Order relation between intervals and its application to shortest path problem

Okada, Shinkoh; Gen, Mitsuo

doi:10.1016/0360-8352(93)90242-p

Cited by 31 publications

(14 citation statements)

References 3 publications

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“…(18) It is evident that, for non-comparable fuzzy numbersã andb, the fuzzy Min operation results in a fuzzy number different from both of them. For example, forã = (5, 10, 13, 19) andb = (6,9,15,20), we get from (18) a fuzzy MV = Min(ã,b) = (5, 9,13,19), which is different from bothã andb. To alleviate this drawback, we use a method based on the distance between fuzzy numbers.…”

Section: Distance Between Fuzzy Numbersmentioning

confidence: 95%

“…Lin and Chern [3] defined the denomination of vital arcs as being those whose removal from the path resulted in an increase of the cost. Another algorithm for this problem, presented by Okada and Gen [9,10], is a generalization of Djikstra's algorithm. In this algorithm, the weights of the arcs are considered to be interval numbers and are defined using a partial order between interval numbers.…”

Section: Introductionmentioning

confidence: 98%

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A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths

Hassanzadeh

Mahdavi

Mahdavi–Amiri

et al. 2013

Mathematical and Computer Modelling

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Shortest path Regression model a b s t r a c tWe are concerned with the design of a model and an algorithm for computing the shortest path in a network having various types of fuzzy arc lengths. First, a new technique is devised for the addition of various fuzzy numbers in a path using α-cuts by proposing a least squares model to obtain membership functions for the considered additions. Due to the complexity of the addition of various fuzzy numbers for larger problems, a genetic algorithm is presented for finding the shortest path in the network. For this, we apply a recently proposed distance function for comparison of fuzzy numbers. Examples are worked out to illustrate the applicability of the proposed approach.

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Section: Distance Between Fuzzy Numbersmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 98%

A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths

Hassanzadeh

Mahdavi

Mahdavi–Amiri

et al. 2013

Mathematical and Computer Modelling

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show abstract

“…A series of extended criteria for comparison originating from the two aforementioned order relations exist [13,23]. The details of these are not presented due to space constraints.…”

Section: [ ]mentioning

confidence: 99%

“…Here, the "values" are interval numbers rather than real numbers due to the interval uncertainties that exist in the problem. Many criteria have been proposed for interval number comparison [11][12][13][14]. Interval analysis, on the other hand, refers to obtaining an interval response to a candidate solution that is substituted into the objective function.…”

Section: Introductionmentioning

confidence: 99%

A two-layer optimization framework for UAV path planning with interval uncertainties

Bai

Chiong

2014

2014 IEEE Symposium on Computational Intelligence in Production and Logistics Systems (CIPLS)

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We propose a two-layer optimization framework for the unmanned aerial vehicle path planning problem to handle interval uncertainties that exist in the combat field. When evaluating a candidate flight path, we first calculate the interval response (i.e., the upper and lower bounds) of the candidate flight path within the inner layer of the framework using a collocation interval analysis method (CIAM). Then, in the outer layer, we introduce a novel criterion for interval response comparison. The artificial bee colony algorithm is used to search for the optimal flight path according to this new criterion. Our experimental results show that the CIAM adopted is a feasible option, which largely eases the computational burden. Moreover, our derived flight paths can effectively handle bounded uncertainties without knowing the corresponding uncertainty distributions.

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“…There are different approaches to the comparison of fuzzy numbers and interval numbers proposed in the literature; see Ishibuchi and Tanaka (1990), Okada and Gen (1994), Nakahara et al (1992), Kundu (1997). In this paper, we use the acceptability index idea suggested by Sengupta et al (2001) and Sengupta and Pal (2009).…”

Section: Comparison Of Interval Numbersmentioning

confidence: 99%