THE GENERALIZED ADEQUACY COEFFICIENT AND ITS APPLICATION IN STRATEGIC DECISION MAKING

Bonferroni means with distance measures and the adequacy coefficient in entrepreneurial group theory

With respect to multicriteria supplier selection problems with interval 2-tuple linguistic information, a new decision making approach that uses distance measures is proposed. Motivated by the ordered weighted distance (OWD) measures, in this paper, we develop some interval 2-tuple linguistic distance operators such as the interval 2-tuple weighted distance (ITWD), the interval 2-tuple ordered weighted distance (ITOWD), and the interval 2-tuple hybrid weighted distance (ITHWD) operators. These aggregation operators are very useful for the treatment of input data in the form of interval 2-tuple linguistic variables. We study some desirable properties of the ITOWD operator and further generalize it by using the generalized and the quasi-arithmetic means. Finally, the new approach is utilized to complete a supplier selection study for an actual hospital from the healthcare industry.

Induced and heavy aggregation operators with distance measures

This article introduces the uncertain ordered weighted averaging adequacy coefficient (UOWAAC) operator. This novel operator uses the ordered weighted averaging (OWA) operator, the adequacy coefficient, and the interval numbers in a single formulation. This article also extends the UOWAAC operator by using order-inducing variables in the reordering process of the input arguments. This new extension is called the uncertain induced ordered weighted averaging adequacy coefficient (UIOWAAC) operator. The article also presents an application of the new approach in a multi-criteria group decision making (MCGDM) problem about international expansion. In addition, a comparative analysis is conducted with the purpose of demonstrating the superiority of the UOWAAC and UIOWAAC aggregation operators in specific situations. Likewise, the use of basic uncertain information (BUI) is discussed. The results show the usefulness of these new aggregation operators in real-life decision making problems under uncertainty, particularly when the decision maker wants to compare different alternatives with an ideal but without giving any penalty or reward in the case that the ideal levels are exceeded.

The power Heronian aggregation (PHA) operator can use the advantages of power average and the Heronian mean operator, which together could take into account the interrelationship of the aggregated arguments, and therefore alleviate the effects caused by unreasonable data through considering the support degree between input arguments. However, PHA operators cannot be used to process single-valued neutrosophic numbers (SVNNs), which is significant for extending it to SVNNs. We propose some new PHA operators for SVNNs and introduce a novel MAGDM method on the basis of the proposed operators. Firstly, the definition, properties, comparison method, and operational rules of SVNNs are introduced briefly. Then, some PHA operators are proposed, such as the single-valued neutrosophic power Heronian aggregation (SVNPHA) operator, the single-valued neutrosophic weighted power Heronian aggregation (SVNWPHA) operator, single-valued neutrosophic geometric power Heronian aggregation (SVNGPHA) operator, single-valued neutrosophic weighted geometric power Heronian aggregation (SVNWGPHA) operator. Furthermore, we discuss some properties of these new aggregation operators and several special cases. Moreover, the method to solve the MAGDM problems with SVNNs is proposed, based on the SVNWPHA and SVNWGPHA operators. Lastly, we verified the application and effectiveness of the proposed method by using an example for the MAGDM problem.

A new decision making method called linguistic induced ordered weighted averaging distance (LIOWAD) operator by using induced aggregation operators and linguistic information in the Hamming distance. This aggregation operator provides a parameterized family of linguistic aggregation operators that includes the maximum distance, the minimum distance, the linguistic normalized Hamming distance, the linguistic weighted Hamming distance and the linguistic ordered weighted averaging distance, among others. So give special attention to the analysis of different particular types of LlOWAD operators. End the paper with an application of the new approach in a decision making problem about selection of investments under linguistic environment.KeywordsLinguistic InformationIOWA OperatorDistance MeasureDecision Making

A k-nearest neighbor (k-NN) query retrieves k objects from a database that are considered to be the closest to a given query point. Numerous techniques have been proposed in the past for supporting efficient k-NN searches in continuous data spaces. No such work has been reported in the literature for k-NN searches in a non-ordered discrete data space (NDDS). Performing k-NN searches in an NDDS raises new challenges. The Hamming distance is usually used to measure the distance between two vectors (objects) in an NDDS. Due to the coarse granularity of the Hamming distance, a k-NN query in an NDDS may lead to a large set of candidate solutions, creating a high degree of non-determinism for the query result. We propose a new distance measure, called granularity-enhanced Hamming (GEH) distance, that effectively reduces the number of candidate solutions for a query. We have also considered using multidimensional database indexing for implementing k-NN searches in NDDSs. Our experiments on synthetic and genomic data sets demonstrate that our index-based k-NN algorithm is effective and efficient in finding k-NNs in NDDSs.

Decision-making in sport management based on the OWA operator

In this paper, a new version of distance measure for hesitant fuzzy linguistic term sets is developed. The new version of distance measure provides an objective way to handle the diverse dimensions of two HFLTSs, i.e., without shortening the HFLTS to be a linguistic interval or extending the shorter one by adding linguistic terms. The Hamming distance, the Euclidean distance and the corresponding forms are put forward. By the relationship between the distance measure and the similarity measure, some parallel similarity measures are also investigated. As applications of the proposed measures, the issues of pattern recognition, clustering analysis and multi-criteria decision making are considered.

This paper proposes a new method to deal with the multi-attribute group decision making (MAGDM) problem. Firstly, a new distance measure between two linguistic terms is defined, then a new linguistic information aggregation operator based on the distance measure is proposed and their properties are studied. Secondly, in order to deal with multi-attribute group decision making problem under linguistic environment, a similarity measure between two linguistic preference matrices is proposed. The aggregation operator and the similarity measure are applied to a MAGDM problem. Finally, a numerical example is proposed to prove that the new operator is effective in the MAGDM problems. This method avoid the case that a numerical value times a linguistic information and the results of evaluation are still belongs to the original linguistic term set no matter how to calculate. By using the supporting of the order, the linguistic information can not be lose in the aggregation process. Keywords-Distance measure; linguistic information; aggregation operator; similarity measure; MAGDM

ABSTRACTThis paper presents the heavy ordered weighted moving average (HOWMA) operator. It is an aggregation operator that uses the main characteristics of two well-known techniques: the heavy ordered weighted averaging (OWA) and the moving averages. Therefore, this operator provides a parameterized family of aggregation operators from the minimum to the total operator and includes the OWA operator as a special case. It uses a heavy weighting vector in the moving average formulation and it represents the information available and the knowledge of the decision maker about the future scenarios of the phenomenon, according to his attitudinal character. Some of the main properties of this operator are studied, including a wide range of families of HOWMA operators such as the heavy moving average and heavy weighted moving average operators. The HOWMA operator is also extended using generalized and quasi-arithmetic means. An example concerning the foreign exchange rate between US dollars and Mexican pesos is also presented.

Nine oat cultivars and experimental lines from four diverse germ plasm sources were crossed in a diallel mating design, without reciprocals. Heterosis for grain yield was evaluated in two experiments and 48 F2-derived lines from each of the 36 matings were evaluated for bundle weight, grain yield, straw yield, harvest index, and heading date in two experiments. The number of transgressive segregates per trait and generalized genetic variances were calculated for each mating. Euclidean distance between parents was calculated by using the first five principal components of the parental correlation matrix. The distance measures of W. D. Hanson and E. Casas (1968. Biometrics, 24: 867–880) and T. S. Cervantes, M. M. Goodman, E. Casas, and J. O. Rawlings (1978. Genetics, 90: 339–348) were calculated for each of two experiments. The relationships between the three distance measures and the three types of breeding behavior were examined via correlation and regression. Euclidean distance was negatively correlated with transgressive segregation and generalized genetic variances. Hanson and Casas' distance measure was positively correlated with transgressive segregation and generalized genetic variances. The distance measure of Cervantes et al. was negatively correlated with heterosis in one experiment. Regressions on the three distances measures, when significant, were linear. The single exception was the regression of heterosis on Euclidean distance, which had significant linear and quadratic coefficients and high R2. No distance measure was closely associated with all three types of breeding behavior. Using information from more than one measure improved the R2 value for polynomial regressions. Key words: oats, genetic distance, heterosis, generalized variances.

Managing ambiguous and asymmetric types of information is a very challenging task under the consideration of classical data. Furthermore, Aczel-Alsina aggregation operators are the new developments in fuzzy sets theory. However, when decision-makers need to use these structures in fuzzy rough structures, these operators fail to deal with such types of values, as fuzzy rough structures use lower and upper approximation spaces. Thus, an encasement of an intuitionistic fuzzy set has a chance of data loss, whereas an intuitionistic fuzzy rough set can resolve the problem of data loss. Motivated by the notion of intuitionistic fuzzy rough sets and new aggregation operators i.e., intuitionistic fuzzy Aczel-Alsina operators, this paper firstly initiates some basic Aczel-Alsina operational rules for intuitionistic fuzzy rough numbers. Secondly, based on these newly defined operational rules, we have developed some new aggregation operators, such as intuitionistic fuzzy rough Aczel-Alsina weighted average (IFRAAWA), intuitionistic fuzzy rough Aczel-Alsina ordered weighted average (IFRAAOWA), and intuitionistic fuzzy rough Aczel-Alsina hybrid average (IFRAAHA) aggregation operators. Moreover, the properties of these aggregation operators have been initiated. These operators can help in evaluating awkward and asymmetric information in real-life problems. The use of aggregation operators in medical diagnosis and MADM is an efficient method that can help in healthcare and decision-making applications. To present an effective use of these developed operators in medical diagnosis and the selection of the best next-generation firewall, we have established an algorithm along with a numerical example to provide authenticity and clarity to the established work. Furthermore, a comparative analysis of the introduced work shows the superiority of the introduced approach.

The natural properties of the aggregation operators and the most elementary ones are the idempotence, the monotonicity and the continuity from below. We assume only these properties for the aggregation operators with infinitely many inputs, defined by functionals on the family of measurable functions. A family of fuzzy measures is associated with each aggregation operator. The properties of horizontal or vertical pseudo-additivity are recognizable by means of this family of fuzzy measures.

Aggregation operators are important tools for solving multi-attribute group decision-making (MAGDM) problems. The main challenging issue for aggregating data in a MAGDM problem is how to develop a symmetric aggregation operator expressing the decision makers’ behavior. In the literature, there are some methods dealing with this difficulty; however, they lack an effective approach for multi-polar inputs. In this study, a new aggregation operator for m-polar fuzzy soft sets (M-pFSMWM) reflecting different agreement scenarios within a group is presented to proceed MAGDM problems in which both attributes and experts have different weights. Moreover, some desirable properties of M-pFSMWM operator, such as idempotency, monotonicity, and commutativity (symmetric), that means being invariant under any permutation of the input arguments, are studied. Further, m-polar fuzzy soft induced ordered weighted average (M-pFSIOWA) operator and m-polar fuzzy soft induced ordered weighted geometric (M-pFSIOWG) operator, which are extensions of IOWA and IOWG operators, respectively, are developed. Two algorithms are also designed based on the proposed operators to find the final solution in MAGDM problems with weighted multi-polar fuzzy soft information. Finally, the efficiency of the proposed methods is illustrated by some numerical examples. The characteristic comparison of the proposed aggregation operators shows the M-pFSMWM operator is more adaptable for solving MAGDM problems in which different cases of agreement affect the final outcome.