On the dispersion measure of OWA operators

We describe some basic features of the OWA operator. We turn to the problem of determining the weights associated with this operator and particularly the maximal dispersion (entropy) approach. We consider the possibility of using minimization of dispersion. After discussing concerns with both maximization and minimization of dispersion we investigate the possibility of finding an optimal solution intermediate to these extremes. We next consider alternative measures of dispersion. We introduce a fundamental requirement for a measure of dispersion called the Preference for Equal Division. A number of general classes of dispersion measures are provided notable among these are those based on t-norm and t-conorm operators.     

OWA aggregation of intuitionistic fuzzy sets

We recall the concept of an intuitionistic fuzzy subset (IFS). Fundamental to an IFS is the fact that it is defined using two values, a degree of membership and degree of non-membership. The ordered weighted averaging (OWA) operator is introduced and several of its features are described. Particularly notable is the idea of the dual of an OWA operator. We next discuss the aggregation of a collection of IFS using a prescribed OWA operator. It is shown that while the aggregation of the degrees of membership is performed using the prescribed OWA operator, the aggregation of the degrees of non-membership requires use of the dual of the prescribed OWA operator. The Choquet integral aggregation operator is introduced and applied to the aggregation of IFSs. Here again the concept of the dual is needed to perform the aggregation of the degrees of non-membership. We also discuss the aggregation of IFSs using the Sugeno integral. Fundamental to this work is our realisation of the importance of the concept of the dual operators in dealing with the aggregation of IFS.     

Decision Making in Reinsurance with Induced OWA Operators and Minkowski Distances

The decision to choose a reinsurance program has many complexities because it is difficult to simultaneously achieve high levels in different optimal criteria including maximum gain, minimum variance, and probability of ruin. This article suggests a new method by which, through membership functions, we can measure the distance of each alternative to an optimal result and aggregate it by using different types of aggregations. In this article, particular attention is given to the induced Minkowski ordered weighted averaging distance operator and the induced Minkowski probabilistic ordered weighted averaging distance operator. The main advantage of these operators is that they include a wide range of special cases. Thus, they can adapt efficiently to the specific needs of the calculation processes. By doing so, the reinsurance system can make better decisions by using different scenarios in the uncertain environment considered.     

On generalized intuitionistic fuzzy rough approximation operators

In rough set theory, the lower and upper approximation operators defined by binary relations satisfy many interesting properties. Various generalizations of Pawlak’s rough approximations have been made in the literature over the years. This paper proposes a general framework for the study of relation-based intuitionistic fuzzy rough approximation operators within which both constructive and axiomatic approaches are used. In the constructive approach, a pair of lower and upper intuitionistic fuzzy rough approximation operators induced from an arbitrary intuitionistic fuzzy relation are defined. Basic properties of the intuitionistic fuzzy rough approximation operators are then examined. By introducing cut sets of intuitionistic fuzzy sets, classical representations of intuitionistic fuzzy rough approximation operators are presented. The connections between special intuitionistic fuzzy relations and intuitionistic fuzzy rough approximation operators are further established. Finally, an operator-oriented characterization of intuitionistic fuzzy rough sets is proposed, that is, intuitionistic fuzzy rough approximation operators are defined by axioms. Different axiom sets of lower and upper intuitionistic fuzzy set-theoretic operators guarantee the existence of different types of intuitionistic fuzzy relations which produce the same operators.     

Fuzzy quantifiers in sensitivity analysis of OWA operator

The efficient use of the Ordered Weighted Averaging (OWA) operator in decision making problems depends on the choice of the order weights. Using fuzzy quantifiers is one of the most popular methods to obtain them. In this study, a new method will be introduced for determining the order weights from the quantifiers, which is especially useful in the case of unimodal quantifiers. The new method is generic and has better computational efficiency in comparison to the previously applied methods. In addition, a new measure for sensitivity analysis on the outputs of OWA operator will be introduced. The theoretical results will be illustrated by a Ph.D. student selection problem discussed earlier in the literature.     

Weighted‐selective aggregated majority‐OWA operator and its application in linguistic group decision making

This paper focuses on the aggregation operations in the group decision‐making model based on the concept of majority opinion. The weighted‐selective aggregated majority‐OWA (WSAM‐OWA) operator is proposed as an extension of the SAM‐OWA operator, where the reliability of information sources is considered in the formulation. The WSAM‐OWA operator is generalized to the quantified WSAM‐OWA operator by including the concept of linguistic quantifier, mainly for the group fusion strategy. The QWSAM‐IOWA operator, with an ordering step, is introduced to the individual fusion strategy. The proposed aggregation operators are then implemented for the case of alternative scheme of heterogeneous group decision analysis. The heterogeneous group includes the consensus of experts with respect to each specific criterion. The exhaustive multicriteria group decision‐making model under the linguistic domain, which consists of two‐stage aggregation processes, is developed in order to fuse the experts’ judgments and to aggregate the criteria. The model provides greater flexibility when analyzing the decision alternatives with a tolerance that considers the majority of experts and the attitudinal character of experts. A selection of investment problem is given to demonstrate the applicability of the developed model.     

Induced cluster-based OWA operators with reliability measures and the application in group decision-making

Considering the distributed structural characteristics of arguments to be aggregated, we propose a new type of aggregation operator, called induced cluster-based ordered weighted averaging (OWA; abbreviated as cluster-IOWA) operator, in this article. The main characteristic of the cluster-IOWA operator is that the arguments are aggregated by local clusters, and the order-inducing variable is used for representing a particular characteristic with respect to a local cluster. The cluster-OWA operator is commutativity, idempotence, and boundedness. We then discuss two important issues with respect to the cluster-IOWA operator. The order-inducing variables are determined by considering the overall reliability of the local cluster. Based on this, the position weighting vector of the local clusters is designed by taking into account both the reliability measures and the decision maker's preference. Finally, a numerical example, regarding the performance evaluation of middle managers carried out by a group of participants, is developed to illustrate the application and validity of the cluster-IOWA operator.     

Reversed fuzzy Petri nets and their application for fault diagnosis

An alterative approach to the backward reasoning is presented. In classical reasoning, both users and developers of many expert systems are dedicated to the forward reasoning. However, in many newly arising expert systems such as various diagnosis systems, the backward reasoning is of special interest and often preferable. In this paper, the fuzzy Petri nets are used to analytically represent the knowledge of fault diagnosis in manufacturing systems and an iterative algorithm based on max-algebra is used to deduce the consequence–antecedent relationship between their manifestation and antecedent. Finally, the legitimacy and efficiency of the proposed approach are proved and validated by an illustrative example.     

Aggregating linguistic expert knowledge in type-2 fuzzy ontologies

In many industrial contexts, knowledge and data provided by experts are imprecise as there seems to be an understanding that “experts do not need precise details as they understand anyway what is meant”. The imprecision inherent in the knowledge that experts acquire in their practice require decision support tools that can be tailored to the specific application contexts to aid complex decisions. As a specific example, expert knowledge expressed in linguistic terms is not precisely structured and concepts are not defined specifically enough in order to be easy to use and process. If we want to represent and use expert knowledge for knowledge-based systems on a general level, that is easily adaptable, we need to find ways to represent and process knowledge elements; our approach is to use interval-valued fuzzy sets, fuzzy ontology and aggregation operators. We show that these instruments will offer us a novel approach for aggregation of imprecise data to obtain actionable knowledge to aid complex decisions. The framework is described and the approach is shown through the context of a fuzzy wine ontology; the problem formulation resembles many features of important and complex decision making problems found in different industries. We describe the potential application of the framework in the case of paper machine maintenance. A web-based application is introduced to better demonstrate the benefits decision-makers can receive from the proposed framework. Additionally, we present an approach to utilize the framework in finding consensual solutions in situations involving several experts.     

Uncertain induced aggregation operators and its application in tourism management

We develop a new decision making approach for dealing with uncertain information and apply it in tourism management. We use a new aggregation operator that uses the uncertain weighted average (UWA) and the uncertain induced ordered weighted averaging (UIOWA) operator in the same formulation. We call it the uncertain induced ordered weighted averaging - weighted averaging (UIOWAWA) operator. We study some of the main advantages and properties of the new aggregation such as the uncertain arithmetic UIOWA (UA-UIOWA) and the uncertain arithmetic UWA (UAUWA). We study its applicability in a multi-person decision making problem concerning the selection of holiday trips. We see that depending on the particular type of UIOWAWA operator used, the results may lead to different decisions.     

Incorporating fuzzy operators in the decision network to improve classification reliability

One type of hierarchical fuzzy-operator-based network implementation is investigated. In this approach, we generalized the Dombi operator as an effective component for decision analysis and making. This methodology provides several advantages due to the fact that the input to each node is the evidence supplied by the degree of satisfaction of sub-criteria and the output is the aggregated evidence. Thus, the decision making process is to aggregate and propagate the evidence information through such a hierarchical network. This trainable network is able to perceive and interpret complex decisions by using those transparent fuzzy models. This study examines the behavior of the fuzzy additive operator in more detail and the results show that the proposed framework exhibits reliable decision in the pattern classification domain.     

Pythagorean Dombi fuzzy aggregation operators with application in multicriteria decision-making

A Pythagorean fuzzy set, an extension of intuitionistic fuzzy sets, is very helpful in representing vague information that occurs in real world scenarios. The Dombi operators with operational parameters, have excellent flexibility. Due to the flexible nature of these Dombi operational parameters, this research paper introduces some new aggregation operators under Pythagorean fuzzy environment, including Pythagorean Dombi fuzzy weighted arithmetic averaging (PDFWAA) operator, Pythagorean Dombi fuzzy weighted geometric averaging (PDFWGA) operator, Pythagorean Dombi fuzzy ordered weighted arithmetic averaging operator and Pythagorean Dombi fuzzy ordered weighted geometric averaging operator. Further, this paper presents several advantageous characteristics, including idempotency, monotonicity, boundedness, reducibility and commutativity of preceding operators. By utilizing PDFWAA and PDFWGA operators, this article describes a multicriteria decision-making (MCDM) technique for solving MCDM problems. Finally, a numerical example related to selection of a leading textile industry is presented to illustrate the applicability of our proposed technique.     

Rough fuzzy approximations on two universes of discourse

In rough set theory, the lower and upper approximation operators can be constructed via a variety of approaches. Various fuzzy generalizations of rough approximation operators have been made over the years. This paper presents a framework for the study of rough fuzzy sets on two universes of discourse. By means of a binary relation between two universes of discourse, a covering and three relations are induced to a single universe of discourse. Based on the induced notions, four pairs of rough fuzzy approximation operators are proposed. These models guarantee that the approximating sets and the approximated sets are on the same universes of discourse. Furthermore, the relationship between the new approximation operators and the existing rough fuzzy approximation operators on two universes of discourse are scrutinized, and some interesting properties are investigated. Finally, the connections of these approximation operators are made, and conditions under which some of these approximation operators are equivalent are obtained.     

Characterization of rough set approximations in Atanassov intuitionistic fuzzy set theory

The primitive notions in rough set theory are lower and upper approximation operators defined by a fixed binary relation and satisfying many interesting properties. Many types of generalized rough set models have been proposed in the literature. This paper discusses the rough approximations of Atanassov intuitionistic fuzzy sets in crisp and fuzzy approximation spaces in which both constructive and axiomatic approaches are used. In the constructive approach, concepts of rough intuitionistic fuzzy sets and intuitionistic fuzzy rough sets are defined, properties of rough intuitionistic fuzzy approximation operators and intuitionistic fuzzy rough approximation operators are examined. Different classes of rough intuitionistic fuzzy set algebras and intuitionistic fuzzy rough set algebras are obtained from different types of fuzzy relations. In the axiomatic approach, an operator-oriented characterization of rough sets is proposed, that is, rough intuitionistic fuzzy approximation operators and intuitionistic fuzzy rough approximation operators are defined by axioms. Different axiom sets of upper and lower intuitionistic fuzzy set-theoretic operators guarantee the existence of different types of crisp/fuzzy relations which produce the same operators.     

Some realizations and instances of Yager prioritized preference frame with application in evaluation and decision making

This study first revamps Yager prioritized ordered weighted averaging operators, and condenses them into a conceptual frame with putting aside one realization from Yager's original proposal. Then, based on elicited conceptual frame called Yager prioritized preference conceptual frame, this article proposes three distinct realizations to the conceptual frame with corresponding different instances, in which some evaluation models with weights determination methods are provided. Numerical examples are also presented immediately after every instance. Lastly, this study proposes the concepts of outer monotonic, inner monotonic, and global monotonic weights functions, and discusses some related properties, which are often embodied in preferences of decision makers.     

基于多级模糊神经网络的故障诊断在化工生产过程中的应用

化工生产过程一般都非常复杂，如柠檬酸蒸发。由于控制回路与测控参数很多，生产过程的故障检测与诊断问题非常困难，难以做到实时检查，得到其故障信息。所以本文提出一种基于神经网络的多级故障诊断系统。采用三级递阶模糊神经网络，降解整个系统故障诊断问题的复杂性，同时采用所有子神经网络全局并行的推理方式，具有快速处理能力，适合系统实时在线故障诊断。     

Algorithms of discrete optimization and their application to problems with fuzzy coefficients

An approach to solving optimization problems with fuzzy coefficients in objective functions and constraints is described. It consists in formulating and solving one and the same problem within the framework of mutually related models with constructing equivalent analogs with fuzzy coefficients in objective functions alone. It enables one to maximally cut off dominated alternatives “from below” as well as “from above”. Since the approach is applied within the context of fuzzy discrete optimization problems, several modified algorithms of discrete optimization are discussed. These algorithms are associated with the method of normalized functions, are based on a combination of formal and heuristic procedures, and allow one to obtain quasi-optimal solutions after a small number of steps, thus overcoming the computational complexity posed the NP-completeness of discrete optimization problems. The subsequent contraction of the decision uncertainty regions is associated with reduction of the problem to multiobjective decision making in a fuzzy environment with using techniques based on fuzzy preference relations. The techniques are also directly applicable to situations in which the decision maker is required to choose alternatives from a set of explicitly available alternatives. The results of the paper are of a universal character and can be applied to the design and control of systems and processes of different purposes as well as the enhancement of corresponding CAD/CAM systems and intelligent decision making systems. The results of the paper are already being used to solve problems of power engineering.     

减法聚类-ANFIS在网络故障诊断的应用研究

提出了一种基于减法聚类-自适应模糊神经网络（ANFIS）的网络故障诊断建模方法。减法聚类算法生成初始模糊推理系统,ANFIS建立网络故障诊断原始模型,应用混合算法对模糊规则的参数进行训练并建立最终的模型。仿真实验表明基于减法聚类-ANFIS的建模方法是有效的;通过仿真结果比较,减法聚类-ANFIS的网络故障诊断能力及收敛速度均优于BP神经网络,更适合作为网络故障诊断模型。     

A fuzzy reasoning design for fault detection and diagnosis of a computer-controlled system

A fuzzy reasoning and verification Petri nets (FRVPNs) model is established for an error detection and diagnosis mechanism applied to a complex fault-tolerant PC-controlled system. The inference accuracy can be improved through the hierarchical design of a two-level fuzzy rule decision tree and a Petri nets technique to transform the fuzzy rule into the FRVPNs model. Several simulation examples of the assumed failure events were carried out by using the FRVPNs and the Mamdani fuzzy method with MATLAB tools. The reasoning performance of the developed FRVPNs was verified by comparing the inference outcome to that of the Mamdani method. Both methods result in the same conclusions. Thus, the present study demonstrates that the proposed FRVPNs model is able to achieve the purpose of reasoning, and furthermore, determining of the failure event of the monitored application program.