scholarly journals Some Construction Methods of Aggregation Operators in Decision Making Problems: An Overview

2020 ◽  
Author(s):  
Azadeh Zahedi Khameneh ◽  
Adem Kilicman
Keyword(s):  
Decision Making ◽  
Basic Problem ◽  
Real Life ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Knowledge Based Systems ◽  
Knowledge Based ◽  
Construction Methods ◽  
Life Problems ◽  
Aggregation Functions

Aggregating data is the main line of any discipline dealing with fusion of information from the knowledge-based systems to the decision-making. The purpose of aggregation methods is to convert a list of objects, all belonging to a given set, into a single representative object of the same set usually by an n-ary function, so-called aggregation operator. Since the useful aggregation functions for modeling real-life problems are limit, the basic problem is to construct a proper aggregation operator for each situation. During the last decades, a number of construction methods for aggregation functions have been developed to build new classes based on the well-known operators. This paper reviews some of these construction methods where they are based on transformation, composition and weighted rule.

scholarly journals Some Construction Methods of Aggregation Operators in Decision-Making Problems: An Overview

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 694 ◽  
Author(s):  
Azadeh Zahedi Khameneh ◽  
Adem Kilicman
Keyword(s):  
Decision Making ◽  
Basic Problem ◽  
Convex Combination ◽  
Real Life ◽  
Aggregation Operator ◽  
Knowledge Based ◽  
Construction Methods ◽  
Life Problems ◽  
Aggregation Functions ◽  
Main Construction

Aggregating data is the main line of any discipline dealing with fusion of information from the knowledge-based systems to decision-making. The purpose of aggregation methods is to convert a list of objects, all belonging to a given set, into a single representative object of the same set usually by an n-ary function, so-called aggregation operator. As the useful aggregation functions for modeling real-life problems are limited, the basic problem is to construct a proper aggregation operator, usually a symmetric one, for each situation. During the last decades, a number of construction methods for aggregation functions have been developed to build new classes based on the existing well-known operators. There are three main construction methods in common use: transformation, composition, and convex combination. This paper compares these methods with respect to the type of aggregating problems that can be handled by each of them.

Multi-Criteria Decision-Making Approach Based on Moderator Intuitionistic Fuzzy Hybrid Aggregation Operators

2019 ◽  
pp. 237-251
Author(s):  
Bhagawati Prasad Joshi ◽  
Akhilesh Singh
Keyword(s):  
Decision Making ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Uncertainty Index ◽  
Geometric Point ◽  
Membership Grade

It has been seen in literature that the notion of intuitionistic fuzzy sets (IFSs) is very powerful tool to deal with real life problems under the environment of uncertainty. This notion of IFSs favours the intermingling of the uncertainty index in membership functions. The uncertainty index is basically generated from a lot of parameters such as lack of awareness, historical information, situation, short of standard terminologies, etc. Hence, the uncertainty index appended finding the membership grade under IFSs needs additional enhancement. Then, the concept of a moderator intuitionistic fuzzy set (MIFS) is defined by adding a parameter in the IFSs environment to make the uncertain behaviour more accurate. In this chapter, some new moderator intuitionistic fuzzy hybrid aggregation operators are presented on the basis of averaging and geometric point of views to aggregate moderator intuitionistic fuzzy information. Then, a multi-criteria decision-making (MCDM) approach is provided and successfully implemented to real-life problems of candidate selection.

Decision Making Methods Based on Fuzzy Aggregation Operators: Three Decades Review from 1986 to 2017

2018 ◽  
Vol 17 (02) ◽  
pp. 391-466 ◽  
Author(s):  
Abbas Mardani ◽  
Mehrbakhsh Nilashi ◽  
Edmundas Kazimieras Zavadskas ◽  
Siti Rahmah Awang ◽  
Habib Zare ◽  
...  
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Operator Theory ◽  
Real Life ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Aggregation

In many real-life decision making (DM) situations, the available information is vague or imprecise. To adequately solve decision problems with vague or imprecise information, fuzzy set theory and aggregation operator theory have become powerful tools. In last three decades, DM theories and methods under fuzzy aggregation operator have been proposed and developed for effectively solving the DM problems and numerous applications have been reported in the literature. While various aggregation operators have been suggested and developed, there is a lack of research regarding systematic literature review and classification of study in this field. Regarding this, Web of Science database has been nominated and systematic and meta-analysis method called “PRISMA” has been proposed. Accordingly, a review of 312 published articles appearing in 33 popular journals related to fuzzy set theory, aggregation operator theory and DM approaches between July 1986 and June 2017 have been attained to reach a comprehensive review of DM methods and aggregation operator environment. Consequently, the selected published articles have been categorized by name of author(s), the publication year, technique, application area, country, research contribution and journals in which they appeared. The findings of this study found that, ordered weighted averaging (OWA) has been the highest frequently accessed more than other areas. This systematic review shows that the DM theories under fuzzy aggregation operator environment have received a great deal of interest from researchers and practitioners in many disciplines.

scholarly journals Harmonic Aggregation Operator with Trapezoidal Picture Fuzzy Numbers and Its Application in a Multiple-Attribute Decision-Making Problem

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 135
Author(s):  
Chittaranjan Shit ◽  
Ganesh Ghorai ◽  
Qin Xin ◽  
Muhammad Gulzar
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Real Life ◽  
Information Aggregation ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Harmonic Mean ◽  
Life Problems ◽  
Multiple Attribute ◽  
Fuzzy Order

Picture fuzzy sets (PFSs) can be used to handle real-life problems with uncertainty and vagueness more effectively than intuitionistic fuzzy sets (IFSs). In the process of information aggregation, many aggregation operators under PFSs are used by different authors in different fields. In this article, a multi-attribute decision-making (MADM) problem is introduced utilizing harmonic mean aggregation operators with trapezoidal fuzzy number (TrFN) under picture fuzzy information. Three harmonic mean operators are developed namely trapezoidal picture fuzzy weighted harmonic mean (TrPFWHM) operator, trapezoidal picture fuzzy order weighted harmonic mean (TrPFOWHM) operator and trapezoidal picture fuzzy hybrid harmonic mean (TrPFHHM) operator. The related properties about these operators are also studied. At last, an MADM problem is considered to interrelate among these operators. Furthermore, a numerical instance is considered to explain the productivity of the proposed operators.

scholarly journals ACO with Intuitionistic Fuzzy Pheromone Updating Applied on Multiple-Constraint Knapsack Problem

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1456
Author(s):  
Stefka Fidanova ◽  
Krassimir Todorov Atanassov
Keyword(s):  
Decision Making ◽  
Knapsack Problem ◽  
Propositional Logic ◽  
Optimization Problems ◽  
Real Life ◽  
Combinatorial Optimization Problems ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Multiple Constraint

Some of industrial and real life problems are difficult to be solved by traditional methods, because they need exponential number of calculations. As an example, we can mention decision-making problems. They can be defined as optimization problems. Ant Colony Optimization (ACO) is between the best methods, that solves combinatorial optimization problems. The method mimics behavior of the ants in the nature, when they look for a food. One of the algorithm parameters is called pheromone, and it is updated every iteration according quality of the achieved solutions. The intuitionistic fuzzy (propositional) logic was introduced as an extension of Zadeh’s fuzzy logic. In it, each proposition is estimated by two values: degree of validity and degree of non-validity. In this paper, we propose two variants of intuitionistic fuzzy pheromone updating. We apply our ideas on Multiple-Constraint Knapsack Problem (MKP) and compare achieved results with traditional ACO.

Introduction and Historical Background

2019 ◽  
pp. 1-26
Keyword(s):  
Decision Making ◽  
Historical Development ◽  
Real Life ◽  
Literature Survey ◽  
Historical Background ◽  
Simultaneous Occurrence ◽  
Special Interests ◽  
Life Problems ◽  
Complex Decision Making ◽  
Complex Decision

This chapter describes the evolution of different multi-objective decision-making (MODM) models with their historical backgrounds. Starting from MODM models in deterministic environments along with various solution techniques, the chapter presents how different kinds of uncertainties may be associated with such decision-making models. Among several types of uncertainties, it has been found that probabilistic and possibilistic uncertainties are of special interests. A brief literature survey on different existing methods to solve those types of uncertainties, independently, is discussed and focuses on the need of considering simultaneous occurrence of those types of uncertainties in MODM contexts. Finally, a bibliographic survey on several approaches for MODM under hybrid fuzzy environments has been presented. Through this chapter the readers can be able to get some concepts about the historical development of MODM models in hybrid fuzzy environments and their importance in solving various real-life problems in the current complex decision-making arena.

A Biologically Inspired Autonomous Robot Control Based on Behavioural Coordination in Evolutionary Robotics

2011 ◽  
pp. 107-129 ◽  
Author(s):  
José A. Fernández-León ◽  
Gerardo G. Acosta ◽  
Miguel A. Mayosky ◽  
Oscar C. Ibáñez
Keyword(s):  
Mobile Robots ◽  
Autonomous Vehicle ◽  
Trajectory Generation ◽  
Real Life ◽  
Evolutionary Robotics ◽  
Knowledge Based ◽  
Planning And Control ◽  
Life Problems ◽  
Path Planner ◽  
And Control

This work is intended to give an overview of technologies, developed from an artificial intelligence standpoint, devised to face the different planning and control problems involved in trajectory generation for mobile robots. The purpose of this analysis is to give a current context to present the Evolutionary Robotics approach to the problem, which is now being considered as a feasible methodology to develop mobile robots for solving real life problems. This chapter also show the authors’ experiences on related case studies, which are briefly described (a fuzzy logic based path planner for a terrestrial mobile robot, and a knowledge-based system for desired trajectory generation in the Geosub underwater autonomous vehicle). The development of different behaviours within a path generator, built with Evolutionary Robotics concepts, is tested in a Khepera© robot and analyzed in detail. Finally, behaviour coordination based on the artificial immune system metaphor is evaluated for the same application.

scholarly journals Hybrid Weighted Arithmetic and Geometric Aggregation Operator of Neutrosophic Cubic Sets for MADM

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 278 ◽  
Author(s):  
Lilian Shi ◽  
Yue Yuan
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Arithmetic Average ◽  
Weighted Arithmetic ◽  
Geometric Average ◽  
Multi Attribute Decision Making

Neutrosophic cubic sets (NCSs) can express complex multi-attribute decision-making (MADM) problems with its interval and single-valued neutrosophic numbers simultaneously. The weighted arithmetic average (WAA) and geometric average (WGA) operators are common aggregation operators for handling MADM problems. However, the neutrosophic cubic weighted arithmetic average (NCWAA) and neutrosophic cubic geometric weighted average (NCWGA) operators may result in some unreasonable aggregated values in some cases. In order to overcome the drawbacks of the NCWAA and NCWGA, this paper developed a new neutrosophic cubic hybrid weighted arithmetic and geometric aggregation (NCHWAGA) operator and investigates its suitability and effectiveness. Then, we established a MADM method based on the NCHWAGA operator. Finally, a MADM problem with neutrosophic cubic information was provided to illustrate the application and effectiveness of the proposed method.

scholarly journals A Novel Hybrid Fuzzy Grey TOPSIS Method: Supplier Evaluation of a Collaborative Manufacturing Enterprise

2019 ◽  
Vol 9 (18) ◽  
pp. 3770 ◽  
Author(s):  
Yixiong Feng ◽  
Zhifeng Zhang ◽  
Guangdong Tian ◽  
Amir Mohammad Fathollahi-Fard ◽  
Nannan Hao ◽  
...  
Keyword(s):  
Decision Making ◽  
Comprehensive Evaluation ◽  
Real Life ◽  
Fuzzy Topsis ◽  
Supplier Evaluation ◽  
Manufacturing Enterprise ◽  
Collaborative Manufacturing ◽  
Life Problems ◽  
Order Preference ◽  
The Difference

Recently, there is of significant interest in developing multi-criteria decision making (MCDM) techniques with large applications for real-life problems. Making a reasonable and accurate decision on MCDM problems can help develop enterprises better. The existing MCDM methods, such as the grey comprehensive evaluation (GCE) method and the technique for order preference by similarity to an ideal solution (TOPSIS), have their one-sidedness and shortcomings. They neither consider the difference of shape and the distance of the evaluation sequence of alternatives simultaneously nor deal with the interaction that universally exists among criteria. Furthermore, some enterprises cannot consult the best professional expert, which leads to inappropriate decisions. These reasons motivate us to contribute a novel hybrid MCDM technique called the grey fuzzy TOPSIS (FGT). It applies fuzzy measures and fuzzy integral to express and integrate the interaction among criteria, respectively. Fuzzy numbers are employed to help the experts to make more reasonable and accurate evaluations. The GCE method and the TOPSIS are combined to improve their one-sidedness. A case study of supplier evaluation of a collaborative manufacturing enterprise verifies the effectiveness of the hybrid method. The evaluation result of different methods shows that the proposed approach overcomes the shortcomings of GCE and TOPSIS. The proposed hybrid decision-making model provides a more accurate and reliable method for evaluating the fuzzy system MCDM problems with interaction criteria.

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