ON THE UNIFICATION BETWEEN THE PROBABILITY, THE WEIGHTED AVERAGE AND THE OWA OPERATOR

2009 ◽  
Author(s):  
JOSÉ M. MERIGÓ
Keyword(s):  
Weighted Average ◽  
Owa Operator

scholarly journals METHODS FOR PROBABILISTIC DECISION MAKING WITH LINGUISTIC INFORMATION

2014 ◽  
Vol 20 (2) ◽  
pp. 193-209 ◽  
Author(s):  
Guiwu Wei ◽  
Xiaofei Zhao
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Uncertain Information ◽  
Owa Operator ◽  
Linguistic Information ◽  
Probabilistic Information ◽  
Ordered Weighted Average ◽  
Linguistic Labels ◽  
Selection Of

With respect to decision making problems by using probabilities, immediate probabilities and information that can be represented with linguistic labels, some new decision analysis are proposed. Firstly, we shall develop three new aggregation operators: generalized probabilistic 2-tuple weighted average (GP-2TWA) operator, generalized probabilistic 2-tuple ordered weighted average (GP-2TOWA) operator and generalized immediate probabilistic 2-tuple ordered weighted average (GIP-2TOWA) operator. These operators use the weighted average (WA) operator, the ordered weighted average (OWA) operator, linguistic information, probabilistic information and immediate probabilistic information. They are quite useful because they can assess the uncertain information within the problem by using both linguistic labels and the probabilistic information that considers the attitudinal character of the decision maker. In these approaches, alternative appraisal values are calculated by the aggregation of 2-tuple linguistic information. Thus, the ranking of alternative or selection of the most desirable alternative(s) is obtained by the comparison of 2-tuple linguistic information. Finally, we give an illustrative example about selection of strategies to verify the developed approach and to demonstrate its feasibility and practicality.

scholarly journals Ranking the competitiveness of tourist destinations: An analysis using the OWA operator and the SAW method

2021 ◽  
Vol 21 (2) ◽  
pp. 15-34
Author(s):  
Martín Huesca-Gastélum ◽  
Martín León-Santiesteban
Keyword(s):  
Weighted Average ◽  
Aggregation Operators ◽  
Relative Importance ◽  
Owa Operator ◽  
Jel Codes ◽  
Tourist Destinations ◽  
Ordered Weighted Average ◽  
Tourism Destinations ◽  
The Government ◽  
Simple Additive Weighting

The objective of this paper is to rank the competitiveness of tourist destinations based on different aggregation operators, specifically, the ordered weighted average (OWA) operator and the simple additive weighting (SAW) method. The use of these methods allows tourist destinations to be sorted according to their competitiveness. In addition, it enables the generation of different scenarios that highlight the relative importance of each criterion. This information is useful for the government and recreation sites when generating different evaluations based on the specific characteristics of each municipality. An application of these methods to determine the competitiveness of the tourism destinations of Sinaloa, Mexico has been performed.  JEL Codes: D49, L83, C44 Received: 10/07/2020.  Accepted: 03/11/2020.  Published: 01/12/2021. 

scholarly journals Fuzzy Branch-and-Bound Algorithm with OWA Operators in the Case of Consumer Decision Making

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3045
Author(s):  
Emili Vizuete-Luciano ◽  
Sefa Boria-Reverter ◽  
José M. Merigó-Lindahl ◽  
Anna Maria Gil-Lafuente ◽  
Maria Luisa Solé-Moro
Keyword(s):  
Decision Making ◽  
Branch And Bound ◽  
Average Distance ◽  
Weighted Average ◽  
Branch And Bound Algorithm ◽  
Weighted Averaging ◽  
Consumer Decision Making ◽  
Owa Operator ◽  
Consumer Decision ◽  
The City

The ordered weighted averaging (OWA) operator is one of the most used techniques in the operator’s aggregation procedure. This paper proposes a new assignment algorithm by using the OWA operator and different extensions of it in the Branch-and-bound algorithm. The process is based on the use of the ordered weighted average distance operator (OWAD) and the induced OWAD operator (IOWAD). We present it as the Branch-and-bound algorithm with the OWAD operator (BBAOWAD) and the Branch-and-bound algorithm with the IOWAD operator (BBAIOWAD). The main advantage of this approach is that we can obtain more detailed information by obtaining a parameterized family of aggregation operators. The application of the new algorithm is developed in a consumer decision-making model in the city of Barcelona regarding the selection of groceries by districts that best suit their needs. We rely on the opinion of local commerce experts in the city. The key advantage of this approach is that we can consider different sources of information independent of each other.

AN INTUITIONISTIC OWA OPERATOR

2004 ◽  
Vol 12 (06) ◽  
pp. 843-860 ◽  
Author(s):  
H. B. MITCHELL
Keyword(s):  
Fuzzy Sets ◽  
Multiple Criteria Decision Making ◽  
Weighted Average ◽  
Intuitionistic Fuzzy Sets ◽  
Extension Principle ◽  
Owa Operator ◽  
Simple Application ◽  
Average Operator ◽  
Ordered Weighted Average ◽  
Non Linear Operator

The OWA (Ordered Weighted Average) operator is a powerful non-linear operator for aggregating a set of inputs ai,i∈{1,2,…,M}. In the original OWA operator the inputs are crisp variables ai. This restriction was subsequently removed by Mitchell and Schaefer who by application of the extension principle defined a fuzzy OWA operator which aggregates a set of ordinary fuzzy sets Ai. We continue this process and define an intuitionistic OWA operator which aggregates a set of intuitionistic fuzzy sets Ãi. We describe a simple application of the new intuitionistic OWA operator in multiple-expert multiple-criteria decision-making.

scholarly journals A NEW MEASURE OF VOLATILITY USING INDUCED HEAVY MOVING AVERAGES

2019 ◽  
Vol 25 (4) ◽  
pp. 576-599 ◽  
Author(s):  
Ernesto León-Castro ◽  
Luis Fernando Espinoza-Audelo ◽  
Ezequiel Aviles-Ochoa ◽  
Jose M. Merigó ◽  
Janusz Kacprzyk
Keyword(s):  
Standard Deviation ◽  
Exchange Rates ◽  
Moving Average ◽  
Weighted Average ◽  
Owa Operator ◽  
Information Process ◽  
Aggregate Information ◽  
Ordered Weighted Average ◽  
Dispersion Technique ◽  
Weighted Moving Average

The volatility is a dispersion technique widely used in statistics and economics. This paper presents a new way to calculate volatility by using different extensions of the ordered weighted average (OWA) operator. This approach is called the induced heavy ordered weighted moving average (IHOWMA) volatility. The main advantage of this operator is that the classical volatility formula only takes into account the standard deviation and the average, while with this formulation it is possible to aggregate information according to the decision maker knowledge, expectations and attitude about the future. Some particular cases are also presented when the aggregation information process is applied only on the standard deviation or on the average. An example in three different exchange rates for 2016 are presented, these are for: USD/MXN, EUR/MXN and EUR/USD

Fuzzy Methods of Multiple-Criteria Evaluation and Their Software Implementation

2012 ◽  
pp. 388-411
Author(s):  
Pavel Holecek ◽  
Jana Talašová ◽  
Ivo Müller
Keyword(s):  
Set Theory ◽  
Fuzzy Set Theory ◽  
Choquet Integral ◽  
Weighted Average ◽  
Multiple Criteria ◽  
Software Implementation ◽  
Owa Operator ◽  
Complex Interactions ◽  
Fuzzy Methods ◽  
Multiple Criteria Evaluation

This chapter describes a system of fuzzy methods designed to solve a broad range of problems in multiple-criteria evaluation, and also their software implementation, FuzzME. A feature common to all the presented methods is the type of evaluation, well suited to the paradigm of fuzzy set theory. All evaluations take on the form of fuzzy numbers, expressing the extent to which goals of evaluation are fulfilled. The system of fuzzy methods is conceived to allow for different types of interaction among criteria of evaluation. Under no interaction, the fuzzy weighted average, fuzzy OWA operator, or WOWA operator are used to aggregate partial evaluations (depending on the evaluator’s requirements regarding type of evaluation). If interactions appear as redundancy or complementarity, the fuzzified discrete Choquet integral is the appropriate aggregation operator. Under more complex interactions, the aggregation function is defined through an expertly set base of fuzzy rules.

THE UNCERTAIN GENERALIZED OWA OPERATOR AND ITS APPLICATION TO FINANCIAL DECISION MAKING

2011 ◽  
Vol 10 (02) ◽  
pp. 211-230 ◽  
Author(s):  
JOSÉ M. MERIGÓ ◽  
MONTSERRAT CASANOVAS
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Uncertain Information ◽  
Owa Operator ◽  
Arithmetic Means ◽  
Interval Numbers ◽  
Wide Range ◽  
Decision Making Problem ◽  
Financial Decision ◽  
Selection Of

We introduce the uncertain generalized OWA (UGOWA) operator. This operator is an extension of the OWA operator that uses generalized means and uncertain information represented as interval numbers. By using UGOWA, it is possible to obtain a wide range of uncertain aggregation operators such as the uncertain average (UA), the uncertain weighted average (UWA), the uncertain OWA (UOWA) operator, the uncertain ordered weighted geometric (UOWG) operator, the uncertain ordered weighted quadratic averaging (UOWQA) operator, the uncertain generalized mean (UGM), and many specialized operators. We study some of its main properties, and we further generalize the UGOWA operator using quasi-arithmetic means. The result is the Quasi-UOWA operator. We end the paper by presenting an application to a decision-making problem regarding the selection of financial strategies.

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