• Honam Mathematical Journal
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• v.31 no.3
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• pp.351-368
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• 2009

Quick ideals and the fuzzification of quick ideals in d-algebras are considered, and some related properties are investigated. The intuitionistic fuzzification of quick ideals of a d-algebra is established, and related results are studied. The notion of equivalence relations on the family of all intuitionistic fuzzy quick ideals of a d-algebra is introduced, and then some properties are discussed.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.511-522
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• 2010

Rough sets, rough quick ideals and rough fuzzy quick ideals in d-algebras are established, and some related properties are investigated.

• East Asian mathematical journal
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• v.27 no.1
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• pp.75-82
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• 2011

In this paper, we will introduce the concept of fuzzy mulitplication module. We will define a new operation called a product on th family of all fuzzy submodules of a fuzzy mulitplication module. We will define a fuzzy subset of the idealization ring R+M and find some relations with the product of fuzzy submodules and product of fuzzy ideals of the idealization ring R+M. Some properties of weakly fuzzy prime submoduels and fuzzy prime submodules which are de ned by T.K.Mukherjee M.K.Sen and D.Roy will be introduced. We will investigate some properties of fuzzy prime submodules of a fuzzy multiplication module.

• Membrane and Water Treatment
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• v.14 no.2
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• pp.65-76
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• 2023

Given the limited water resources and the presence of multiple decision makers with different and usually conflicting objectives in the exploitation of water resources systems, especially dam's reservoirs; therefore, the decision to determine the optimal allocation of reservoir water among decision-makers and stakeholders is a difficult task. In this study, by combining a fuzzy VIKOR technique or fuzzy multi-criteria decision making (FMCDM) and the Young's bilateral bargaining model, a new method was developed to determine the optimal quantitative and qualitative water allocation of dam's reservoir water with the aim of increasing the utility of decision makers and stakeholders and reducing the conflicts among them. In this study, by identifying the stakeholders involved in the exploitation of the dam reservoir and determining their utility, the optimal points on trade-off curve with quantitative and qualitative objectives presented by Mojarabi et al. (2019) were ranked based on the quantitative and qualitative criteria, and economic, social and environmental factors using the fuzzy VIKOR technique. In the proposed method, the weights of the criteria were determined by each decision maker using the entropy method. The results of a fuzzy decision-making method demonstrated that the Young's bilateral bargaining model was developed to determine the point agreed between the decisions makers on the trade-off curve. In the proposed method, (a) the opinions of decision makers and stakeholders were considered according to different criteria in the exploitation of the dam reservoir, (b) because the decision makers considered the different factors in addition to quantitative and qualitative criteria, they were willing to participate in bargaining and reconsider their ideals, (c) due to the use of a fuzzy-logic based decision-making approach and considering different criteria, the utility of all decision makers was close to each other and the scope of bargaining became smaller, leading to an increase in the possibility of reaching an agreement in a shorter time period using game theory and (d) all qualitative judgments without considering explicitness of the decision makers were applied to the model using the fuzzy logic. The results of using the proposed method for the optimal exploitation of Iran's 15-Khordad dam reservoir over a 30-year period (1968-1997) showed the possibility of the agreement on the water allocation of the monthly total dissolved solids (TDS)=1,490 mg/L considering the different factors based on the opinions of decision makers and reducing conflicts among them.