Benchmarking in linguistic importance weighted aggregations

doi:10.1016/S0165-0114(98)00047-5

Fuzzy Sets and Systems

Volume 114, Issue 1, 16 August 2000, Pages 35-41

https://doi.org/10.1016/S0165-0114(98)00047-5 Get rights and content

Abstract

In this work we concentrate on the issue of weighted aggregations and provide a possibilistic approach to the process of importance weighted transformation when both the importances (interpreted as benchmarks) and the ratings are given by symmetric triangular fuzzy numbers. We will show that using the possibilistic approach (i) small changes in the membership function of the importances can cause only small variations in the weighted aggregate; (ii) the weighted aggregate of fuzzy ratings remains stable under small changes in the nonfuzzy importances; (iii) the weighted aggregate of crisp ratings still remains stable under small changes in the crisp importances whenever we use a continuous implication operator for the importance weighted transformation. We illustrate the proposed method by some simple examples.

References (30)

D. Dubois et al.
A review of fuzzy sets aggregation connectives
Inform. Sci.
(1985)
D. Dubois et al.
Weighted minimum and maximum operations in fuzzy sets theory
Inform. Sci.
(1986)
R. Fullér
On stability in possibilistic linear equality systems with Lipschitzian fuzzy numbers
Fuzzy Sets and Systems
(1990)
R. Goetschel et al.
Topological properties of fuzzy numbers
Fuzzy Sets and Systems
(1983)
F. Herrera et al.
A model of consensus in group decision making under linguistic assessments
Fuzzy Sets and Systems
(1996)
F. Herrera et al.
Applications of the linguistic OWA operator in group decision making
R.R. Yager
Fuzzy decision making using unequal objectives
Fuzzy Sets and Systems
(1978)
R.R. Yager
Families of OWA operators
Fuzzy Sets and Systems
(1993)
R.R. Yager
Aggregation operators and fuzzy systems modeling
Fuzzy Sets and Systems
(1994)
C. Carlsson, R. Fullér, On fuzzy screening system, in: Proc. of EUFIT’95 Conf., 28–31 August, 1995 Aachen, Germany,...

C. Carlsson et al.

Possibility and necessity in weighted aggregation

C. Carlsson, R. Fullér, OWA operators for decision support, in: Proc. of EUFIT’97 Conf., 8–11 September, 1997 Aachen,...

M. Delgado et al.

On aggregation operations of linguistic labels

Int. J. Intelligent Systems

(1993)

M. Delgado, F. Herrera, E. Herrera-Viedma, L. Martinez, Combining Numerical and Linguistic Information in Group...

D. Dubois et al.

Criteria aggregation and ranking of alternatives in the framework of fuzzy set theory

TIMS/Stud. Mgmt. Sci.

(1984)

Cited by (60)

Beta-Bézier OWA operator
2023, International Journal of Approximate Reasoning
Determination of associated weight vectors for an ordered weighted averaging (OWA) operator is always a crucial issue, and for this purpose, several weight vector determination models have been introduced in the literature. In this article, we propose a new biparametric OWA operator, called a “beta-Bézier OWA operator”. The beta-Bézier OWA operator provides an infinite number of weight vectors for a fixed degree of orness. The orness value of this class of OWA operators is its most essential characteristic, which always depends on one of its parameters, and can be prefixed according to the decision-maker choice and also irrespective of the number of arguments aggregated. The optimum OWA weight vector can be calculated without solving a complicated optimization problem. It becomes the same as several other OWA operators at particular values of parameters. The maximum Bayesian entropy OWA operator weight vector is measured with use of the proposed OWA operator for a given level of optimism/pessimism (orness). It is also compared with many other OWA operators.
New statistical analysis in marketing research with fuzzy data
2016, Journal of Business Research
This research proposes new statistical methods for marketing research and decision making. The study employs a soft computing technique and a new statistical tool to evaluate people's thinking. Because the classical measurement system has difficulties in dealing with the non-real valued information, the study aims to find an appropriate measurement system to overcome this problem. The main idea is to decompose the data into a two-dimensional type, centroid and its length (area). The two-dimensional questionnaires this study proposes help reaching market information.
Subjective and objective information in linguistic multi-criteria group decision making
2016, European Journal of Operational Research
Citation Excerpt :
That is, aggregations that considers different degrees of importance for the available information. Some examples are the aggregation with the weighted average (Carlsson & Fuller, 2000; Grabisch et al., 2011), belief structures that use the weighted average (Merigó et al., 2010) and the weighted OWA (WOWA) operator (Torra, 1997). The weighted average can be defined as follows.
Linguistic decision making systems represent situations that cannot be assessed with numerical information but it is possible to use linguistic variables. This paper introduces new linguistic aggregation operators in order to develop more efficient decision making systems. The linguistic probabilistic weighted average (LPWA) is presented. Its main advantage is that it considers subjective and objective information in the same formulation and considering the degree of importance that each concept has in the aggregation. A key feature of the LPWA operator is that it considers a wide range of linguistic aggregation operators including the linguistic weighted average, the linguistic probabilistic aggregation and the linguistic average. Further generalizations are presented by using quasi-arithmetic means and moving averages. An application in linguistic multi-criteria group decision making under subjective and objective risk is also presented in the context of the European Union law.
An evaluation method for innovation capability based on uncertain linguistic variables
2015, Applied Mathematics and Computation
Due to new challenges from emergent markets, companies increasingly expect to be able to offer innovative products and improve the innovation ability. Thus it is necessary to use a comprehensive evaluation method to evaluate the innovation capability for companies. Firstly, the evaluation indicators system is developed in terms of process capability, organization capability and knowledge capability. Secondly, the evaluation method based on uncertain linguistic variables is proposed. Finally, the evaluation method and the indictors system are applied into a practical problem.
A reconstruction decoder for computing with words
2014, Information Sciences
The Word decoder is a very important approach for decoding in the Perceptual Computer. It maps the computing with words (CWWs) engine output, which is a fuzzy set, into a word in a codebook so that it can be understood. However, the Word decoder suffers from significant information loss, i.e., the fuzzy set model of the mapped word may be quite different from the fuzzy set output by the CWW engine, especially when the codebook is small. In this paper we propose a Reconstruction decoder, which represents the CWW engine output as a combination of two successive codebook words with minimum information loss by solving a constrained optimization problem. The Reconstruction decoder preserves the shape information of the CWW engine output in a simple form without sacrificing much accuracy. It can be viewed as a generalized Word decoder and is also implicitly a Rank decoder. Moreover, it is equivalent to the 2-tuple representation under certain conditions. The effectiveness of the Reconstruction decoder is verified by three experiments.
Extension of VIKOR method for multi-criteria group decision making problem with linguistic information
2013, Applied Mathematical Modelling
Citation Excerpt :
The paper is concluded in Section 6. The basic concept of VIKOR method lies in defining the positive and negative ideal points, which was first put forth by Opricovic and Tzeng [27,28]. The VIKOR method is based on the compromise idea of MCDM.
A new method is proposed to solve multi-criteria group decision making problems in which both the criteria values and criteria weights take the form of linguistic information based on the traditional idea of VIKOR method. Firstly, the linguistic criteria weights given by all decision makers are transformed into trapezoidal fuzzy numbers, and then aggregated and defuzzified to crisp values. Secondly, the individual linguistic decision matrix given by each decision maker (DM) is transformed into 2-tuple linguistic decision matrix, and then aggregated into collective 2-tuple linguistic decision matrix by 2-tuple linguistic arithmetic mean operation. Thirdly, the 2-tuple linguistic values $(S_{i}, α_{i}),$ $(R_{i}, α_{i})$ and $(Q_{i}, α_{i})$ are calculated by defining the 2-tuple linguistic positive ideal solution (TL-PIS) and 2-tuple linguistic negative ideal solution (TL-NIS). Furthermore, the compromise solution can be obtained. Finally, a numerical example is used to illustrate the application of the proposed approach, and the method is verified by comparing the evaluation result with that of 2-tuple linguistic TOPSIS (TL-TOPSIS) method.

View all citing articles on Scopus

¹: On leave from Department of Operations Research, Eötvös Loránd University, Muzeum körut 6-8, H-1088 Budapest, Hungary.

View full text

Benchmarking in linguistic importance weighted aggregations

Abstract

Inform. Sci.

Inform. Sci.

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Possibility and necessity in weighted aggregation

On aggregation operations of linguistic labels

Int. J. Intelligent Systems

Criteria aggregation and ranking of alternatives in the framework of fuzzy set theory

TIMS/Stud. Mgmt. Sci.