The main purpose of this paper is to build a new approach for solving a fuzzy linear multi-criterion problem by defining a function called “error function”. For this end, the concept of level set is used to co...The main purpose of this paper is to build a new approach for solving a fuzzy linear multi-criterion problem by defining a function called “error function”. For this end, the concept of level set is used to construct the error function. In addition, we introduce the concept of deviation variable in the definition of the error function. The algorithm of the new approach is summarized in three main steps: first, we transform the original fuzzy problem into a deterministic one by choosing a specific level . second, we solve separately each uni-criteria problem and we compute the error function for each criteria. Finally, we minimize the sum of error functions in order to obtain the desired compromise solution. A numerical example is done for a comparative study with some existing approaches to show the effectiveness of the new approach.展开更多
The last three decades ha</span><span style="font-family:"">ve</span><span style="font-family:""> witnessed development of optimization under fuzziness and randomn...The last three decades ha</span><span style="font-family:"">ve</span><span style="font-family:""> witnessed development of optimization under fuzziness and randomness also called Fuzzy Stochastic Optimization. The main objective </span><span style="font-family:"">of </span><span style="font-family:"">this new field is the need for basing many human decisions on information which is both fuzzily imprecise and probabilistically uncertain. Consistency indexes providing a union nexus between possibilities and probabilities of uncertain events exist in the literature. Nevertheless, there are no reliable transformations between them. This calls for new paradigms for coping with mathematical models involving both fuzziness and randomness. Fuzzy Stochastic Optimization (FSO) is an attempt to fulfill this need. In this paper, we present a panoramic view of Fuzzy Stochastic Optimization emphasizing the methodological aspects. The merits of existing methods are also briefly discussed along with some related theoretical aspects.展开更多
Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe ...Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe limitations on objectivity are encountered in this field because of the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice cannot hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this paper, we resort to the bounded rationality principle to introduce satisfying solution for multiobjective stochastic linear programming problems. These solutions that are based on the chance-constrained paradigm are characterized under the assumption of normality of involved random variables. Ways for singling out such solutions are also discussed and a numerical example provided for the sake of illustration.展开更多
In this paper<i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> fuzzy techniques have been used to track the problem of malaria tran...In this paper<i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> fuzzy techniques have been used to track the problem of malaria transmission dynamics. The fuzzy equilibrium of the proposed model was discussed for different amounts of parasites in the body. We proved that when the amounts of parasites are less than the minimum amounts required for disease transmission (<img src="Edit_bced8210-1c24-4e78-bb5b-60ea7d37361c.png" alt="" /></span><span></span><span style="font-family:Verdana;">)</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> we reach the model disease-free equilibrium. Using Choquet integral</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> the fuzzy basic reproduction number through the expected value of fuzzy variable was introduced for the fuzzy Susceptible</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Exposed</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Infected</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Recovered</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> susceptible-Susceptible</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Exposed and Infected (SEIRS-SEI) malaria model. The fuzzy global stabilities were introduced and discussed. The disease-free equilibrium <img src="Edit_cc2d122d-7c04-4fb7-a96a-3eb919a3785d.png" alt="" /> </span><span style="font-family:Verdana;">is globally asymptotically stable if <img src="Edit_0974e52f-cf63-4bfa-9781-1ebce366a4a3.png" alt="" /></span><span></span><span style="font-family:Verdana;"> or if the basic reproduction number is less than one (<img src="Edit_dbffcb03-cd00-4213-b7e1-ada9a0cf5c98.png" alt="" /></span><span></span><span style="font-family:Verdana;">). When <img src="Edit_5fc38f3d-2561-4189-87c2-197e3ff30b2e.png" alt="" /></span><span></span><span style="font-family:Verdana;"> and <img src="Edit_bfe99d90-7e55-4466-96b2-ce107483f69b.png" alt="" /></span><span></span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> there exists a co-existing endemic equilibrium which is globally asymptotically stable in the interior of feasible set <img src="Edit_543608fd-d8c9-4109-a285-bcf9377f43cc.png" alt="" /></span><span></span><span style="font-family:Verdana;">. Finally</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> the numerical simulation has been done for showing the effectiveness of our analytical results.</span>展开更多
文摘The main purpose of this paper is to build a new approach for solving a fuzzy linear multi-criterion problem by defining a function called “error function”. For this end, the concept of level set is used to construct the error function. In addition, we introduce the concept of deviation variable in the definition of the error function. The algorithm of the new approach is summarized in three main steps: first, we transform the original fuzzy problem into a deterministic one by choosing a specific level . second, we solve separately each uni-criteria problem and we compute the error function for each criteria. Finally, we minimize the sum of error functions in order to obtain the desired compromise solution. A numerical example is done for a comparative study with some existing approaches to show the effectiveness of the new approach.
文摘The last three decades ha</span><span style="font-family:"">ve</span><span style="font-family:""> witnessed development of optimization under fuzziness and randomness also called Fuzzy Stochastic Optimization. The main objective </span><span style="font-family:"">of </span><span style="font-family:"">this new field is the need for basing many human decisions on information which is both fuzzily imprecise and probabilistically uncertain. Consistency indexes providing a union nexus between possibilities and probabilities of uncertain events exist in the literature. Nevertheless, there are no reliable transformations between them. This calls for new paradigms for coping with mathematical models involving both fuzziness and randomness. Fuzzy Stochastic Optimization (FSO) is an attempt to fulfill this need. In this paper, we present a panoramic view of Fuzzy Stochastic Optimization emphasizing the methodological aspects. The merits of existing methods are also briefly discussed along with some related theoretical aspects.
文摘Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe limitations on objectivity are encountered in this field because of the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice cannot hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this paper, we resort to the bounded rationality principle to introduce satisfying solution for multiobjective stochastic linear programming problems. These solutions that are based on the chance-constrained paradigm are characterized under the assumption of normality of involved random variables. Ways for singling out such solutions are also discussed and a numerical example provided for the sake of illustration.
文摘In this paper<i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> fuzzy techniques have been used to track the problem of malaria transmission dynamics. The fuzzy equilibrium of the proposed model was discussed for different amounts of parasites in the body. We proved that when the amounts of parasites are less than the minimum amounts required for disease transmission (<img src="Edit_bced8210-1c24-4e78-bb5b-60ea7d37361c.png" alt="" /></span><span></span><span style="font-family:Verdana;">)</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> we reach the model disease-free equilibrium. Using Choquet integral</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> the fuzzy basic reproduction number through the expected value of fuzzy variable was introduced for the fuzzy Susceptible</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Exposed</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Infected</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Recovered</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> susceptible-Susceptible</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Exposed and Infected (SEIRS-SEI) malaria model. The fuzzy global stabilities were introduced and discussed. The disease-free equilibrium <img src="Edit_cc2d122d-7c04-4fb7-a96a-3eb919a3785d.png" alt="" /> </span><span style="font-family:Verdana;">is globally asymptotically stable if <img src="Edit_0974e52f-cf63-4bfa-9781-1ebce366a4a3.png" alt="" /></span><span></span><span style="font-family:Verdana;"> or if the basic reproduction number is less than one (<img src="Edit_dbffcb03-cd00-4213-b7e1-ada9a0cf5c98.png" alt="" /></span><span></span><span style="font-family:Verdana;">). When <img src="Edit_5fc38f3d-2561-4189-87c2-197e3ff30b2e.png" alt="" /></span><span></span><span style="font-family:Verdana;"> and <img src="Edit_bfe99d90-7e55-4466-96b2-ce107483f69b.png" alt="" /></span><span></span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> there exists a co-existing endemic equilibrium which is globally asymptotically stable in the interior of feasible set <img src="Edit_543608fd-d8c9-4109-a285-bcf9377f43cc.png" alt="" /></span><span></span><span style="font-family:Verdana;">. Finally</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> the numerical simulation has been done for showing the effectiveness of our analytical results.</span>
