Solutions in Composite Fuzzy Relation Equations: Application to Medical Diagnosis in Brouwerian Logic

Sanchez, Élie

doi:10.1016/b978-1-4832-1450-4.50017-1

Cited by 88 publications

(81 citation statements)

References 5 publications

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“…As equações relacionais fuzzy foram primeiramente citadas em Diagnóstico Médico [37]. Vamos apresentar um resumo da formulação matemática das mesmas.…”

Section: Equações Relacionais Fuzzyunclassified

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Teoria dos conjuntos fuzzy com aplicações.

2005

Notas Em Matemática Aplicada

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“…As equações relacionais fuzzy foram primeiramente citadas em Diagnóstico Médico [37]. Vamos apresentar um resumo da formulação matemática das mesmas.…”

Section: Equações Relacionais Fuzzyunclassified

“…As primeiras aplicações desta teoria em Biomatemática foi em diagnóstico médico [37] e [38]. Mais recentemente outros autores têm utilizado esta abordagem em problemas de epidemiologia [7], [10], [14], [16], [17], [24] e [30].…”

Section: Introductionunclassified

Teoria dos conjuntos fuzzy com aplicações.

2005

Notas Em Matemática Aplicada

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“…Generally, FRE and FRI have a number of properties that make them suitable for formulating the uncertain information upon which many applied concepts are usually based. FRE theory has been applied different fields including fuzzy decision making [17] fuzzy control [18], fuzzy modeling [19], medical diagnosis [20,21], fuzzy analysis, compression , , , , ,…”

Section: Introductionmentioning

confidence: 99%

Monomial geometric programming with an arbitrary fuzzy relational inequality

Shivanian

Sohrabi²

2015

Communications in Numerical Analysis

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In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with an arbitrary function. The feasible solution set is determined and compared with some common results in the literature. A necessary and sufficient condition and three other necessary conditions are presented to conceptualize the feasibility of the problem. In general a lower bound is always attainable for the optimal objective value by removing the components having no effect on the solution process. By separating problem to non-decreasing and non-increasing function to prove the optimal solution, we simplify operations to accelerate the resolution of the problem.

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“…Its structure of solution set was determined by Sanchez [30] in 1977 and extended to max-T FREs by Di Nola et al [5,7]. The complete solution set of a consistent finite system of max-T FREs can be determined by a maximum solution and a finite number of minimal solutions.…”

Section: Introductionmentioning

confidence: 99%