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Convex Analysisの二,三の進展について

An intuitionistic fuzzy set, characterized by a membership function and a non-membership function, is a generalization of fuzzy set. In this paper, based on score function and accuracy function, we introduce a method for the comparison between two intuitionistic fuzzy values and then develop some aggregation operators, such as the intuitionistic fuzzy weighted averaging operator, intuitionistic fuzzy ordered weighted averaging operator, and intuitionistic fuzzy hybrid aggregation operator, for aggregating intuitionistic fuzzy values and establish various properties of these operators.

Intuitionistic Fuzzy Aggregation Operators

Theory of fuzzy integrals and its applications

Aggregation of information is of primary importance in the construction of knowledge based systems in various domains, ranging from medicine, economics, and engineering to decision-making processes, artificial intelligence, robotics, and machine learning. This book gives a broad introduction into the topic of aggregation functions, and provides a concise account of the properties and the main classes of such functions, including classical means, medians, ordered weighted averaging functions, Choquet and Sugeno integrals, triangular norms, conorms and copulas, uninorms, nullnorms, and symmetric sums. It also presents some state-of-the-art techniques, many graphical illustrations and new interpolatory aggregation functions. A particular attention is paid to identification and construction of aggregation functions from application specific requirements and empirical data. This book provides scientists, IT specialists and system architects with a self-contained easy-to-use guide, as well as examples of computer code and a software package. It will facilitate construction of decision support, expert, recommender, control and many other intelligent systems.

Aggregation Functions: A Guide for Practitioners

We introduce a new class of non-standard fuzzy subsets called Pythagorean fuzzy subsets and the related idea of Pythagorean membership grades. We focus on the negation operation and its relationship to the Pythagorean theorem. We compare Pythagorean fuzzy subsets with intuitionistic fuzzy subsets. We look at the basic set operations for the Pythagorean fuzzy subsets.

Pythagorean fuzzy subsets

Aggregation (fusion) of several input values into a single output value is an indispensable tool not only of mathematics or physics, but of majority of engineering, economical, social and other sciences. The problems of aggregation are very broad and heterogeneous, in general. Therefore we restrict ourselves in this contribution to the specific topic of the aggregation of finite number of real inputs only. Closely related topics of aggregating infinitely many real inputs [23,109,64,52,43,42,44,99], of aggregating inputs from some ordinal scales [41,50], of aggregating complex inputs (such as probability distributions [107,114], fuzzy sets [143]), etc., are treated, among others, in the quoted papers, and we will not deal with them. In this spirit, if the number of input values is fixed, say n, an aggregation operator is a real function of n variables. This is still a too general topic. Therefore we restrict our considerations regarding inputs as well as outputs to some fixed interval (scale) I = [a, b] ⊑ [-∞, ∞]. It is a matter of rescaling to fix I = [0,1].

Aggregation operators: properties, classes and construction methods

1 Aggregation Operators: Basic Concepts, Issues and Properties.- Aggregation Operators: Properties, Classes and Construction Methods.- 2 Theoretical Aspects of Aggregation Operators.- Aggregation Based on Integrals: Recent Results and Trends.- Associative Aggregation Operators.- Continuous WOWA Operators with Application to Defuzzification.- Using Importances in Group Preference Aggregation to Block Strategic Manipulation.- 3 Applications of Aggregation Operators.- Aggregation Operators in Engineering Design.- Aggregation of Interacting Criteria by Means of the Discrete Choquet Integral.- Representation Models for Aggregating Linguistic Information: Issues and Analysis.- Aggregation Techniques for Statistical Confidentiality.- Quantifier Guided Aggregation of Fuzzy Criteria with Associated Importances.- 4 Fuzzy Quantities and Their Aggregation.- Verbally Generated Fuzzy Quantities and Their Aggregation.

Aggregation operators: new trends and applications

The functional equations of Frank and Alsina for uninorms and nullnorms

From the Publisher:
This book describes the current status of major parts of the theory of aggregation operators and examines potential areas for its applications. The authors have gathered self-contained papers and present essential material on selected topics in a comprehensive manner. In doing so they avoid tedious proofs and unnecessary details - this is not the case for several contributions containing new results and ideas which show the latest streaming of aggregation theory and potential application areas. The book is divided in four parts. The first part contains an overview of aggregation operators, including construction methods and different classes of aggregation operators. The second part is devoted to the theoretical aspects of aggregation and the third part looks at the field of applications. The final part offers an alternative look at the aggregation of verbal variables as fuzzy quantities.

Tomasa Calvo

Papers

Aggregation Functions: A Guide for Practitioners

Aggregation operators: properties, classes and construction methods

Aggregation operators: new trends and applications

The functional equations of Frank and Alsina for uninorms and nullnorms

Aggregation Operators