Sugeno Integral Research Articles

Stolarsky type inequality for Sugeno integrals on fuzzy convex functions

Stolarsky type inequality for Sugeno integrals on fuzzy convex functions

H-Index and Other Sugeno Integrals: Some Defects and Their Compensation

The famous Hirsch index has been introduced just ca. ten years ago. Despite that, it is already widely used in many decision-making tasks, like in evaluation of individual scientists, research grant allocation, or even production planning. It is known that the $h$ -index is related to the discrete Sugeno integral and the Ky Fan metric introduced in the 1940s. The aim of this paper is to propose a few modifications of this index as well as other fuzzy integrals—also on bounded chains—that lead to better discrimination of some types of data that are to be aggregated. All of the suggested compensation methods try to retain the simplicity of the original measure.

Generalized comonotonicity and new axiomatizations of Sugeno integrals on bounded distributive lattices

Two new generalizations of the relation of comonotonicity of lattice-valued vectors are introduced and discussed. These new relations coincide on distributive lattices and they share several properties with the comonotonicity for the real-valued vectors (which need not hold for L-valued vectors comonotonicity, in general). Based on these newly introduced generalized types of comonotonicity of L-valued vectors, several new axiomatizations of L-valued Sugeno integrals are introduced. One of them brings a substantial decrease of computational complexity when checking an aggregation function to be a Sugeno integral.

Fuzzy classifier fusion: an application to reservoir facies identification

An application of classifier fusion technique is presented to improve the performance of automated reservoir facies identification system. The algorithm presented in this study uses three well-known classifiers, namely Bayesian, k-nearest neighbor (kNN), and support vector machine (SVM) to automatically identify four defined facies of Asmari Formation from log-derived amplitude versus offset (AVO) attributes. Fuzzy Sugeno integral (FSI) method is then employed to combine the outputs of three investigated classifiers and increase the consistency of reservoir facies identification process. The experimental results obtained from applying the presented algorithm on data related to three wells drilled in Asmari Formation provide evidence of the effectiveness of the proposed algorithm regarding true positive (TP), false positive (FP), and classification accuracy criteria.

Look back on the path the Sugeno integral has walked and will walk along －Essays in honor of Michio Sugeno's Kiju (77th birthday)－ Part III. The mathematical aspect of the Sugeno integral.

Look back on the path the Sugeno integral has walked and will walk along －Essays in honor of Michio Sugeno's Kiju (77th birthday)－ Part III. The mathematical aspect of the Sugeno integral.

Nash equilibrium for binary convexities

This paper is devoted to Nash equilibrium for games in capacities. Such games with payoff expressed by the Choquet integral were considered by Kozhan and Zarichnyi (2008) and existence of Nash equilibrium was proved. We also consider games in capacities but with expected payoff expressed by the Sugeno integral. We prove existence of Nash equilibrium in a general context of abstract binary (non-linear) convexity and then we obtain an existence theorem for games in capacities.

Jensen-type inequalities for Sugeno integral

In this paper, the classical Jensen inequalities for concave function φ, i.e.,φ(∫f(x)dμ)⩾∫φ(f)dμandφ(∑i=1nλixi)⩾∑i=1nλiφ(xi),are adapted for the Sugeno integral using the notion of the supergradient. Moreover, we give some modifications of previous results of Román-Flores et al. concerning Jensen-type inequalities for Sugeno integral. Some examples in the framework of the Lebesgue measure and counting measure to illustrate the results are presented.

Look back on the path the Sugeno integral has walked and will walk along －Essays in honor of Michio Sugeno's Kiju (77th birthday)－ Part II. the progress of the Sugeno integral.

Look back on the path the Sugeno integral has walked and will walk along －Essays in honor of Michio Sugeno's Kiju (77th birthday)－ Part II. the progress of the Sugeno integral.

On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application

In this paper, we use a new method to obtain the necessary and sufficient condition guaranteeing the validity of the Minkowski-H\"{o}lder type inequality for the generalized upper Sugeno integral in the case of functions belonging to a wider class than the comonotone functions. As a by-product, we show that the Minkowski type inequality for seminormed fuzzy integral presented by Daraby and Ghadimi in General Minkowski type and related inequalities for seminormed fuzzy integrals, Sahand Communications in Mathematical Analysis 1 (2014) 9--20 is not true. Next, we study the Minkowski-H\"{o}lder inequality for the lower Sugeno integral and the class of $\mu$-subadditive functions introduced in On Chebyshev type inequalities for generalized Sugeno integrals, Fuzzy Sets and Systems 244 (2014) 51--62. The results are applied to derive new metrics on the space of measurable functions in the setting of nonadditive measure theory. We also give a partial answer to the open problem 2.22 posed by Borzov\'a-Moln\'arov\'a and et al in The smallest semicopula-based universal integrals I: Properties and characterizations, Fuzzy Sets and Systems 271 (2015) 1--17.

Look back on the path the Sugeno integral has walked and will walk along －Essays in honor of Michio Sugeno's Kiju (77th birthday)－ Part I. The Sugeno integral has disappeared and reappeared.

Look back on the path the Sugeno integral has walked and will walk along －Essays in honor of Michio Sugeno's Kiju (77th birthday)－ Part I. The Sugeno integral has disappeared and reappeared.

Congruences and the discrete Sugeno integrals on bounded distributive lattices

We study compatible aggregation functions on a general bounded distributive lattice L, where the compatibility is related to the congruences on L. As a by-product, a new proof of an earlier result of G. Grätzer is obtained. Moreover, our results yield a new characterization of discrete Sugeno integrals on bounded distributive lattices.

Improving pore type identification from thin section images using an integrated fuzzy fusion of multiple classifiers

A semi-automatic algorithm for identification of five pore types in carbonate rocks of a gas field, including inter-particle, intra-particle, oomoldic, biomoldic, and vuggy, from thin section images is presented. The proposed algorithm involves four main steps. Firstly, a color-based image segmentation procedure is carried out using K-means clustering algorithm to separate regions corresponding to the considered pores. Secondly, six geometrical shape parameters of 384 pores are extracted from each segmented region to obtain the distinctive features for each pore type. Three classifiers (i.e. kNN, RBF, and SVM) are considered for classification to identify the type and percentage of interested porosities. Experimental results show that SVM with polynomial kernel function yields the highest accuracy and can effectively identify the pores with average accuracy of 94.4% whereas the kNN gives the lowest accuracy. The final step include combination of outputs of three employed classifiers that are trained separately on same dataset to recognize each pore space using Fuzzy Sugeno Integral (FSI) method. As expected, the fuzzy fusion of single classifiers improves the results of classification up to 9.4%, which is a considerable improvement in the classification from the stand point of petroleum geology.

Sugeno Integral with Possibilistic Inputs with Application to Multi-Criteria Decision Making

We introduce the Sugeno integral and describe how it can be used to provide a weighted mean-like aggregation of a collection of values drawn from the unit interval. We explain that the underlying measure provides information about the weights associated with the arguments. We provide an alternative view of the Sugeno integral that enables us to extend its use to situations in which the arguments in the aggregation are possibility distributions. We look at the application of the Sugeno integral to the formulation of decision functions in the case of multi-criteria decision making. We focus on the situation where there exists some possibilistic uncertainty in our knowledge of criteria satisfactions by an alternative. We provide operational formulations for the calculation of some notable decision functions in the case of possibilistically uncertain criteria satisfactions.

Berwald and Favard Type Inequalities for Fuzzy Integrals

This paper propose a Berwald type inequality and a Favard type inequality for Sugeno integrals. That is, we first show that [Formula: see text] holds for some constant [Formula: see text] where f is a monotone and concave function on [0, 1] and [Formula: see text] is the Lebesgue measure on [Formula: see text]. If q = 1, then as a special case of the Berwald type inequality, we show that the following Favard type inequality holds for Sugeno integrals [Formula: see text] A deeper discussion for Favard type inequality for Sugeno integrals using Berwald type inequality is also considered. Some examples are provided to illustrate the optimality of the proposed inequality.

Berwald-type inequalities for Sugeno integral with respect to ( α , m , r ) g ${ ( {\alpha,m,r} )_{g}}$ -concave functions

In this paper, we introduce the concept of an ${ ( {\alpha,m,r} )_{g}}$ -concave function as a generalization of a concave function. Then we establish Berwald-type inequalities for the Sugeno integral based on this kind of functions. Our work generalizes the previous results in the literature. Finally, we give some conclusions and problems for further investigations.

Equivalent conditions of Hermite-Hadamard type inequality for Sugeno integrals

Equivalent conditions of Hermite-Hadamard type inequality for Sugeno integrals

Stolarsky’s inequality for Choquet-like expectation

AbstractExpectation is the fundamental concept in statistics and probability. As two generalizations of expectation, Choquet and Choquet-like expectations are commonly used tools in generalized probability theory. This paper considers the Stolarsky inequality for two classes of Choquet-like integrals. The first class generalizes the Choquet expectation and the second class is an extension of the Sugeno integral. Moreover, a new Minkowski’s inequality without the comonotonicity condition for two classes of Choquet-like integrals is introduced. Our results significantly generalize the previous results in this field. Some examples are given to illustrate the results.

EARTHQUAKE VULNERABILITY ASSESSMENT FOR HOSPITAL BUILDINGS USING A GIS-BASED GROUP MULTI CRITERIA DECISION MAKING APPROACH: A CASE STUDY OF TEHRAN, IRAN

Abstract. Nowadays, urban areas are threatened by a number of natural hazards such as flood, landslide and earthquake. They can cause huge damages to buildings and human beings which necessitates disaster mitigation and preparation. One of the most important steps in disaster management is to understand all impacts and effects of disaster on urban facilities. Given that hospitals take care of vulnerable people reaction of hospital buildings against earthquake is vital. In this research, the vulnerability of hospital buildings against earthquake is analysed. The vulnerability of buildings is related to a number of criteria including age of building, number of floors, the quality of materials and intensity of the earthquake. Therefore, the problem of seismic vulnerability assessment is a multi-criteria assessment problem and multi criteria decision making methods can be used to address the problem. In this paper a group multi criteria decision making model is applied because using only one expert’s judgments can cause biased vulnerability maps. Sugeno integral which is able to take into account the interaction among criteria is employed to assess the vulnerability degree of buildings. Fuzzy capacities which are similar to layer weights in weighted linear averaging operator are calculated using particle swarm optimization. Then, calculated fuzzy capacities are included into the model to compute a vulnerability degree for each hospital.

Decision-Making with Sugeno Integrals

This paper clarifies the connection between multiple criteria decision-making and decision under uncertainty in a qualitative setting relying on a finite value scale. While their mathematical formulations are very similar, the underlying assumptions differ and the latter problem turns out to be a special case of the former. Sugeno integrals are very general aggregation operations that can represent preference relations between uncertain acts or between multifactorial alternatives where attributes share the same totally ordered domain. This paper proposes a generalized form of the Sugeno integral that can cope with attributes having distinct domains via the use of qualitative utility functions. It is shown that in the case of decision under uncertainty, this model corresponds to state-dependent preferences on consequences of acts. Axiomatizations of the corresponding preference functionals are proposed in the cases where uncertainty is represented by possibility measures, by necessity measures, and by general order-preserving set-functions, respectively. This is achieved by weakening previously proposed axiom systems for Sugeno integrals.

Design of criteria to assess craniofacial correspondence in forensic identification based on computer vision and fuzzy integrals

Craniofacial superimposition is one of the most relevant skeleton-based identification techniques. Within this process, the skull-face overlay stage focuses on achieving the best possible overlay of a skull found and an ante mortem image of a candidate person. In previous work, we proposed an automatic skull-face overlay method, based on evolutionary algorithms and fuzzy sets. The following stage, decision making, consists of determining the degree of support of being the same person or not. This decision is based on the analysis of some criteria assessing the skull-face morphological correspondence through the resulting skull-face overlay. In this work, we take a first step to design a decision support system for craniofacial superimposition. To do so, we consider the modeling of two of the most discriminative criteria for assessing craniofacial correspondence: the morphological and spatial relationship between the bony and facial chin, and the relative position of the orbits and the eyeballs. For each criterion, different computer vision-based approaches have been studied. The accuracy of each method has been calculated as its capability to discriminate in a cross-comparison identification scenario. Sugeno integral has been used to aggregate the results of the different methods taking into account the corresponding individual accuracy index. This allows us to provide a single global output specifying the matching of each criterion while combining the capabilities of different methods. Finally, the performance of the designed criteria and methods have been tested on 172 skull-face overlay problem instances of positive and negative cases to illustrate the discriminative power of each criterion. It has been shown that thanks to the use of Sugeno integral for aggregating different methods, a more robust measurement output is achieved.