Iranian Journal of Fuzzy Systems
Year:2010 | Volume:7 | Issue:3|Papers Count:9

Numerous algorithms have been proposed to solve the shortest path problem; many of them consider a single-mode network and crisp costs. Other attempts have addressed the problem of fuzzy costs in a single-mode network, the so-called fuzzy shortest-path problem (FSPP). The main contribution of the present work is to solve the optimum path problem in a multimodal transportation network, in which the costs of the arcs are fuzzy values. Metropolitan transportation systems are multimodal in that they usually contain multiple modes, such as bus, metro, and monorail. The proposed algorithm is based on the path algebra and dioid of k-shortest fuzzy paths. The approach considers the number of mode changes, the correct order of the modes used, and the modeling of two-way paths. An advantage of the method is that there is no restriction on the number and variety of the services to be considered. To track the algorithm step by step, it is applied to a pseudo-multimodal network.

Due to the explosive growth of the world-wide web, automatic text summarization has become an essential tool for web users. In this pa- per, we present a novel approach for creating text summaries. Using fuzzy logic and word-net, our model extracts the most relevant sentences from an original document. The approach utilizes fuzzy measures and inference on the extracted textual information from the document to find the most significant sentences. Experimental results reveal that the proposed approach extracts the most relevant sentences when compared to other commercially available text summarizers. Text pre-processing based on word-net and fuzzy analysis is the main part of our work.

In this paper difference methods to solve "fuzzy partial differential equations" (FPDE) such as fuzzy hyperbolic and fuzzy parabolic equations are considered.The existence of the solution and stability of the method are examined in detail .finally examples are presented to show that the Hausdorff distance between the exact solution and approximate solution tends to zero.

In this paper, we study the finitely many constraints of the fuzzy relation inequality problem and optimize the linear objective function on the region defined by the fuzzy max-product operator. Simplification operations have been given to accelerate the resolution of the problem by removing the components having no effect on the solution process. Also, an algorithm and some numerical and applied examples are presented to abbreviate and illustrate the steps of the problem resolution.

We prove a related fixed point theorem for n mappings which are not necessarily continuous in n fuzzy metric spaces using an implicit relation one of them is a sequentially compact fuzzy metric space which generalizes results of Aliouche, et al. [2], Rao et al. [14] and [15].

The main purpose of this paper is to consider the t-best simultaneous approximation in fuzzy normed spaces. We develop the theory of t-best simultaneous approximation in quotient spaces. Then, we discuss the relationship in t-proximinality and t-Chebyshevity of a given space and its quotient space.

The aim of this paper is the study of fuzzy basis and dimension of fuzzy hypervector spaces. In this regard, first the notions of fuzzy linear independence and fuzzy basis are introduced and then some related results are obtained. In particular, it is shown that for a large class of fuzzy hypervector space the fuzzy basis exist. Finally, dimension of a fuzzy hypervector space is defined and the basic properties of that are investigated.

In this paper, we introduce and study the prime, strongly prime, semi prime and irreducible fuzzy bi-ideals of a semi group. We characterize those semi groups for which each fuzzy bi-ideal is semi prime. We also characterize those semi groups for which each fuzzy bi-ideal is strongly prime.

In the present paper we define the notion of fuzzy inner product and study the properties of the corresponding fuzzy norm. In particular, it is shown that the Cauchy-Schwarz inequality holds. Moreover, it is proved that every such fuzzy inner product space can be imbedded in a complete one and that every subspace of a fuzzy Hilbert space has a complementary subspace. Finally, the notions of fuzzy boundedness and operator norm are introduced and the relationship between continuity and boundedness are investigated. It is shown also that the space of all fuzzy bounded operators is complete.