Types Of Aggregation Operators Research Articles

Power aggregation operators based on hamacher t-norm and t-conorm for complex intuitionistic fuzzy information and their application in decision-making problems

Algebraic and Einstein are two different types of norms which are the special cases of the Hamacher norm. These norms are used for evaluating or constructing three different types of aggregation operators, such as averaging/geometric, Einstein averaging/geometric, and Hamacher averaging/geometric aggregation operators. Moreover, complex Atanassov intuitionistic fuzzy (CA-IF) information is a very famous and dominant technique or tool which is used for depicting unreliable and awkward information. In this manuscript, we present the Hamacher operational laws for CA-IF values. Furthermore, we derive the power aggregation operators (PAOs) for CA-IF values, called CA-IF power Hamacher averaging (CA-IFPHA), CA-IF power Hamacher ordered averaging (CA-IFPHOA), CA-IF power Hamacher geometric (CA-IFPHG), and CA-IF power Hamacher ordered geometric (CA-IFPHOG) operators. Some dominant and valuable properties are also stated. Moreover, the multi-attribute decision-making (MADM) methods are developed based on the invented operators for CA-IF information and the detailed decision steps are given. Many prevailing operators are selected as special cases of the invented theory. Finally, the derived technique will offer many choices to the expert to evaluate the best alternatives during comparative analysis.

Multilinear target-based decision analysis with hybrid-information targets and performance levels

For several classes of decisions, the use of target-based decision analysis (TBDA) is more appropriate than utility analysis. Recent literature on TBDA mainly focuses on different expression forms of targets and performance levels, and on different types of aggregation operators in terms of multi-attribute preference functions. However, different expression forms are usually introduced separately in literature, which cannot fully support the inherent complexity of problems along with different perception and knowledge levels of decision makers during assessing targets and performance levels. Furthermore, although there are attractive features of multilinear target-based preference functions (MTPFs), its applications are seldom considered because of the complexity of identifying their coefficients. In order to solve these two issues, an integrated approach is proposed for multilinear hybrid-information target-based decision analysis, which can deal with diverse forms of targets and performance levels, and identify the coefficients of MTPFs. First, given targets and performance levels for each attribute being expressed in multiple forms simultaneously, a generalized procedure is proposed to transform different forms into probability distributions, and to measure probability of target achievement for each attribute. Second, a novel procedure to identify the coefficients of MTPFs is proposed. This procedure is based on the multilinear model and 2-additive fuzzy measures, which is based on the equivalence between multilinear model based on fuzzy measures and MTPFs. The approach is applied to a case study involving customer competitive evaluation of smart thermometer patches to demonstrate its feasibility and advantages.

Analysis of Einstein aggregation operators based on complex intuitionistic fuzzy sets and their applications in multi-attribute decision-making

<abstract><p>The main influence of this analysis is to derive two different types of aggregation operators under the consideration of algebraic <italic>t</italic>-norm and <italic>t</italic>-conorm and Einstein <italic>t</italic>-norm and <italic>t</italic>-conorm for CIF set theory. Because these operators are very effective for evaluating the collection of information into a singleton preference. For this, first, we discover the Algebraic and Einstein operational laws for CIF sets. Then, we aim to discover the theory of CCIFWA, CCIFOWA, CCIFWG, CCIFOWG operators and their valuable properties "idempotency, monotonicity and boundedness" and results. Furthermore, we also derive the theory of CCIFEWA, CCIFEOWA, CCIFEWG, CCIFEOWG operators and their valuable properties "idempotency, monotonicity, and boundedness" and results. Some special cases of the derived work are also described in detail. Finally, we illustrate a MADM procedure under the consideration of derived operators to enhance the worth of the presented information. Finally, we compare the presented operators with various existing operators with the help of various suitable examples for showing the reliability and stability of the derived approaches.</p></abstract>

Application of Choquet Integral-Fuzzy Measures for Aggregating Customers’ Satisfaction

Choquet integral is a type of aggregation operator that is commonly used to aggregate the interrelated information. Nowadays, this operator has been successfully embedded with fuzzy measures in solving various evaluation problems. Inspired from this new development, this paper aims to introduce a combined Choquet integral-fuzzy measures (CI-FM) operator that uses the Shapley value standard and interaction index to deal with the interactions between elements of information. The proposed operator takes into account not only the importance of elements or their ordered positions but also the interaction among criteria during the evaluation process. A case of customers’ satisfaction over two fast restaurants in Malaysia is presented to illustrate the application of the proposed aggregation operator. Based on three customers’ satisfaction criteria, restaurant 1 and restaurant 2 received CI-FM scores of 0.711011 and 0.704945, respectively. Interestingly, the criterion “services” constantly received the highest rating across both restaurants. In addition, the proposed aggregation operator successfully identified which restaurant is superior in the eyes of customers. Finally, this study offers some research ideas for the future.

Ordered Weighted Aggregation Networks for Video Face Recognition

Video face recognition generally includes a step where all descriptors extracted for each frame are aggregated to generate a single video face representation. The most commonly used operator for aggregation is average, which gives the same relevance to each frame. Some adaptive aggregation algorithms have been developed, but most of them rely on the use of weighted mean as aggregation operator, thus disregarding many other types of aggregation operators. In this paper, we propose a novel adaptive aggregation scheme based on ordered weighted average (OWA) operators in contrast with the mainly used weighted mean scheme. Furthermore, besides presenting the theoretical aspects of our aggregation scheme, we develop two different concrete implementations to validate its suitability for video face recognition: Ordered weighted aggregation network (OWANet) and Weighted OWANet (WOWANet). Both algorithms are based on neural networks and are trainable through gradient descent in a classic supervised learning way. We conduct extensive experiments on YouTube Faces, COX Face and the IARPA Janus Benchmark A for evaluating recognition performance on verification and identification tasks. The experimentation process shows that both proposals achieve very competitive results in accuracy with respect to the existent state-of-the-art methods, while significantly reducing space and inference time.

ВИБІР ОПЕРАТОРІВ АГРЕГУВАННЯ ДЛЯ БАГАТОКРИТЕРІАЛЬНОЇ ОЦІНКИ ПРИДАТНОСТІ ТЕРИТОРІЙ

The article discusses the issues of improving the adequacy and validity of the results of the convolution of criteria evaluation into a generalized evaluation when conducting a multi-criteria analysis of the land suitability  by choosing the appropriate type of aggregation operator that can be performed in the GIS environment and has the properties that allow the most complete formalization of expert knowledge about the features of this applied area. Based on the analysis of the causes of the fuzziness of information in multicriteria decision-making models, the properties that the aggregation operator must have are formulated. A comparative analysis of various aggregation operators for the construction of complex maps of the suitability of territories is carried out. The features of the execution of aggregation operators are investigated: minimum, maximum, arithmetic mean, weighted sum, OWA Yager operator. It is shown that the most justified choice is to use the OWA Yager operator with fuzzy quantifiers, which allows you to provide expert information on the acceptable form of a compromise between evalutions by individual criteria. The use a family of the RIM quantifiers to formalize the attitude of DM to risk in making decisions is proposed. An example of the use of the OWA Yager operator with fuzzy quantifiers for calculating the convolution of criteria evalutions is given. It is shown that the Yager OWA operator with fuzzy quantifiers is a universal aggregation operator, since it has the ability to implement a wide range of decision-making strategies: from  minimum operator to maximum operator.

Quantile induced heavy ordered weighted averaging operators and its application in incentive decision making

To integrate incentives into the information aggregation process in decision making, we propose a new type of aggregation operator, denominated as the quantile induced heavy ordered weighted averaging (QI-HOWA) operator in this paper. A primary characteristic of this type of operator is that the quantile variable can be used not only to measure the relative performance of alternatives but also to facilitate the incentive preference expression of the decision maker. We further provide a calculation technology of the QI-HOWA weights, in which various incentive preferences of the decision maker can be considered through parameter adjustment. In addition, we discuss certain properties of the QI-HOWA operator and note the extent to which they are effective. Finally, a numerical example regarding the selection of optimal alternatives by incentive measures is provided, and the aggregations are compared with those of ordered weighted averaging and unweighted averaging operators to illustrate the validity of the QI-HOWA operator.

Consistency of the fused intuitionistic fuzzy preference relation in group intuitionistic fuzzy analytic hierarchy process

Intuitionistic fuzzy preference relations (IFPRs), which are based on Atanassov's intuitionistic fuzzy sets (A-IFS), have turned out to be a useful structure in expressing the experts’ uncertain judgments, and the intuitionistic fuzzy analytic hierarchy process (IFAHP) is a method for solving multiple criteria decision making problems. To provide a theoretical support for group decision making with IFAHP, this paper presents some straightforward and useful results regarding to the aggregation of IFPRs. Firstly, a new type of aggregation operator, namely, simple intuitionistic fuzzy weighted geometric (SIFWG) operator, is developed to synthesize individual IFPRs. It is well known that for traditional comparison matrices, if all individual comparison matrices are of acceptable consistency, then their weighted geometric mean complex judgment matrix is of acceptable consistency. In this paper, we prove that this property holds for IFPRs as well if we use the SIFWG operator to synthesize the individual IFPRs. A numerical example is given to verify the theorems. It is pointed out that the well-known simple intuitionistic fuzzy weighted averaging (SIFWA) operator, the intuitionistic fuzzy weighted averaging (IFWA) operator, the intuitionistic fuzzy weighted geometric (IFWG) operator and the symmetric intuitionistic fuzzy weighted geometric (SYIFWG) operator do not have this property. Finally, the group IFAHP (GIFAHP) procedure is developed to aid group decision making process with IFPRs.

Modeling decisions with dempster-shafer belief structures

The paper presents the theoretical concepts and problems of decision making with Dempster-Shafer belief structures. We have presented a method of decision support based on belief structures which allows taking into consideration the subjective expert information that formalized in the form of family of estimations by forming the combination of hypotheses and using the ordered weighted average operators. We have developed the decision making process allowing estimate the minimum and maximum objectives (risks and gains) and using different types of aggregation operators. Depending on the particular problem the different types of ordering operators has been used to ensure the variability of objectives: descending order for tasks where the purpose is to obtain the best results and the ascending order for the problems in which the lowest value is the best one. Finally, an illustrative example has been given to modeling different decisions.

SOME INDUCED UNCERTAIN GEOMETRIC AGGREGATION OPERATORS WITH PURE LINGUISTIC INFORMATION AND THEIR APPLICATION TO GROUP DECISION MAKING

In this paper, we develop some new aggregation operators with pure linguistic information including the uncertain pure linguistic weighted geometric mean (UPLWGM) operator, the induced uncertain pure linguistic ordered weighted geometric mean (IUPLOWGM) operator, and the induced uncertain pure linguistic hybrid geometric mean (IUPLHGM) operator. These developed aggregation operators are very suitable to deal with the situation where the input arguments are represented in uncertain pure linguistic variables. Also, as a more general type of aggregation operator, the IUPLHGM operator is based on the UPLWGM and IUPLOWGM operators, and it can reflect the importance degrees of both the given uncertain linguistic variables and their ordered positions. Moreover, in the situations where the information about all the attribute weights, the attribute values and the expert weights are expressed in the form of linguistic labels variables, we develop an approach based on the IUPLHGM operator for multiple attribute group decision making with pure linguistic information. Finally, an application of the developed approach to group decision making problem regarding the selection of investments is given. Also, we present a comparative analysis with other related decision making methods to demonstrate the effectiveness of the developed approach.

Fuzzy aggregation operators in decision making with Dempster–Shafer belief structure

We study the decision-making problem with Dempster–Shafer theory of evidence. We analyze how to deal with this model when the available information is uncertain and it can be represented with fuzzy numbers. We use different types of aggregation operators that aggregate fuzzy numbers such as the fuzzy weighted average (FWA), the fuzzy ordered weighted averaging (FOWA) operator and the fuzzy hybrid averaging (FHA) operator. As a result, we get the belief structure fuzzy weighted average (BS-FWA), the belief structure fuzzy ordered weighted averaging (BS-FOWA) operator and the belief structure fuzzy hybrid averaging (BS-FHA) operator. We further generalize this new approach by using generalized and quasi-arithmetic means. We also develop an illustrative example regarding the selection of investments where we can see the different results obtained by using different types of fuzzy aggregation operators.

Induced generalized intuitionistic fuzzy operators

We study the induced generalized aggregation operators under intuitionistic fuzzy environments. Choquet integral and Dempster–Shafer theory of evidence are applied to aggregate inuitionistic fuzzy information and some new types of aggregation operators are developed, including the induced generalized intuitionistic fuzzy Choquet integral operators and induced generalized intuitionistic fuzzy Dempster–Shafer operators. Then we investigate their various properties and some of their special cases. Additionally, we apply the developed operators to financial decision making under intuitionistic fuzzy environments. Some extensions in interval-valued intuitionistic fuzzy situations are also pointed out.

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.

Induced aggregation operators in decision making with the Dempster-Shafer belief structure

We study the induced aggregation operators. The analysis begins with a revision of some basic concepts such as the induced ordered weighted averaging (IOWA) operator and the induced ordered weighted geometric (IOWG) operator. We then analyze the problem of decision making with Dempster-Shafer theory of evidence. We suggest the use of induced aggregation operators in decision making with Dempster-Shafer theory. We focus on the aggregation step and examine some of its main properties, including the distinction between descending and ascending orders and different families of induced operators. Finally, we present an illustrative example in which the results obtained using different types of aggregation operators can be seen.

A retrospective study of a hybrid document-context based retrieval model

This paper describes our novel retrieval model that is based on contexts of query terms in documents (i.e., document contexts). Our model is novel because it explicitly takes into account of the document contexts instead of implicitly using the document contexts to find query expansion terms. Our model is based on simulating a user making relevance decisions, and it is a hybrid of various existing effective models and techniques. It estimates the relevance decision preference of a document context as the log-odds and uses smoothing techniques as found in language models to solve the problem of zero probabilities. It combines these estimated preferences of document contexts using different types of aggregation operators that comply with different relevance decision principles (e.g., aggregate relevance principle). Our model is evaluated using retrospective experiments (i.e., with full relevance information), because such experiments can (a) reveal the potential of our model, (b) isolate the problems of the model from those of the parameter estimation, (c) provide information about the major factors affecting the retrieval effectiveness of the model, and (d) show that whether the model obeys the probability ranking principle. Our model is promising as its mean average precision is 60–80% in our experiments using different TREC ad hoc English collections and the NTCIR-5 ad hoc Chinese collection. Our experiments showed that (a) the operators that are consistent with aggregate relevance principle were effective in combining the estimated preferences, and (b) that estimating probabilities using the contexts in the relevant documents can produce better retrieval effectiveness than using the entire relevant documents.

ASA and its application to multi-criteria decision making

Aggregation plays an important role in many applications related to the development of intelligent systems. In a fuzzy environment the existing aggregation operators are generally the t-norm, t-conorm, mean operators, Yager's operator and γ-operator. However, these aggregation operators do not properly reflect the situation in the aggregation process. That is, these types of aggregation operators are independent of the aggregation situation. In order to solve these problems we propose a new aggregation method to reflect the situation in the aggregation process. It is the aggregation based on situation assessment (ASA) method. It consists of the situation assessment model (SAM) and the ASA algorithm. In this ASA method, the SAM is utilized to reflect the situation in the aggregation process. This model generates the parameter, which is controlled by decision-maker. It indicates the current degree of aggregation situation. Therefore, our method can be adapted to certain situations by using the parameter. In this paper, ASA method is applied to the multi-criteria decision making environment.

A new aggregation method in a fuzzy environment

Information aggregation provides a starting point for the ability to make useful inferences from large collections of data, and so it plays an important role in many applications related to the development of intelligent systems. In a fuzzy environment, the existing aggregation operators are generally the t-norm, t-conorm, mean operators, Yager's operator and γ-operator. However, these aggregation operators do not reflect the situation in the aggregation process, i.e., these types of aggregation operators are independent of the aggregation situation. In order to solve these problems, we propose a new aggregation method to reflect the situation in the aggregation process. It is the aggregation based on situation assessment (ASA) method. It consists of the situation assessment model (SAM) and the ASA algorithm. In this ASA method, the SAM is utilized to reflect the situation in the aggregation process. This model generates the parameter, which is controlled by the decision maker. It indicates the current degree of aggregation situation. Therefore, our method can be adapted to certain situations by using the parameter.

Controlling selectivity in nonstandard pattern recognition algorithms

A type of aggregation operator, referred to as mixed connectives, is used to summarize the information about objects to be classified (supplied by the descriptors). Because mixed connectives depend on a parameter, this leads to the concept of families for these operators. Therefore, given such a family, it is possible to associate different classifications with the same data set, depending on the value chosen for the parameter. The manner in which the algorithm selectivity classifications are compared is illustrated by an example involving a quantitative data basis. >