Regular Increasing Monotone Quantifier Research Articles

A hesitant fuzzy wind speed forecasting system with novel defuzzification method and multi-objective optimization algorithm

Owing to the nondeterministic nature of wind speed, the conventional fuzzy time series forecasting model has difficulty in establishing a common membership level. Therefore, in this study, the fuzzy series forecasting model was improved based on hesitant fuzzy sets. A hesitant fuzzy wind speed forecasting system with a novel defuzzification method and multiobjective optimization algorithm was developed. First, an advanced decomposition model is employed to extract the effective feature and remove the noise component from the raw wind speed series. Then, the universe of discourse is partitioned into equal and unequal intervals by multifuzzification methods and merged by aggregating hesitant information. A multiobjective intelligent optimization algorithm is applied to determine the optimal weights of different intervals accurately and stably. Furthermore, a novel defuzzification model based on an ordered weighted averaging operator and a regular increasing monotone quantifier is proposed to calculate the final forecasting results. The crucial strengths of the developed system are verifying the possibility of enhancing the performance of wind speed forecasting models by improving conventional fuzzy time series forecasting models and integrating them with decomposition models and artificial-intelligence models. Typical wind speed series datasets with different resolutions were selected to evaluate the performance of the proposed system, and experimental results prove that the proposed system outperforms other comparison models with high forecasting accuracy and computing efficiency.

The General Model for Least Convex Disparity RIM Quantifier Problems

Hong (Mathematics 2019, 7, 326) recently introduced the general least squares deviation (LSD) model for ordered weighted averaging (OWA) operator weights. In this paper, we propose the corresponding generalized least square disparity model for regular increasing monotone (RIM) quantifier determination under a given orness level. We prove this problem mathematically. Using this result, we provide the full solution of the least square disparity RIM quantifier model as an illustrative example.

Elliptical distribution-based weight-determining method for ordered weighted averaging operators

The ordered weighted averaging (OWA) operators play a crucial role in aggregating multiple criteria evaluations into an overall assessment supporting the decision makers’ choice. One key point steps is to determine the associated weights. In this paper, we first briefly review some main methods for determining the weights by using distribution functions. Then we propose a new approach for determining OWA weights by using the regular increasing monotone quantifier. Motivated by the idea of normal distribution-based method to determine the OWA weights, we develop a method based on elliptical distributions for determining the OWA weights, and some of its desirable properties have been investigated.

Classification of Denver System of Chromosomes Using Similarity Classifier Guided by OWA Operators

This paper proposes a Similarity Classifier guided by Ordered Weighted Averaging (OWA) operators to classify ‘Denver System’ of human chromosomes. A chromosome is assigned to one of the seven groups from A to G, based on the ‘Denver System’ of classification of chromosomes. Chromosomes within the group are difficult to identify, possessing almost identical characteristics including the length and centromere position. The proposed method is applied to the chromosome dataset and the similarity values using the generalized Lukasiewicz structure are calculated. The similarity values are aggregated with the help of Ordered Weighted Averaging (OWA) operators with a Regular Increasing Monotone (RIM) quantifier and the chromosome is assigned to that group for which it has the highest value of similarity. This work evaluates the performance of classifiers including Naive Bayes, Quadratic classifier and a novel, unsupervised, Fuzzy Similarity Classifier guided by OWA Operators, in classifying the Denver Group of chromosomes. A fundamental review on fuzzy similarity based classification is also presented. Experimental results clearly demonstrates that the proposed Fuzzy Similarity Classifier guided by OWA Operators with a RIM quantifier, produces the best classification results with a mean classification accuracy of 96.0028% and variance of 5.0871e-005. Statistical testing with one-way Analysis of Variance (ANOVA) at 95% and 99% level of confidence and Tukey’s post-hoc analysis is performed to validate the selection of the classifier. The proposed Fuzzy Similarity Classifier gives the most promising classification results and can be applied to any large scale biomedical data and other applications. Keywords: Analysis of variance, chromosomes, classification, denver system, fuzzy similarity classifier, lukasiewicz structure, ordered weighted averaging, operators, regular increasing monotone, quantifier, Tukey's post-hoc.

The orness measures for two compound quasi-arithmetic mean aggregation operators

The paper first summarizes the orness measures and their common characteristics of some averaging operators: the quasi-arithmetic mean, the ordered weighted averaging (OWA) operator, the regular increasing monotone (RIM) quantifier and the weighted function average operator, respectively. Then it focuses on the aggregation properties and operator determination methods for two kinds of quasi-arithmetic mean-based compound aggregation operators: the quasi-OWA (ordered weighted averaging) operator and the Bajraktarević mean. The former is the combination of the quasi-arithmetic mean and the OWA operator, while the latter is the combination of the quasi-arithmetic mean and the weighted function average operator. Two quasi-OWA operator forms are given, where the OWA operator is assigned directly or generated from a RIM (regular increasing monotone) quantifier indirectly. The orness indexes to reflect the or-like level of the quasi-OWA operator and Bajraktarević mean are proposed. With generating function techniques, the properties of the quasi-OWA operator and Bajraktarević mean are discussed to show the rationality of these orness definitions. Based on these properties, two families of parameterized quasi-OWA operator and Bajraktarević mean with exponential and power function generators are proposed and compared. It shows that the method of this paper can also be applied to other function-based aggregation operators.

On the properties of regular increasing monotone (RIM) quantifiers with maximum entropy††

Compared with the large number of research papers dealing with the ordered weighted averaging (OWA) operators, the research on relative quantifiers has been relatively sparse so far. With the quantifier guided aggregation method of OWA operators and the generating function representation of regular increasing monotone (RIM) quantifiers, a parameterized RIM quantifier family with the maximum entropy principle is proposed. This quantifier family can be regarded as the continuous case of the commonly used maximum entropy OWA (MEOWA) operator. Like the MEOWA operator, the RIM quantifier with maximum entropy generating function also possesses some interesting properties. One of them is that the aggregation value for any aggregated set always monotonically increases with the orness level. This can be used to represent the decision maker's preference information, but with free dimension.

On the equivalence of some approaches to the OWA operator and RIM quantifier determination

The ordered weighted averaging (OWA) operator is a widely used aggregation method, and its determination is usually a prerequisite step in many related applications. The regular increasing monotone (RIM) quantifier can be seen as the continuous case of the OWA operator with the quantifier aggregation method. Some approaches with optimization criteria for the determination of OWA operator and RIM quantifier were proposed. Although these problems look different at the first sight, a deeper investigation can reveal the equivalence of solutions between them. Inspired by the solution equivalence of minimum variance problems and minimax disparity problem for OWA operator, we propose the minimax disparity RIM quantifier problem and two minimax ratio problems for OWA operator and RIM quantifier, respectively. We investigate the equivalence of solutions for the maximum entropy and minimax ratio problems, and solutions for the minimum variance and minimax disparity problems of OWA operator and RIM quantifier, respectively, by a theoretical point of view.

A general model of parameterized OWA aggregation with given orness level

The paper proposes a general optimization model with separable strictly convex objective function to obtain the consistent OWA (ordered weighted averaging) operator family. The consistency means that the aggregation value of the operator monotonically changes with the given orness level. Some properties of the problem are discussed with its analytical solution. The model includes the two most commonly used maximum entropy OWA operator and minimum variance OWA operator determination methods as its special cases. The solution equivalence to the general minimax problem is proved. Then, with the conclusion that the RIM (regular increasing monotone quantifier) can be seen as the continuous case of OWA operator with infinite dimension, the paper further proposes a general RIM quantifier determination model, and analytically solves it with the optimal control technique. Some properties of the optimal solution and the solution equivalence to the minimax problem for RIM quantifier are also proved. Comparing with that of the OWA operator problem, the RIM quantifier solutions are usually more simple, intuitive, dimension free and can be connected to the linguistic terms in natural language. With the solutions of these general problems, we not only can use the OWA operator or RIM quantifier to obtain aggregation value that monotonically changes with the orness level for any aggregated set, but also can obtain the parameterized OWA or RIM quantifier families in some specific function forms, which can incorporate the background knowledge or the required characteristic of the aggregation problems.

Orness and parameterized RIM quantifier aggregation with OWA operators: A summary

A necessary and sufficient condition for the ordered weighted average (OWA) aggregation value of an arbitrary aggregated set to consistently increase with the orness level is proposed. The OWA operator properties associated with the orness level are extended. Then, with the generating function representation of Regular Increasing Monotone (RIM) quantifier, all these conditions and properties are extended to the case of RIM quantifiers, which can be seen as the continuous OWA operator with free dimension. Some families of consistency RIM quantifiers and their corresponding OWA operators are summarized. Some existing linguistic term RIM quantifiers are collected and two parameterized generalization forms of them are proposed, which can be useful for the selection and comparison of the linguistic quantifier in theory and applications.

On the properties of equidifferent OWA operator

Getting OWA weights under given orness level is an active topic in the OWA operator research. The paper proposes a series of weights generating methods in equidifferent forms. Similar to the geometric (maximum entropy) OWA operator, we propose a parameterized OWA operator called equidifferent OWA operator, which consist the adjacent weighes with a common difference. The maximum spread equidifferent OWA (MSEOWA) operator is equivalent to the minimum variance OWA operator, but is more computational efficient. Some properties associated with the orness level are discussed. One of them is that the aggregation value for any elements set is always increasing with the orness level, which can used as a parameterized aggregation method with orness as its control parameter. These properties similar to that of the geometric (maximum entropy) OWA operator, which can also be seen as the discrete case of equidifferent RIM (regular increasing monotone) quantifiers. The general forms of equidifferent OWA operator are proposed, and the weights generating methods are also extended in a similar way.

Some properties of the weighted OWA operator

Based on the researches on ordered weighted average (OWA) operator, the weighted OWA operator (WOWA) and especially the quantifier guided aggregation method, with the generating function representation of regular increasing monotone (RIM) quantifier technique, we discuss the properties of WOWA operator with RIM quantifier in the respect of orness. With the continuous OWA and WOWA ideas recently proposed by Yager, an improvement on the continuous OWA and WOWA operator is proposed. The properties of WOWA are also extended from discrete to the continuous case. Based on these properties, two families of parameterized RIM quantifiers for WOWA operator are proposed, which have exponential generating function and piecewise linear generating function respectively. One interesting property of these two kinds of RIM quantifiers is that for any aggregated set (or variable) under any weighted (distribution) function, the aggregation values are always consistent with the orness (optimistic) levels, so they can be used to represent the decision maker's preference, and we can get the preference value of fuzzy sets or random variables with the orness level of RIM quantifier as their control parameter.

On the properties of equidifferent RIM quantifier with generating function†

Comparing the large number of research papers on the ordered weighted averaging (OWA) operator, the researches on relative quantifier are relatively rare so far. In the present paper, based on the quantifier guided aggregation method with OWA operator which was proposed by Yager [“Quantifier guided aggregation using OWA operators”, Int. J. Intell. Syst., 11, pp. 49–73, 1996], a generating function representation method for regular increasing monotone (RIM) quantifiers is proposed. We extend the the properties of OWA operator to the RIM quantifier which is represented with a monotone function instead of the OWA weighting vector. A class of parameterized equidifferent RIM quantifier which has minimum variance generating function is proposed and its properties are also analyzed. The equidifferent RIM quantifier is consistent with its orness level for any aggregated elements, which can be used to represent the decision maker's preference.

Preference solutions of probability decision making with rim quantifiers

This article extends the quantifier-guided aggregation method to include probabilistic information. A general framework for the preference solution of decision making under an uncertainty problem is proposed, which can include decision making under ignorance and decision making under risk methods as special cases with some specific preference parameters. Almost all the properties, especially the monotonicity property, are kept in this general form. With the generating function representation of the Regular Increasing Monotone (RIM) quantifier, some properties of the RIM quantifier are discussed. A parameterized RIM quantifier to represent the valuation preference for probabilistic decision making is proposed. Then the risk attitude representation method is integrated in this quantifier-guided probabilistic decision making model to make it a general form of decision making under uncertainty. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 1253–1271, 2005.