SUOWA operators: Constructing semi-uninorms and analyzing specific cases

Llamazares

2016

Fuzzy Sets and Systems

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A Behavioral Analysis of WOWA and SUOWA Operators

Llamazares

2016

Int. J. Intell. Syst.

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Weighted ordered weighted averaging (WOWA) and semiuninorm-based ordered weighted averaging (SUOWA) operators are two families of aggregation functions that simultaneously generalize weighted means and OWA operators. Both families can be obtained by using the Choquet integral with respect to normalized capacities. Therefore, they are continuous, monotonic, idempotent, compensative and homogeneous of degree 1 functions. Although both families fulfill good properties, there are situations where their behavior is quite different. The aim of this paper is to analyze both families of functions regarding some simple cases of weighting vectors, the capacities from which they are building, the weights affecting the components of each vector, and the values they return.

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Monotonic argument-dependent OWA operators

Zeng

2018

Int. J. Intell. Syst.

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The ordered weighted averaging (OWA) operator introduced by Yager is one of the most popular aggregation technique. In this paper, we develop two kinds of argument‐dependent OWA (DOWA) operators including the pessimistic‐dependent OWA (PE‐DOWA) operator and optimistic‐dependent OWA (OP‐DOWA) operator, that point out that the PE‐DOWA operator is decreasing and the OP‐DOWA operator is increasing, and investigate some properties of our proposed monotonic DOWA operators in detail. Furthermore, we introduce the concept of original function in which a gradient vector generates the weights of the PE‐DOWA and OP‐DOWA operators. Meanwhile, we propose two classes of original functions including summing‐type original function and multiplying‐type original function and investigate the sufficient monotonic conditions for the DOWA operators generated by the original functions. Finally, we discuss the characteristics and properties of our proposed DOWA operators in detail and use a numerical example to illustrate the flexibility of our proposed operators.

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Constructing Choquet integral-based operators that generalize weighted means and OWA operators

Cited by 48 publications

References 29 publications

SUOWA operators: Constructing semi-uninorms and analyzing specific cases

SUOWA operators: Constructing semi-uninorms and analyzing specific cases

A Behavioral Analysis of WOWA and SUOWA Operators

Monotonic argument-dependent OWA operators

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