Intuitionistic fuzzy Choquet integral operator-based approach for black-start decision-making

Determining the optimal of black-start strategies is very important for speeding the restoration speed of a power system after a global blackout. Most existing black-start decision-making methods are based on the assumption that all indexes are independent of each other, and little attention has been paid to the group decision-making method which is more reliable. Given this background, the intuitionistic fuzzy set and further intuitionistic fuzzy Choquet integral operator are presented, and a black-start decision-making method based on this integral operator is presented. Compared to existing methods, the proposed algorithm cannot only deal with the relevance among the indexes, but also overcome some shortcomings of the existing methods. Finally, an example is used to demonstrate the proposed method. © 2012 The Institution of Engineering and Technology.

A fuzzy decision support method for customer preferences analysis based on Choquet integral

The explosion of the Web 2:0 platforms, with massive volume of user generated data, has presented many new opportunities as well as challenges for organizations in understanding consumer's behavior to support for business planning process. Feature based sentiment mining has been an emerging area in providing tools for automated opinion discovery and summarization to help business managers with achieving such goals. However, the current feature based sentiment mining systems were only able to provide some forms of sentiments summary with respect to product features, but impossible to provide insight into the decision making process of consumers. In this paper, we will present a relatively new decision support method based on Choquet Integral aggregation function, Shapley value and Interaction Index which is able to address such requirements of business managers. Using a study case of Hotel industry, we will demonstrate how this technique can be applied to effectively model the user's preference of (hotel) features. The presented method has potential to extend the practical capability of sentiment mining area, while, research findings and analysis are useful in helping business managers to define new target customers and to plan more effective marketing strategies.

Discovering implicit criteria preferences reflected in tourism journal ranking lists using the Choquet Integral

Variations between journal rankings may cause confusion. As such, prior attempts were made to compare and evaluate journal ranking criteria for obtaining insightful knowledge on how different research communities have ranked journals. However, existing approaches are unable to model the journal ranking process closely enough as they are incapable of considering the relationship between multiple criteria simultaneously. In this paper, we address the challenges by introducing the Choquet Integral (CI) for evaluating journal ranking criteria. The new approach is able to account for interactions between criteria in relation to overall ranking score, using a fuzzy measure in its computation. Its properties, the Shapley value and the Interaction index, allow for good representations of importance and interactions between criteria. We demonstrate the efficiency of the CI through a case study of journal ranking lists in tourism and service journals.

Using Choquet integrals for kNN approximation and classification

k-nearest neighbors (kNN) is a popular method for function approximation and classification. One drawback of this method is that the nearest neighbors can be all located on one side of the point in question x. An alternative natural neighbors method is expensive for more than three variables. In this paper we propose the use of the discrete Choquet integral for combining the values of the nearest neighbors so that redundant information is canceled out. We design a fuzzy measure based on location of the nearest neighbors, which favors neighbors located all around x.

Using choquet integrals for evaluating citation indices in journal ranking

The use of citation-based indices to evaluate the quality of journals is becoming increasingly widespread. Recently, ISI Web of Knowledge has begun to include three new indices in their journal statistics, including a 5-year impact factor. Here, we continue our earlier research which modeled the behavior of journal assessors based on some of these indices and the Choquet integral. We interpret the obtained fuzzy measures of many new datasets toward understanding the importance of these newly published indices and how indicative they may be of a journal's quality. The problem is one of ordinal classification, and the values of the best-fitting fuzzy measures can be obtained using the FMtools software package.

Integral representation with convex capacities that are squeeze of (additive) probability measures

In this paper I will investigate the conditions under which a convex capacity (or a non-additive probability which exhibts uncertainty aversion) can be represented as a squeeze of a(n) (additive) probability measure associate to an uncertainty aversion function. Then I will present two alternatives forrnulations of the Choquet integral (and I will extend these forrnulations to the Choquet expected utility) in a parametric approach that will enable me to do comparative static exercises over the uncertainty aversion function in an easy way.

A Representation of Risk Measures

We provide a representation theorem for risk measures satisfying (i) monotonicity; (ii) positive homogeneity; and (iii) translation invariance. As a simple corollary to our theorem, we obtain the usual representation of coherent risk measures (i.e., risk measures that are, in addition, sub-additive; see Artzner et al. [2]).

Ambiguity on the insurer's side: the demand for insurance

Empirical evidence suggests that ambiguity is prevalent in insurance pricing and underwriting, and that often insurers tend to exhibit more ambiguity than the insured individuals (e.g., [23]). Motivated by these findings, we consider a problem of demand for insurance indemnity schedules, where the insurer has ambiguous beliefs about the realizations of the insurable loss, whereas the insured is an expected-utility maximizer. We show that if the ambiguous beliefs of the insurer satisfy a property of compatibility with the non-ambiguous beliefs of the insured, then there exist optimal monotonic indemnity schedules. By virtue of monotonicity, no ex-post moral hazard issues arise at our solutions (e.g., [25]). In addition, in the case where the insurer is either ambiguity-seeking or ambiguity-averse, we show that the problem of determining the optimal indemnity schedule reduces to that of solving an auxiliary problem that is simpler than the original one in that it does not involve ambiguity. Finally, under additional assumptions, we give an explicit characterization of the optimal indemnity schedule for the insured, and we show how our results naturally extend the classical result of Arrow [5] on the optimality of the deductible indemnity schedule.

Ambiguity on the insurer's side: the demand for insurance

Empirical evidence suggests that ambiguity is prevalent in insurance pricing and underwriting, and that often insurers tend to exhibit more ambiguity than the insured individuals (e.g., [23]). Motivated by these findings, we consider a problem of demand for insurance indemnity schedules, where the insurer has ambiguous beliefs about the realizations of the insurable loss, whereas the insured is an expected-utility maximizer. We show that if the ambiguous beliefs of the insurer satisfy a property of compatibility with the non-ambiguous beliefs of the insured, then there exist optimal monotonic indemnity schedules. By virtue of monotonicity, no ex-post moral hazard issues arise at our solutions (e.g., [25]). In addition, in the case where the insurer is either ambiguity-seeking or ambiguity-averse, we show that the problem of determining the optimal indemnity schedule reduces to that of solving an auxiliary problem that is simpler than the original one in that it does not involve ambiguity. Finally, under additional assumptions, we give an explicit characterization of the optimal indemnity schedule for the insured, and we show how our results naturally extend the classical result of Arrow [5] on the optimality of the deductible indemnity schedule.

Fitting generated aggregation operators to empirical data

This paper treats the problem of fitting general aggregation operators with unfixed number of arguments to empirical data. We discuss methods applicable to associative operators (t-norms, t-conorms, uninorms and nullnorms), means and Choquet integral based operators with respect to a universal fuzzy measure. Special attention is paid to k-order additive symmetric fuzzy measures.

Learning weights in the generalized OWA operators

This paper discusses identification of parameters of generalized ordered weighted averaging (GOWA) operators from empirical data. Similarly to ordinary OWA operators, GOWA are characterized by a vector of weights, as well as the power to which the arguments are raised. We develop optimization techniques which allow one to fit such operators to the observed data. We also generalize these methods for functional defined GOWA and generalized Choquet integral based aggregation operators.