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Mathematics
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Mathematical Methods for Decision Making and Optimization
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Mathematical Methods for Decision Making and Optimization

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Fuzzy Sets, Systems and Decision Making".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 5345

Special Issue Editor

Dr. Prasenjit Chatterjee

E-Mail Website
Guest Editor
Department of Mechanical Engineering, MCKV Institute of Engineering, Howrah 711204, India
Interests: multi-criteria optimization; multi-criteria decision-making; operations research; fuzzy optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Numerous real-world problems in science, engineering, industry, economics, and business are solved using sets of mathematical concepts and techniques called optimization and decision making. These fields are extremely rich as a result of the creation of numerous novel algorithms. The quantitative measurement of quality has become the most effective foundation for developing and enhancing policies over the last few years. Mathematical techniques, statistical analysis, and optimization techniques can all improve decision-making processes. A number of new challenges have recently emerged in the fields of mathematical modeling due to the development of new techniques and algorithms based on artificial intelligence, machine learning, neural networks, fuzzy theory, evolutionary computation, multi-objective optimization, multi-criteria decision making, rough set theory, and data analytics, to name a few. The decision-making process can be carried out by employing numerous methods and tools, as well as using diverse objectives, in order to provide an acceptable solution to the new problems encountered. The formulation of decision-making problems and the application of optimization techniques to support decisions are particularly complex in real-world issues, and a variety of techniques and methodologies are used to reduce risks or raise the quality of decisions being made concurrently.

The goal of this Special Issue is to collect the most recent developments in mathematical decision-making and optimization techniques for a variety of engineering, science, and management applications. Both original research pieces and review papers are welcome to be submitted to this Special Issue.

Topics include, but are not limited to:

  • Application of AI, ML, fuzzy and other techniques;
  • Data mining and statistical learning;
  • Decision support systems;
  • Design optimization;
  • Evolutionary algorithm;
  • Fuzzy computing;
  • High-performance computing;
  • Intelligent computing;
  • Mathematical modeling;
  • Machine learning applications;
  • Multi-objective programming;
  • Multi-criteria decision making;
  • Metaheuristic algorithms predictive modeling and analytics; 
  • Rough set theory;
  • Neural networks.

Dr. Prasenjit Chatterjee
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • application of AI, ML, fuzzy and other techniques
  • data mining and statistical learning
  • decision support systems
  • design optimization
  • evolutionary algorithm
  • fuzzy computing
  • high performance computing
  • intelligent computing
  • mathematical modelling
  • machine learning applications
  • multi-objective programming
  • multi-criteria decision making
  • metaheuristic algorithms predictive modeling and analytics
  • rough set theory
  • neural networks

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (4 papers)

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Research

23 pages, 2748 KiB  
Article
Centroidous Method for Determining Objective Weights
by Irina Vinogradova-Zinkevič
Mathematics 2024, 12(14), 2269; https://doi.org/10.3390/math12142269 - 20 Jul 2024
Viewed by 456
Abstract
When using multi-criteria decision-making methods in applied problems, an important aspect is the determination of the criteria weights. These weights represent the degree of each criterion’s importance in a certain group. The process of determining weight coefficients from a dataset is described as [...] Read more.
When using multi-criteria decision-making methods in applied problems, an important aspect is the determination of the criteria weights. These weights represent the degree of each criterion’s importance in a certain group. The process of determining weight coefficients from a dataset is described as an objective weighting method. The dataset considered here contains quantitative data representing measurements of the alternatives being compared, according to a previously determined system of criteria. The purpose of this study is to suggest a new method for determining objective criteria weights and estimating the proximity of the studied criteria to the centres of their groups. It is assumed that the closer a criterion is to the centre of the group, the more accurately it describes the entire group. The accuracy of the description of the entire group’s priorities is interpreted as the importance, and the higher the value, the more significant the weight of the criterion. The Centroidous method suggested here evaluates the importance of each criterion in relation to the centre of the entire group of criteria. The stability of the Centroidous method is examined in relation to the measures of Euclidean, Manhattan, and Chebyshev distances. By slightly modifying the data in the original normalised data matrix by 5% and 10% 100 and 10,000 times, stability is examined. A comparative analysis of the proposed Centroidous method obtained from the entropy, CRITIC, standard deviation, mean, and MEREC methods was performed. Three sets of data were generated for the comparative study of the methods, as follows: the mean value for alternatives with weak and strong differences and criteria with linear dependence. Additionally, an actual dataset from mobile phones was also used for the comparison. Full article
(This article belongs to the Special Issue Mathematical Methods for Decision Making and Optimization)
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15 pages, 277 KiB  
Article
Two Approaches to Estimate the Shapley Value for Convex Partially Defined Games
by Satoshi Masuya
Mathematics 2024, 12(1), 17; https://doi.org/10.3390/math12010017 - 20 Dec 2023
Cited by 1 | Viewed by 750
Abstract
In the classical approach of von Neumann and Morgenstern to cooperative games, it was assumed that the worth of all coalitions must be given. However, in real-world problems, the worth of some coalitions may be unknown. Therefore, in this study, we consider the [...] Read more.
In the classical approach of von Neumann and Morgenstern to cooperative games, it was assumed that the worth of all coalitions must be given. However, in real-world problems, the worth of some coalitions may be unknown. Therefore, in this study, we consider the Shapley value for convex partially defined games using two approaches. Firstly, we introduce a polytope that includes the set of Shapley values that can be obtained from a given convex partially defined game and select one rational value in some sense from the set. The elements of this polytope are said to be the Shapley payoff vectors. Secondly, we obtain the set of Shapley values that can be obtained from a given convex partially defined game and select one rational value in some sense from the set. Moreover, we axiomatize the proposed two values. Full article
(This article belongs to the Special Issue Mathematical Methods for Decision Making and Optimization)
26 pages, 1515 KiB  
Article
GRA-Based Dynamic Hybrid Multi-Attribute Three-Way Decision-Making for the Performance Evaluation of Elderly-Care Services
by Fan Jia, Yujie Wang and Yiting Su
Mathematics 2023, 11(14), 3176; https://doi.org/10.3390/math11143176 - 19 Jul 2023
Cited by 1 | Viewed by 1060
Abstract
As an important branch of modern decision-making theory, multi-attribute decision-making (MADM) plays an important role in various fields. Classic MADM methods can provide a ranking of alternatives, and decision-makers need to evaluate the level subjectively based on the ranking results. Because of the [...] Read more.
As an important branch of modern decision-making theory, multi-attribute decision-making (MADM) plays an important role in various fields. Classic MADM methods can provide a ranking of alternatives, and decision-makers need to evaluate the level subjectively based on the ranking results. Because of the limitation of knowledge, this is likely to lead to potential individual losses. Three-way decision (3WD) theory has good classification ability. Therefore, this paper proposes a dynamic hybrid multi-attribute 3WD (MA3WD) model. First, a new scheme for constructing loss functions is proposed from the perspective of gray relational analysis (GRA), which is an accurate and objective way to describe the relationship between loss functions and attribute values. Then, conditional probabilities are determined by employing the gray relational analysis technique for order preference by similarity to the ideal solution (GRA-TOPSIS). With these discussions, a GRA-based hybrid MA3WD model for a single period is proposed by considering multi-source information. Furthermore, by extending the single-period scenario to a multi-period one, we construct a dynamic hybrid MA3WD model, which can obtain the final three-way decision rules as well as the results of each period and each attribute. Finally, the proposed method is applied to the case of performance evaluation of elderly-care services to demonstrate the effectiveness of the method, and comparative analyses are given to verify the superiority of the proposed method. Full article
(This article belongs to the Special Issue Mathematical Methods for Decision Making and Optimization)
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9 pages, 302 KiB  
Article
ES Structure Based on Soft J-Subset
by Xi Chen, Pooja Yadav, Rashmi Singh and Sardar M. N. Islam
Mathematics 2023, 11(4), 853; https://doi.org/10.3390/math11040853 - 7 Feb 2023
Cited by 9 | Viewed by 1287
Abstract
The ES structure described by soft subsets or soft M-subsets does not yield a lattice structure due to its restriction on parameter sets, and so cannot be used in information theory. This study proposes a new ES structure on soft sets that addresses [...] Read more.
The ES structure described by soft subsets or soft M-subsets does not yield a lattice structure due to its restriction on parameter sets, and so cannot be used in information theory. This study proposes a new ES structure on soft sets that addresses the deficiencies of the prior structure. Using mathematical concepts, we can construct and entirely new system of soft sets. As a result, the ES structure is derived from a finite collection of basic soft sets and offers complicated soft sets via its ES components, allowing for it to be operated by computers, as this is more acceptable to conventional mathematical viewpoints. We rewrote this using a soft J-subset and demonstrated that (ES, ∨˜ES, ∧˜ES) is a distributive lattice. This will play an important role in decision-making problems and contribute to a better understanding of human recognition processes. During the process of reaching a decision, several groups of parameters develop, and the ES structure in this article takes these parameters into consideration in order to handle the intricate issues that arise. In soft set theory, this research gives insight into the cognitive field. Full article
(This article belongs to the Special Issue Mathematical Methods for Decision Making and Optimization)
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