Min-Product Fuzzy Relation Inequalities with Application in Supply Chain

Guo, Hui-Mei; Zheng, Cai-Fen; Tianxiang, Zhu; Lin, Haitao; Yang, Xiaopeng

doi:10.1109/fskd.2018.8686941

Cited by 6 publications

(12 citation statements)

References 43 publications

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“…Model in a Supply Chain. This subsection provides simple application background for our studied min-product FRIs, which is adopted from [51,52].…”

Section: Pricing Relation and The Corresponding Mathematicalmentioning

confidence: 99%

“…Definition (see [51,52]). The minimum (or minimal) element in ( , ) is called minimum (or minimal) solution of system (16).…”

Section: Consistency Checking For System ( )mentioning

confidence: 99%

“…Recently, fuzzy relation inequality with min-product composition was defined and investigated [51][52][53]. It was first introduced to describe the pricing in the supply and demand scheme [53].…”

Section: Introductionmentioning

confidence: 99%

“…In such case, the requirement of the suppliers might not be fulfilled and a group of min-product fuzzy relation inequalities was constructed. In order to satisfy both requirement of the retailers and the suppliers, Yang et al [51,52] further established and studied the min-product system with one more constraint ≤ . In [51,52], checking method of consistency of a min-product system and structure of its solution set (when consistent) were investigated.…”

Section: Introductionmentioning

confidence: 99%

“…In order to satisfy both requirement of the retailers and the suppliers, Yang et al [51,52] further established and studied the min-product system with one more constraint ≤ . In [51,52], checking method of consistency of a min-product system and structure of its solution set (when consistent) were investigated. Based on the specific structure of the complete solution set of min-product fuzzy relation inequalities system, Yang et al [52] further studied a lexicographic optimization problem.…”

Section: Introductionmentioning

confidence: 99%

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Maximin Optimization Problem Subject to Min‐Product Fuzzy Relation Inequalities with Application in Supply and Demand Scheme

et al. 2019

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In a supply chain system, the prices with which the suppliers supply its local commodity to the retailers should satisfy the requirements of the retailers and the consumers. The supply and demand scheme satisfying these requirements is reduced into fuzzy relation inequalities (FRIs) with min-product composition. Due to the difference between the min-product composition and the classical max-t-norm one, we first study the resolution of such min-product FRI system. For optimization management in the supply chain system, we further investigate a maximin programming problem subject to the min-product FRIs. An algorithm is proposed to obtain the optimal solution based on the quasi-maximal matrix and corresponding index set. To illustrate the efficiency of our proposed algorithm, we provide a simple numerical example. The obtained optimal solution reflects an optimal pricing scheme, which maximizes the minimum prices of the commodity from the suppliers.

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“…Model in a Supply Chain. This subsection provides simple application background for our studied min-product FRIs, which is adopted from [51,52].…”

Section: Pricing Relation and The Corresponding Mathematicalmentioning

confidence: 99%

“…Definition (see [51,52]). The minimum (or minimal) element in ( , ) is called minimum (or minimal) solution of system (16).…”

Section: Consistency Checking For System ( )mentioning

confidence: 99%