On the Optimization of Fuzzy Relation Equations with Continuous t-Norm and with Linear Objective Function

Pandey, Dhaneshwar

doi:10.1007/978-3-540-30176-9_6

Cited by 5 publications

(3 citation statements)

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“…Similar deficiencies were detected in Ghodousian and Khorram (2006a, b) and and amended by Abbasi Molai and Khorram (2007a, b) in which fuzzy relational equation constrained linear optimization problems were investigated under various composite operations. Some other generalizations on this issue can be found in Wu and Guu (2004a), Pandey (2004), Guo and Xia (2006), Abbasi Molai and Khorram (2007) and Ghodousian and Khorram (2007). Note that the algorithm proposed by Pandey (2004) only works for strict triangular norms but not for general continuous triangular norms as claimed.…”

Section: Introductionmentioning

confidence: 89%

“…Some other generalizations on this issue can be found in Wu and Guu (2004a), Pandey (2004), Guo and Xia (2006), Abbasi Molai and Khorram (2007) and Ghodousian and Khorram (2007). Note that the algorithm proposed by Pandey (2004) only works for strict triangular norms but not for general continuous triangular norms as claimed. Lu and Fang (2001) designed a genetic algorithm to solve nonlinear optimization problems subject to a system of sup-T M equations.…”

Section: Introductionmentioning

confidence: 89%

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On the resolution and optimization of a system of fuzzy relational equations with sup-T composition

Fang

2008

Fuzzy Optim Decis Making

121

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This paper provides a thorough investigation on the resolution of a finite system of fuzzy relational equations with sup-T composition, where T is a continuous triangular norm. When such a system is consistent, although we know that the solution set can be characterized by a maximum solution and finitely many minimal solutions, it is still a challenging task to find all minimal solutions in an efficient manner. Using the representation theorem of continuous triangular norms, we show that the systems of sup-T equations can be divided into two categories depending on the involved triangular norm. When the triangular norm is Archimedean, the minimal solutions correspond one-to-one to the irredundant coverings of a set covering problem. When it is non-Archimedean, they only correspond to a subset of constrained irredundant coverings of a set covering problem. We then show that the problem of minimizing a linear objective function subject to a system of sup-T equations can be reduced into a 0-1 integer programming problem in polynomial time. This work generalizes most, if not all, known results and provides a unified framework to deal with the problem of resolution and optimization of a system of sup-T equations. Further generalizations and related issues are also included for discussion.

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Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 89%

On the resolution and optimization of a system of fuzzy relational equations with sup-T composition

Fang

2008

Fuzzy Optim Decis Making

121

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“…Since then, many researchers have been studying the optimization problem and developing solution procedures [3,6,[9][10][11][12][13][14][15][16]18].…”

Section: Introductionmentioning

confidence: 99%

Value-based-matrix-pattern (VBMP) algorithm for fuzzy relation equations with linear objective

Pandey

2011

OPSEARCH

Self Cite

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In this paper a new algorithm is proposed to solve the optimization problem of fuzzy relation equations with linear objective function. Fuzzy relation equation is composed of max-min or max-product composition operator. This algorithm operates systematically on the matrix-pattern to get the solution(s). It is found easier to work with this algorithm. Two examples are given to illustrate the effectiveness of this algorithm.

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Linear Programming Subject to Max-Product Fuzzy Relation Inequalities with Discrete Variables

Fu,

Zhu,

Qin

2024

Lecture Notes on Data Engineering and Communications Technologies

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On the Optimization of Fuzzy Relation Equations with Continuous t-Norm and with Linear Objective Function

Cited by 5 publications

References 20 publications

On the resolution and optimization of a system of fuzzy relational equations with sup-T composition

On the resolution and optimization of a system of fuzzy relational equations with sup-T composition

Value-based-matrix-pattern (VBMP) algorithm for fuzzy relation equations with linear objective

Linear Programming Subject to Max-Product Fuzzy Relation Inequalities with Discrete Variables

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