José M. Merigó

The induced generalized OWA operator

We present the induced generalized ordered weighted averaging (IGOWA) operator. It is a new aggregation operator that generalizes the OWA operator, including the main characteristics of both the generalized OWA and the induced OWA operator. This operator uses generalized means and order-inducing variables in the reordering process. It provides a very general formulation that includes as special cases a wide range of aggregation operators, including all the particular cases of the IOWA and the GOWA operator, the induced ordered weighted geometric (IOWG) operator and the induced ordered weighted quadratic averaging (IOWQA) operator. We further generalize the IGOWA operator via quasi-arithmetic means. The result is the Quasi-IOWA operator. Finally, we present a numerical example to illustrate the new approach in a financial decision-making problem.

Decision-making with distance measures and induced aggregation operators

In this paper, we present a new decision-making approach that uses distance measures and induced aggregation operators. We introduce the induced ordered weighted averaging distance (IOWAD) operator. IOWAD is a new aggregation operator that extends the OWA operator by using distance measures and a reordering of arguments that depends on order-inducing variables. The main advantage of IOWAD is that it provides a parameterized family of distance aggregation operators between the maximum and the minimum distance based on a complex reordering process that reflects the complex attitudinal character of the decision-maker. We studied some of IOWADs main properties and different particular cases and further generalized IOWAD by using Choquet integrals. We developed an application in a multi-person decision-making problem regarding the selection of investments. We found that the main advantage of this approach is that it is able to provide a more complete picture of the decision-making process, enabling the decision-maker to select the alternative that it is more in accordance with his interests.

New decision-making techniques and their application in the selection of financial products

We develop a new approach that uses the ordered weighted averaging (OWA) operator in the selection of financial products. In doing so, we introduce the ordered weighted averaging distance (OWAD) operator and the ordered weighted averaging adequacy coefficient (OWAAC) operator. These aggregation operators are very useful for decision-making problems because they establish a comparison between an ideal alternative and available options in order to find the optimal choice. The objective of this new model is to manipulate the attitudinal character of previous methods based on distance measures, so that the decision maker can select financial products according to his or her degree of optimism, which is also known as the orness measure. The main advantage of using the OWA operator is that we can generate a parameterized family of aggregation operators between the maximum and the minimum. Thus, the analysis developed in the decision process by the decision maker is much more complete, because he or she is able to select the particular case in accordance with his or her interests in the aggregation process. The paper ends with an illustrative example that shows results obtained by using different types of aggregation operators in the selection of financial products.

LINGUISTIC AGGREGATION OPERATORS FOR LINGUISTIC DECISION MAKING BASED ON THE DEMPSTER-SHAFER THEORY OF EVIDENCE

In this paper, we develop a new approach for decision making with Dempster-Shafer theory of evidence by using linguistic information. We suggest the use of different types of linguistic aggregation operators in the model. We then obtain as a result, the belief structure — linguistic ordered weighted averaging (BS-LOWA), the BS — linguistic hybrid averaging (BS-LHA) and a wide range of particular cases. Some of their main properties are studied. Finally, we provide an illustrative example that shows the different results obtained by using different types of linguistic aggregation operators in the new approach.

Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets

The hesitant fuzzy linguistic term set (HFLTS) is a new and flexible tool in representing hesitant qualitative information in decision making. Correlation measures and correlation coefficients have been applied widely in many research domains and practical fields. This paper focuses on the correlation measures and correlation coefficients of HFLTSs. To start the investigation, the definition of HFLTS is improved and the concept of hesitant fuzzy linguistic element (HFLE) is introduced. Motivated by the idea of traditional correlation coefficients of fuzzy sets, intuitionistic fuzzy sets and hesitant fuzzy sets, several different types of correlation coefficients for HFLTSs are proposed. The prominent properties of these correlation coefficients are then investigated. In addition, considering that different HFLEs may have different weights, the weighted correlation coefficients and ordered weighted correlation coefficients are further investigated. Finally, an application example concerning the traditional Chinese medical diagnosis is given to illustrate the applicability and validation of the proposed correlation coefficients of HFLTSs in the process of qualitative decision making.

Fuzzy decision making with immediate probabilities

We developed a new decision-making model with probabilistic information and used the concept of the immediate probability to aggregate the information. This type of probability modifies the objective probability by introducing the attitudinal character of the decision maker. In doing so, we use the ordered weighting average (OWA) operator. When using this model, it is assumed that the information is given by exact numbers. However, this may not be the real situation found within the decision-making problem. Sometimes, the information is vague or imprecise and it is necessary to use another approach to assess the information, such as the use of fuzzy numbers. Then, the decision-making problem can be represented more completely because we now consider the best and worst possible scenarios, along with the possibility that some intermediate event (an internal value) will occur. We will use the fuzzy ordered weighted averaging (FOWA) operator to aggregate the information with the probabilities. As a result, we will get the Immediate Probability-FOWA (IP-FOWA) operator. We will study some of its main properties. We will apply the new approach in a decision-making problem about selection of strategies.

Induced 2-tuple linguistic generalized aggregation operators and their application in decision-making

The induced 2-tuple linguistic generalized ordered weighted averaging (2-TILGOWA) operator is presented. This new aggregation operator extends previous approaches by using generalized means, order-inducing variables in the reordering of the arguments and linguistic information represented with the 2-tuple linguistic approach. Its main advantage is that it includes a wide range of linguistic aggregation operators. Thus, its analyses can be seen from different perspectives and we obtain a much more complete picture of the situation considered and are able to select the alternative that best fits with our interests or beliefs. We further generalize the 2-TILGOWA by using quasi-arithmetic means and Choquet integrals. The result is the Quasi-2-TILOWA operator and the 2-tuple linguistic induced quasi-arithmetic Choquet integral aggregation. We conclude this paper by analysing the applicability of this new approach in a multi-person linguistic decision-making problem concerning product management.

An overview of fuzzy research with bibliometric indicators

Number of annual publications in fuzzy research (articles+reviews) since 1965. Bibliometrics in fuzzy research.List of most cited papers on fuzzy topics of all time.An overview of influential authors, institutions and countries.Journal analysis in fuzzy research. Bibliometrics is a discipline that analyzes bibliographic material from a quantitative perspective. It is very useful for classifying information according to different variables, including journals, institutions and countries. This paper presents a general overview of research in the fuzzy sciences using bibliometric indicators. The main advantage is that these indicators provide a general picture, identifying some of the most influential research in this area. The analysis is divided into key sections focused on relevant journals, papers, authors, institutions and countries. Most of the results are in accordance with our common knowledge, although some unexpected results are also found. Note that the aim of this paper is to be informative, and these indicators identify most of the fundamental research in this field. However, some very influential issues may be omitted if they are not included in the Web of Science database, which is used for carrying out the bibliometric analysis.

A unified model between the weighted average and the induced OWA operator

We present a new model that uses the weighted average (WA) and the induced ordered weighted averaging (IOWA) operator in the same formulation. We call it the induced ordered weighted averaging-weighted average (IOWAWA) operator. We study some of its main properties and we see that it has a lot of particular cases such as the WA and the OWA operator. The main advantage of the IOWAWA operator is that it unifies the IOWA operator with the WA in the same formulation considering the degree of importance that each concept has in the aggregation. We analyze the applicability of this new approach and we see that it is very broad because it can be applied in a wide range of fields such as statistics, economics, decision theory and engineering. Theoretically, we could state that all the previous models and applications based on the WA and the IOWA can be revised and improved with this new approach because they will be included in this framework as a particular case. We focus on an application in a multi-person decision-making in political management.

Fuzzy induced generalized aggregation operators and its application in multi-person decision making

We present a wide range of fuzzy induced generalized aggregation operators such as the fuzzy induced generalized ordered weighted averaging (FIGOWA) and the fuzzy induced quasi-arithmetic OWA (Quasi-FIOWA) operator. They are aggregation operators that use the main characteristics of the fuzzy OWA (FOWA) operator, the induced OWA (IOWA) operator and the generalized (or quasi-arithmetic) OWA operator. Therefore, they use uncertain information represented in the form of fuzzy numbers, generalized (or quasi-arithmetic) means and order inducing variables. The main advantage of these operators is that they include a wide range of mean operators such as the FOWA, the IOWA, the induced Quasi-OWA, the fuzzy IOWA, the fuzzy generalized mean and the fuzzy weighted quasi-arithmetic average (Quasi-FWA). We further generalize this approach by using Choquet integrals, obtaining the fuzzy induced quasi-arithmetic Choquet integral aggregation (Quasi-FICIA) operator. We also develop an application of the new approach in a strategic multi-person decision making problem.