Fuzzy measures and integrals in MCDA

This chapter aims at a unified presentation of various methods of MCDA based onfuzzy measures (capacity) and fuzzy integrals, essentially the Choquet andSugeno integral. A first section sets the position of the problem ofmulticriteria decision making, and describes the various possible scales ofmeasurement (difference, ratio, and ordinal). Then a whole section is devotedto each case in detail: after introducing necessary concepts, the methodologyis described, and the problem of the practical identification of fuzzy measuresis given. The important concept of interaction between criteria, central inthis chapter, is explained in details. It is shown how it leads to k-additivefuzzy measures. The case of bipolar scales leads to thegeneral model based on bi-capacities, encompassing usual models based oncapacities. A general definition of interaction for bipolar scales isintroduced. The case of ordinal scales leads to the use of Sugeno integral, andits symmetrized version when one considers symmetric ordinal scales. Apractical methodology for the identification of fuzzy measures in this contextis given. Lastly, we give a short description of some practical applications.Choquet integral; fuzzy measure; interaction; bi-capacities

Contextual algorithm for decision of fuzzy estimation problems with network-like structure of criteria on the basis of fuzzy measures Sugeno

In this article the algorithm for the decision of alternatives' estimation problems for following conditions is considered. Values of alternative's characteristics (properties) are fuzzy. They are formalized as fuzzy sets. The estimation criteria structure is network-like and is formalized as the oriented graph with one source and many drains. The alternative's estimation result is calculated in criterion-source. Connections between criteria are formalized by fuzzy measures Sugeno. Upper-level criteria are considered as contexts for lower-level criteria. Fuzzy integrals Sugeno or Choquet are used as aggregation operator. In article also the properties of fuzzy measure and fuzzy integrals (Sugeno and Choquet) are analyzed. Properties of fuzzy measure and integrals are comparing with properties of other mathematical tools. As example the car's estimation problem is presented.fuzzy measure (Sugeno); fuzzy integral (Sugeno and Choquet); alternatives estimation; criteria structure

Fuzzy Measures and Integrals

In this paper, we will study the aggregation problem with intera ting riteria,and we will introdu e the on epts of fuzzy measures and integrals. The fuzzyintegrals are powerful aggregation operators whi h are able to take into onsideration the intera tion among riteria and the fuzzy measures an be used formodeling the importan e of all subsets of riteria.We will on entrate in \the Choquet integral ", this fuzzy integral is a weightedaggregation operator, whi h takes into a ount not only the importan e of the riteria, but also the importan e of all subsets of them. The information about theimportan e and the intera tion between riteria is used in the aggregation pro essof the partial evaluations. This paper analyse some hara teristi s and propertiesof this operator

An Application of Non-additive Measures and Corresponding Integrals in Tourism Management

القياسات الغير جمعية والتكاملات المقابلة لها قدمت في الاصل (أولا) من قبل شوكيت في عام 1953 وتم تعريفها بشكل مستقل من قبل سوجينو في عام 1974 من أجل تمديد القياس التقليدي عن طريق استبدال خاصية الإضافة إلى خاصية غير مضافة. ومن السمات(الميزات) الهامة للقياسات الغير جمعية والتكاملات الضبابية أنها يمكن أن تمثل أهمية مصادر المعلومات الفردية والتفاعلات فيما بينها. هناك العديد من التطبيقات حول القياسات الغير جمعية والتكاملات الضبابية مثل، معالجة الصور، صنع القرار متعدد المعايير(المقاييس)، اندماج المعلومات، التصنيف، والتعرف على الأنماط. في هذا البحث قدمنا نموذجًا رياضيًا لمناقشة تطبيق القياسات الغير جمعية والتكاملات المقابلة لها في ادارة السياحة. أولا وصفنا مسألة ادارة السياحة لآحدى شركات السياحة في العراق ثم طبقنا التكاملات الضبابية ( سوجينو, ﭽوكيت, شالكريت) المتعلقة بالقياسات الغير جمعية لتقييم درجة اشباع (رضا, قبول) السائح بالبقاء في مدينة معينة وبالتالي تحديد أفضل تقييم للمدن المقصودة.Non-additive measures and corresponding integrals originally have been introduced by Choquet in 1953 (1) and independently defined by Sugeno in 1974 (2) in order to extend the classical measure by replacing the additivity property to non-additive property. An important feature of non –additive measures and fuzzy integrals is that they can represent the importance of individual information sources and interactions among them. There are many applications of non-additive measures and fuzzy integrals such as image processing, multi-criteria decision making, information fusion, classification, and pattern recognition. This paper presents a mathematical model for discussing an application of non-additive measures and corresponding integrals in tourism management. First, the problem of tourism management is described for one of the tourism companies in Iraq. Then, fuzzy integrals (Sugeno integral, Choquet integral, and Shilkret integral) are applied with respect to non-additive measures to evaluate the grade of the gratification of the tourist of staying in a particular town for determining the best evaluation

Fuzzy measures and integrals in re-identification problems

In this paper we give an overview of our approach of using aggregation operators, and more specifically, fuzzy integrals for solving re-identification problems. We show that the use of Choquet integrals are suitable for some kind of problems.Postprint (author’s final draft

A multi criteria group decision making approach based on fuzzy measure theory to assess the different gene regions used in rodent species

Many mitochondrial and nuclear gene regions are used in phylogenetic and taxonomic studies to investigate the historical background of the species and to present the hierarchy of the species. In this paper, we consider the problem of proposing a favorable gene region that determines the diversification of rodent species as a multi criteria group decision making problem. We use fuzzy measure theory and fuzzy integrals to get the results. We conclude with different fuzzy measures and fuzzy integral techniques that COI gene region which is preferred in animal barcoding studies is more favorable.Publisher's Versio

Genetic Algorithm Optimization for Determining Fuzzy Measures from Fuzzy Data

Fuzzy measures and fuzzy integrals have been successfully used in many real applications. How to determine fuzzy measures is a very difficult problem in these applications. Though there have existed some methodologies for solving this problem, such as genetic algorithms, gradient descent algorithms, neural networks, and particle swarm algorithm, it is hard to say which one is more appropriate and more feasible. Each method has its advantages. Most of the existed works can only deal with the data consisting of classic numbers which may arise limitations in practical applications. It is not reasonable to assume that all data are real data before we elicit them from practical data. Sometimes, fuzzy data may exist, such as in pharmacological, financial and sociological applications. Thus, we make an attempt to determine a more generalized type of general fuzzy measures from fuzzy data by means of genetic algorithms and Choquet integrals. In this paper, we make the first effort to define the σ-λ rules. Furthermore we define and characterize the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based on σ-λ rules. In addition, we design a special genetic algorithm to determine a type of general fuzzy measures from fuzzy data

MODELING RISK OF INTERNATIONAL COUNTRY RELATIONS

In this article we consider the modeling principles and model for estimation of tension of international relations of a country with other countries. We use the tension of international relations as partial indicator of international political-economical country-risk. The model bases on estimation of coincidences and contradictions of views of countries concerning decision of political, economic, military, domestic and international problems and projects. The model aggregates detailed estimations of separate problems into composite estimation of relations tension with using of fuzzy measures and integrals. The model allows receiving quantitative estimations of tension of international relations which are necessary for making investment decisions. We use this model for estimation of international political-economical risk of Ukraine.Model, International relations, Fuzzy measure, Political-economical risks

Modeling risk of international country relations

In this article we consider the modeling principles and model for estimation of tension of international relations of a country with other countries. We use the tension of international relations as partial indicator of international political-economical country-risk. The model bases on estimation of coincidences and contradictions of views of countries concerning decision of political, economic, military, domestic and international problems and projects. The model aggregates detailed estimations of separate problems into composite estimation of relations tension with using of fuzzy measures and integrals. The model allows receiving quantitative estimations of tension of international relations which are necessary for making investment decisions. We use this model for estimation of international political-economical risk of Ukraine.model; international relations; fuzzy measure; political-economical risks

Contextual algorithm for decision of fuzzy estimation problems with network-like structure of criteria on the basis of fuzzy measures Sugeno

In this article the algorithm for the decision of alternatives' estimation problems for following conditions is considered. Values of alternative's characteristics (properties) are fuzzy. They are formalized as fuzzy sets. The estimation criteria structure is network-like and is formalized as the oriented graph with one source and many drains. The alternative's estimation result is calculated in criterion-source. Connections between criteria are formalized by fuzzy measures Sugeno. Upper-level criteria are considered as contexts for lower-level criteria. Fuzzy integrals Sugeno or Choquet are used as aggregation operator. In article also the properties of fuzzy measure and fuzzy integrals (Sugeno and Choquet) are analyzed. Properties of fuzzy measure and integrals are comparing with properties of other mathematical tools. As example the car's estimation problem is presented