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On optimistic, pessimistic and mixed approaches under different membership functions for fully intuitionistic fuzzy multiobjective nonlinear programming problems
Expert Systems with Applications ( IF 8.5 ) Pub Date : 2020-11-30 , DOI: 10.1016/j.eswa.2020.114309
Sumati Mahajan , S.K. Gupta

The concept of measuring the membership degree along with a non-membership degree, gives rise to the intuitionistic fuzzy set theory. The present study formulates a nonlinear programming problem with multiple objectives, including all the parameters and decision variables as intuitionistic fuzzy numbers. The problem is further investigated subject to optimistic, pessimistic and mixed approaches under linear, exponential and hyperbolic membership functions. The article redefines pessimistic and mixed point of view to be in the true spirit compatible with the definition of an intuitionistic fuzzy number. Accuracy function is used to reduce the problem to an equivalent crisp multiobjective nonlinear programming problem and then optimal compromise solution is obtained under different approaches using various membership/non-membership functions. At appropriate places, theorems have also been proved to establish the equivalence between the original formulation and its crisp counterparts under each approach. Further, practical applications in production planning and transportation problem are illustrated to explain the optimistic, pessimistic and mixed approaches using the proposed algorithm and finally a comparison is also drawn.



中文翻译:

完全直觉模糊多目标非线性规划问题在不同隶属度函数下的乐观,悲观和混合方法

测量隶属度和非隶属度的概念提出了直觉模糊集理论。本研究提出了一个具有多个目标的非线性规划问题,包括所有参数和决策变量作为直觉模糊数。在线性,指数和双曲隶属度函数下,应采用乐观,悲观和混合方法进一步研究该问题。本文将悲观和混合观点重新定义为与直觉模糊数的定义兼容的真实精神。使用精度函数将问题简化为等效的清晰多目标非线性规划问题,然后使用各种隶属/非隶属函数在不同方法下获得最佳折衷解。在适当的地方,也证明了定理可以确定每种方法下原始配方与其清晰对应物之间的等效性。进一步地,说明了在生产计划和运输问题中的实际应用,以说明使用该算法的乐观,悲观和混合方法,最后进行了比较。

更新日期:2020-12-05
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