This paper presents fuzzy goal programming approach for solving multilevel programming problems with fuzzy parameters. The proposed approach is based on ? -cut and fuzzy goal programming. In the proposed approach, the tolerance membership functions for the fuzzily described objective functions are defined by determining individual best solution of the objective function of every decision maker....

This paper presents a general framework for the study of rough fuzzy sets in which fuzzy sets are approximated in a crisp approximation space. By the constructive approach, a pair of lower and upper generalized rough fuzzy approximation operators is first defined. The rough fuzzy approximation operators are represented by a class of generalized crisp approximation operators. Properties of rough...

In this paper, we study the concept of S-approximation spaces in fuzzy set theory and investigate its properties. Along introducing three pairs of lower and upper approximation operators for fuzzy S-approximation spaces, their properties under different assumptions, e.g. monotonicity and weak complement compatibility are studied. By employing two thresholds for minimum acceptance accuracy and m...

This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the e...

Proximal Iliac Artery chronic total occlusions (PICTOs) are complex peripheral interventions that typically require an arm approach for adequate leverage. These are typically TransAtlantic Inter-Society Consensus [1] (TASC) Type C/ D lesions that have traditionally treated by Aorto-bifemoral surgery [2] but are being increasingly approached by endovascular methods [3,4]. The endovascular approa...

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Carotid artery pseudoaneurysm is a rare complication of injury to the head and neck, which has been traditionally managed by an open surgical repair to avoid the occurrence of devastating cerebral strokes. Their treatment presents a challenge because of the risk of serious neurological events. This report presents a case of a stab penetrating injury to the left upper neck (Monson`s zone-III), w...

The present report aimed to study an uncommon case of a pair of twins that presented a discordant dental phenotype. Family investigation, clinical, radiographic examination and molecular analysis were performed in both girls. Molecular analysis confirmed the monozygosity by deoxyribonucleic acid chip technology. One twin presented tooth agenesis in left upper lateral incisor and peg-shaped on t...

The aim of this paper is to develop an effective method for solving matrix games with payoffs of triangular fuzzy numbers (TFNs) which are arbitrary. In this method, it always assures that players’ gain-floor and loss-ceiling have a common TFN-type fuzzy value and hereby any matrix game with payoffs of TFNs has a TFN-type fuzzy value. Based on duality theorem of linear programming (LP) and the ...

Compromised teeth often pose a significant challenge to the clinician, complicating the treatment plan and compromising long term prognosis. Upper molar teeth showing periodontal attachment loss, caries or fractures involving the furcation area are prime examples of such challenges. Treatment option for affected teeth can be roughly divided into maintenance of the tooth through root resection t...