Orness Measure of OWA Operators: A New Approach

Kishor, Arun; Singh, Amit Kumar; Pal, Nikhil R.

doi:10.1109/tfuzz.2013.2282299

Cited by 30 publications

(10 citation statements)

References 35 publications

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“…pessimistic) attitudes in the aggregation process, depending on importance weights being rather assigned to the highest or lowest elements to aggregate. Yager defined an measure of optimism, O W ∈ [0, 1], to categorise OWA operators [22]:…”

Section: A Preference Modeling Upon Multiple Criteriamentioning

confidence: 99%

A Collaborative Multiagent Framework Based on Online Risk-Aware Planning and Decision-Making

Palomares¹,

Killough²,

Bauters

et al. 2016

2016 IEEE 28th International Conference on Tools With Artificial Intelligence (ICTAI)

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Section: A Preference Modeling Upon Multiple Criteriamentioning

confidence: 99%

A Collaborative Multiagent Framework Based on Online Risk-Aware Planning and Decision-Making

Palomares¹,

Killough²,

Bauters

et al. 2016

2016 IEEE 28th International Conference on Tools With Artificial Intelligence (ICTAI)

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“…If w n = 1, then F W is the pure "and" operator; while if w 1 = 1, then F W is the pure "or" operator [1], [42]. In order to classify OWA operators in regard to their location between "and" and "or," a measure of orness that is associated with any weight vector W is introduced by Yager [1] as follows:…”

Section: Preliminariesmentioning

confidence: 99%

Stancu OWA Operator

Singh

Kishor

Pal

2015

IEEE Trans. Fuzzy Syst.

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A critical issue when selecting an ordered weighted aggregation (OWA) operator is the determination of the associated weights. For this reason, numerous weight generating methods have appeared in the literature. In this paper, a generalization of the binomial OWA operator on the basis of the Stancu polynomial is proposed and analyzed. We propose a weight function in the parametric form using the Stancu polynomial by which the weights of OWA operators can be generated easily. The proposed Stancu OWA operator provides infinitely many sets of weight vectors for a given level of the orness value. An important property of this kind of OWA operator is its orness, which remains constant, irrespective of the number of objectives aggregated and always equal to one of its parameters. This approach provides a significant advantage for generating the OWA operators' weights over existing methods. One can choose a set of weight vectors based on his/her own preference. This class of OWA operators can utilize a prejudiced preference to determine the corresponding weight vector. The maximum entropy (Shannon) OWA operator's weights for a given level of orness is calculated by the purposed weight function and compared with the existing maximum entropy OWA operator.Index Terms-Maximum entropy, ordered weighted aggregation (OWA) operators, orness, Stancu polynomial. 1063-6706

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“…Recently Kishor et al [9] proposed an axiomatic definition of orness measures introducing four axioms. First, let us adopt the following notation for the set of all possible weighting n-tuples: …”

Section: Fuzzy Orness Definition and Propertiesmentioning

confidence: 99%

“…The corresponding orness measure plays an important role in studies of OWA operators [2,3,4,8,9,11,12,13,14,15,21,22,24,25,26,27,28,29,30,31,32,33,34,35,36,37]. The orness measure reflects the or-like or and-like aggregation result of an aggregation function.…”

Section: Introductionmentioning

confidence: 99%