Computation of Choquet integral for finite sets: Notes on a ChatGPT-driven experience

The Choquet integral, credited to Gustave Choquet in 1954, initially found its roots in decision making under uncertainty following Schmeidler's pioneering work in this field. Surprisingly, it was not until the 1990s that this integral gained recognition in the realm of multi-criteria decision aid. Nowadays, the Choquet integral boasts numerous generalizations and serves as a focal point for intensive research and development across various domains. Here we share our journey of utilizing ChatGPT as a helpful assistant to delve into the computation of the discrete Choquet integral using Mathematica. Additionally, we have demonstrated our ChatGPT experience by crafting a Beamer presentation with its assistance. The ultimate aim of this exercise is to pave the way for the application of the discrete Choquet integral in the context of N-soft sets

Interval-Valued Intuitionistic Fuzzy Einstein Geometric Choquet Integral Operator and Its Application to Multiattribute Group Decision-Making

With respect to the multiattribute decision-making (MADM) problem in which the attributes have interdependent or interactive phenomena under the interval-valued intuitionistic fuzzy environment, we propose a group decision-making approach based on the interval-valued intuitionistic fuzzy Einstein geometric Choquet integral operator (IVIFEGC). Firstly, the Einstein operational laws and some basic principle on interval-valued intuitionistic fuzzy sets are introduced. Then, the IVIFEGC is developed and some desirable properties of the operator are studied. Further, an approach to multiattribute group decision-making with interval-valued intuitionistic fuzzy information is developed, where the attributes have interdependent phenomena. Finally, an illustrative example is used to illustrate the developed approach

Induced hesitant 2-tuple linguistic aggregation operators with application in group decision making

In this article, hesitant 2-tuple linguistic arguments are used to evaluate the group decision making problems which have inter dependent or inter active attributes. Operational laws are developed for hesitant 2-tuple linguistic elements and based on these operational laws hesitant 2- tuple weighted averaging operator and generalized hesitant 2- tuple averaging operator are proposed. Combining Choquet integral with hesitant 2-tuple linguistic information, some new aggregation operators are defined, including the hesitant 2-tuple correlated averaging operator, the hesitant 2-tuple correlated geometric operator and the generalized hesitant 2-tuple correlated averaging operator. These proposed operators successfully manage the correlations among the elements. After investigating the properties of these operators, a multiple attribute decision making method based on these operators, is suggested. Finally, an example is given to illustrate the practicality and feasibility of proposed method

Aggregation operators in group decision making: Identifying citation classics via H-classics

To analyze the past, present and future of a particular research field, classic papers are usually studied because they identify the highly cited papers being a relevant reference point in that specific research area. As a result of the possible mapping between high quality research and high citation counts, highly cited papers are very interesting. The objective of this study is to use the H-classics method, which is based on the popular h-index, to identify and analyze the highly cited documents published about aggregation operators in the research area of group decision making. According to the H-classics method, this research area is represented by 87 citation classics, which have been published from 1988 to 2014. Authors, affiliations (universities/institutions and countries), journals, books and conferences, and the topics covered by these 87 highly cited papers are studied.The authors would like to thank FEDER financial support from the Projects TIN2013-40658-P and TIN2016- 75850-P

Multi-criteria trapezoidal valued intuitionistic fuzzy decision making with Choquet integral based TOPSIS

A generalized trapezoidal-valued intuitionistic fuzzy geometric aggregation operator is proposed which is then used to aggregate decision makers' opinions in group decision making process. An extension of TOPSIS, a multi-criteria trapezoidal-valued intuitionistic fuzzy decision making technique, to a group decision environment is also proposed, where inter-dependent or interactive characteristics among criteria and preference of decision makers are under consideration. Furthermore, Choquet integral-based distance between trapezoidal-valued intuitionistic fuzzy values is defined. Combining the trapezoidal-valued intuitionistic fuzzy geometric aggregation operator with Choquet integral-based distance, an extension of TOPSIS method is developed to deal with a multi-criteria trapezoidal-valued intuitionistic fuzzy group decision making problems. Finally, an illustrative example is provided to understand the proposed method

A Method Based on Intuitionistic Fuzzy Dependent Aggregation Operators for Supplier Selection

Recently, resolving the decision making problem of evaluation and ranking the potential suppliers have become as a key strategic factor for business firms. In this paper, two new intuitionistic fuzzy aggregation operators are developed: dependent intuitionistic fuzzy ordered weighed averaging (DIFOWA) operator and dependent intuitionistic fuzzy hybrid weighed aggregation (DIFHWA) operator. Some of their main properties are studied. A method based on the DIFHWA operator for intuitionistic fuzzy multiple attribute decision making is presented. Finally, an illustrative example concerning supplier selection is given