Choquet Integral Operator Research Articles

Towards An Industrial Performance Quantification Model According To The Balanced Scorecard

This article deals with an industrial performance quantification approach based on the Balanced Scorecard (BSC) tool. Developed by Kaplan and Norton, the BSC has been defined by its strategic control level. In our opinion, it could be more extensively used at an operational level than it is today. In this way, it could be useful for quantifying all the links and performance measures defined in the BSC. For this, we choose to use the multicriteria decision-aiding methodology MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique). Indeed, MACBETH proposes to express in a coherent way elementary and overall performances by using a structured procedure. We propose to apply this methodology with a particular aggregation operator of the Choquet integral family. The Choquet integral operators generalize the weighted arithmetic mean by taking elementary performance interactions into account. The proposed quantified model is illustrated by a case study done on a textile company.

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.

Induced choquet ordered averaging operator and its application to group decision making

Yager (Fuzzy Sets Syst 2003;137:59–69) extended the idea of order-induced aggregation to the Choquet aggregation and defined a more general type of Choquet integral operator called the induced Choquet ordered averaging (I-COA) operator, which take as their argument pairs, in which one component called order-inducing variable is used to induce an ordering over the second components called argument variable and then aggregated. The aim of this paper is to develop the I-COA operator. Some of its properties are investigated. We show its relationship to the induced-ordered weighted averaging operator. Finally, we provide some I-COA operators to aggregate fuzzy preference relations in group decision-making problems. © 2009 Wiley Periodicals, Inc.

Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making

For the real decision making problems, most criteria have inter-dependent or interactive characteristics so that it is not suitable for us to aggregate them by traditional aggregation operators based on additive measures. Thus, to approximate the human subjective decision making process, it would be more suitable to apply fuzzy measures, where it is not necessary to assume additivity and independence among decision making criteria. In this paper, an intuitionistic fuzzy Choquet integral is proposed for multiple criteria decision making, where interactions phenomena among the decision making criteria are considered. First, we introduced two operational laws on intuitionistic fuzzy values. Then, based on these operational laws, intuitionistic fuzzy Choquet integral operator is proposed. Moreover, some of its properties are investigated. It is shown that the intuitionistic fuzzy Choquet integral operator can be represented by some special t-norms and t-conorms, and it is also a generalization of the intuitionistic fuzzy OWA operator and intuitionistic fuzzy weighted averaging operator. Further, the procedure and algorithm of multi-criteria decision making based on intuitionistic fuzzy Choquet integral operator is given under uncertain environment. Finally, a practical example is provided to illustrate the developed approaches.

Towards an aggregation performance measurement system model in a supply chain context

This study deals with the supply chain (SC) performance formalization. We propose to build performance measurement systems (PMSs) by linking an overall performance expression to elementary ones. The overall performance is associated to a global objective whose break-down provides elementary objectives. Elementary performances are thus aggregated in a corollary way. The problem in the design of such PMS's, by the break-down/aggregation model, concerns both the coherent elementary performance expressions and the definition of the links between them. Some answers are proposed in the literature, such as the weighted mean aggregation operator, to handle hierarchical links, the Choquet integral operator, for taking interactions into account. As global frameworks, the AHP or MACBETH methodologies are suggested. By considering the SCOR model break-down, we propose to extend here the proposed approaches for expressing the overall performance of a SC. An aggregation methodology, based on the Choquet integral operator and MACBETH framework, is thus adopted.

Quantitative expression and aggregation of performance measurements based on the MACBETH multi-criteria method

This study deals with the use of the MACBETH methodology as a global framework for multi-criteria industrial performance expressions. This methodology satisfies the measurement theory requirements, and thus ensures the coherence of the elementary and aggregated performance expressions. The MACBETH procedure allows to express commensurate elementary performances and the weights of the weighted mean from decision-maker knowledge, and then to aggregate the elementary performances. Then, in order to take the criteria interactions into account, we extend MACBETH to the Choquet integral operators. Finally, an industrial case study is presented to illustrate the implementation of the methodology in the field.

OVERALL PERFORMANCE MEASUREMENT IN A SUPPLY CHAIN

This study deals with the supply chain SC overall performance expression. The approach is based on the main processes of the SCOR model. In the industrial practice, performance expressions are defined w.r.t. each process; and the overall performance is neither expressed for each company, nor for the whole SC. It induces a complexity in the scorecards analysis. In this view, the MACBETH formalization of the overall expression with an aggregation approach is proposed. More precisely, the Choquet integral operator is adopted to model mutual interactions between processes. The expression of a bearing's manufacturer performance illustrates the proposition.

Convergence properties of the monotone expectation and its application to the extension of fuzzy measures

We define a functional on fuzzy measures (called monotone expectation) based on Choquet's integral operator, and we study its convergence properties. The monotone expectation is used to extend fuzzy measures to fuzzy subsets. Also Sugeno's bound for the difference between his integral and the mathematical expectation is generalized.