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The covariance of uncertain variables: definition and calculation formulae

Mingxuan Zhao, Yuhan Liu, Dan A. Ralescu, Jian Zhou
2017 Fuzzy Optimization and Decision Making  
problems in an uncertain environment.  ...  The definitions and calculation formulae of covariance and correlation coefficient of two uncertain variables are suggested by means of their inverse distributions.  ...  While dealing with practical decision problems, those indices are often used as important criteria.  ... 
doi:10.1007/s10700-017-9270-3 fatcat:nhsi6b3gxjgc7hl4s7mazzfsnm

On the optimal solution definition for many-criteria optimization problems

M. Farina, P. Amato
2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622)  
When dealing with many-criteria decision making and many-objectives optimization problems the concepts of Pareto optimality and Pareto-dominance are inefficient in modelling and simulating human decision  ...  Different fuzzy-based definitions of optimality and dominated solution are introduced and tested on analytical test cases in order to show their validity and closeness to human decision making.  ...  For the convenience of the reader we recall here the well known definition of Pareto-dominance (definition II.3) and Pareto optimum (definition II.4) in a multi-criteria (M criteria) decision making problem  ... 
doi:10.1109/nafips.2002.1018061 fatcat:rlkjhvjauzejnah4esnx3ulafi

Fuzzy Optimality and Evolutionary Multiobjective Optimization [chapter]

M. Farina, P. Amato
2003 Lecture Notes in Computer Science  
A Non-linear constrained multi-criteria (minimum) optimization problem with M objectives is defined as: Definition 1 (Multi-criteria optimization problem).  ...  The Pareto definition of optimality in a multi-criteria decision making problem can be unsatisfactory due to essentially two reasons:  ...  In the following sections we will give two more general definition of optimum for a multi-criteria decision making problem, taking into account one issue at a time.  ... 
doi:10.1007/3-540-36970-8_5 fatcat:i37mm4xsnbge7licff54p644ly

The new definitions of intuitionistic and belief-plausibility based local criteria with interval and fuzzy inputs applied to the multiple criteria problem of a raw material supplier selection

Pavel Sevastjanov, Ludmila Dymova, Krzysztof Kaczmarek
2021 IEEE Access  
For the fuzzy inputs, the definition of the fuzzy-valued BP N is proposed.  ...  The practical usefulness of the introduced approach is illustrated by the solution of the real-world Fuzzy-Valued Belief-Plausibility multiple criteria problem of the raw material suppliers selection on  ...  In [69], we presented the solutions of two fuzzy multiple criteria optimization problems on the BM M P , but their applicability was restricted by the need to solve these problems for everyone new supplier  ... 
doi:10.1109/access.2021.3132696 fatcat:fpazlox6yjhrldalnomfx4a7ue

A fuzzy proportional-derivative controller for engineering optimization problems using an optimality criteria approach

Yeh-liang Hsu, Tze-chi Liu, Tso-lung Liu
2005 Engineering optimization (Print)  
This paper proposes a fuzzy proportional-derivative (PD) controller optimization engine for engineering optimization problems using an optimality criteria approach.  ...  The idea of using the fuzzy PD controller in engineering optimization is that, instead of using purely numerical information to obtain the new design point in the next iteration, engineering knowledge  ...  Conclusions This paper has proposed a fuzzy PD controller optimization engine for engineering optimization problems using an optimality criteria approach.  ... 
doi:10.1080/03052150500100353 fatcat:yrg55uuwrfckhd3qib7fklayra

The use of possibility theory in the definition of fuzzy Pareto-optimality

Ricardo C. Silva, Akebo Yamakami
2010 Fuzzy Optimization and Decision Making  
This work presents a novel approach based on the definition of a fuzzily ordered set with a view to generating the necessary conditions for the Pareto-optimality of candidate solutions in the fuzzy domain  ...  The uncertainties are inserted into the formulation of the studied fuzzy multi-objective optimization problem by means of fuzzy coefficients in the objective function.  ...  These problems with various objective functions belong to a kind of problem that is studied by a branch of mathematical optimization theory called Multi-objective Optimization.  ... 
doi:10.1007/s10700-010-9092-z fatcat:jqkx4pv36zaelndqqwte2e3el4

Logical Fuzzy Optimization [article]

Emad Saad
2013 arXiv   pre-print
We present a logical framework to represent and reason about fuzzy optimization problems based on fuzzy answer set optimization programming.  ...  We show the application of the proposed logical fuzzy optimization framework under the fuzzy answer set optimization programming to the fuzzy water allocation optimization problem.  ...  that are based on minimization and maximization of some desired criteria imposed by the problem.  ... 
arXiv:1304.2384v1 fatcat:36wwu35dvjenznjke3wm6zyxeu

Multi-Criteria Optimization: An Important Foundation of Fuzzy System Design [chapter]

Hung T. Nguyen, Vladik Kreinovich
1998 Studies in Fuzziness and Soft Computing  
Fuzzy logic describes a much more natural way of handling multicriterion optimization problems: when we cannot maximize each of the original conflicting criteria 100%, we optimize each to a certain extent  ...  In many real-life design situations, there are several different criteria that we want to optimize, and these criteria are often in conflict with each other.  ...  The authors are thankful to Leonid Reznik, Vladimir Dimitrov, and Janusz Kacprzyk, the editors of this volume, for their help, and to Bernadette Bouchon-Meunier and Anatole Lokshin for valuable discussions  ... 
doi:10.1007/978-3-7908-1885-7_2 fatcat:i4bh73ftfbg3nga7isvkm6bswy

Parallel Particle Swarm Optimization Optimized Ldi Controller With Lyapunov Stability Criterion For Nonlinear Structural Systems

P.-W. Tsai, W.-L. Hong, C.-W. Chen, C.-Y. Chen
2014 Zenodo  
Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems.  ...  Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.  ...  in Mother Nature, to collaborate a serious of process for solving optimization problems in the fields of management, engineering, and economics.  ... 
doi:10.5281/zenodo.1094094 fatcat:fhsueeg225dzrmnztjqgwfwnpu

Optimal Fuzzy CLOS Guidance Law Design Using Ant Colony Optimization [chapter]

Hadi Nobahari, Seid H. Pourtakdoust
2005 Lecture Notes in Computer Science  
In this regard, the lately developed continuous ant colony system is used to optimize the parameters of a pre-constructed fuzzy sliding mode controller.  ...  The well-known ant colony optimization meta-heuristic is applied to design a new command to line-of-sight guidance law.  ...  Definition of FSMC Design as an Optimization Problem The FSMC considered here, involves a SISO fuzzy inference system with the variable s as the input, and the variable u as the output.  ... 
doi:10.1007/11571155_10 fatcat:dkb55ronz5bbjdquwtiekfox4q

Unsupervised optimal fuzzy clustering

I. Gath, A.B. Geva
1989 IEEE Transactions on Pattern Analysis and Machine Intelligence  
773 The complete form of the transformation equations which map the scene coordinates onto the image coordinates is therefore In order to solve for the unknown parameters. we need to consider the greatest  ...  A suitable technique would be the generalized form of the Newton-Raphson method. The equations to solve are .Y;,) -( X + A X )h = 0 and J, : , -C . ( X + A.Y) -d . ( J + AJ) -e = 0 where (U,:,.  ...  Bar-On for valuable discussions, and to Prof. A . K. Jain for reading the manuscript and providing many useful suggestions.  ... 
doi:10.1109/34.192473 fatcat:cm3ovrk7vjfsxffwdnyxzrxxmi

Optimization in Industrial Systems

Kok Lay Teo, Hsiao-Fan Wang, Changzhi Wu
2014 Mathematical Problems in Engineering  
In "A hybrid fuzzy analytic network process approach to the new product development selection problem" a hybrid multiple criteria decision model for selecting the most suitable new colour calibration device  ...  In "Error bounds and finite termination for constrained optimization problems" a global error bound for the projected gradient of nonconvex constrained optimization problems and a local error bound for  ...  Acknowledgments We would like to thank the authors for their contributions.  ... 
doi:10.1155/2014/824539 fatcat:tq4i6kx5cjbvvnme4qsna2c4t4

Fuzzy Multiobjective Reliability Optimization Problem of Industrial Systems Using Particle Swarm Optimization

Harish Garg
2013 Journal of Industrial Mathematics  
To handle these problems, this work presents an interactive method for solving the fuzzy multiobjective optimization decision-making problem, which can be used for the optimization decision making of the  ...  Based on the preference of the decision makers toward the objectives, fuzzy multi-objective optimization problem is converted into crisp optimization problem and then solved with evolutionary algorithm  ...  For this reason, a classification of the solutions is introduced in terms of Pareto optimality according to the following definitions, in terms of minimization. Definition 1 (Pareto optimal).  ... 
doi:10.1155/2013/872450 fatcat:2akhs6xkeba4rg6v6tomkpwe54

Optimization under fuzzy if–then rules

Christer Carlsson, Robert Fullér
2001 Fuzzy sets and systems (Print)  
The aim of this paper is to introduce a novel statement of fuzzy mathematical programming problems and to provide a method for finding a fair solution to these problems.  ...  ) programming problem to find a fair optimal solution to the original fuzzy problem.  ...  Fuzzy optimization problems can be stated and solved in many different ways (for good surveys see [8, 15] ).  ... 
doi:10.1016/s0165-0114(98)00465-5 fatcat:3k7r53euaremlpq6fveczjeehy

Present-day Problems and Methods of Optimization in Mechatronics

Wojciech Tarnowski
2017 Acta Mechanica et Automatica  
It is justified that design is an inverse problem, and the optimization is a paradigm. Classes of design problems are proposed and typical obstacles are recognized.  ...  Then a set of non-standard approaches and methods are presented and discussed, illustrated by examples: a fuzzy description, a constraint-based iterative optimization, AHP ranking method and a few MADM  ...  There are numerous constraints, many are nonlinear, some are fuzzy. Usually there are a few well defined but conflicted criteria of optimality. Some may be only estimated (like a cost).  ... 
doi:10.1515/ama-2017-0024 fatcat:kqe2q2ldyvfcvc3uaapb7nhcuy
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