Fuzzy relation equations for coding/decoding processes of images and videos

Loia, Vincenzo; Sessa, Salvatore

doi:10.1016/j.ins.2004.04.003

Cited by 120 publications

(80 citation statements)

References 13 publications

(28 reference statements)

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“…The operations proposed by him are specified as the membership function of intersection and union of two fuzzy sets, and that of complement of the normalized fuzzy set. Since the resolution of fuzzy relation equations was proposed by Sanchez [2], many researchers have studied different fuzzy relational equations (FREs) and fuzzy relational inequalities (FRIs) and their connected problems in both theoretical and applied areas, [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. 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.…”

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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Section: Introductionmentioning

confidence: 99%

Monomial geometric programming with an arbitrary fuzzy relational inequality

Shivanian

Sohrabi²

2015

Communications in Numerical Analysis

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“…Fuzzy relational equations play important roles in many applications, such as intelligence technology [7], compression/decompression of images and videos [5,19,24] and fuzzy decision marking [19], etc. The first paper of fuzzy relational equations was due to Sanchez [25], where the max-min composition was adopted.…”

Section: Introductionmentioning

confidence: 99%

“…The first paper of fuzzy relational equations was due to Sanchez [25], where the max-min composition was adopted. Recently, there have been many research papers investigating the solvability of fuzzy relational equations [2,4,7,12,15,16,[19][20][21][22][27][28][29]. In fact, fuzzy relational equations can be categorized based on many different compositions.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, fuzzy relational equations can be categorized based on many different compositions. Some common compositions include max-min [4,7,12,25], max-product [7,23], max-Archimedean tnorm [2,4,7,11,17,19], inf-α [7,15,16] and inf-α T [2,7,30] compositions. Wu [29] and Di Nola et al [6] found that in fuzzy relational calculus and reasoning inf-α composition is better.…”

Section: Introductionmentioning

confidence: 99%

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Fuzzy relational equations and the covering problem

Xiong¹,

Shu²

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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The work considers the problem of solving a system of fuzzy relational equations with inf-implication composition and introduces the concepts of a characteristic matrix and attainable components. It is first shown that solving the system is closely related with the covering problem. Further, it is proved that maximal solutions of the system correspond to irredundant coverings of the characteristic matrix. At last, the necessary and sufficient conditions that the system has a unique(maximal) solution are given.

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“…In [26] the authors propose a watermarking scheme based on table lookup in frequency domain in which the marked image is stored in compressed form. In [9] the authors apply the watermark on images coded via fuzzy relation equations [7,8,12,18].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Transforms and Fragile Watermarking Tamper Detection on Coded Images

Martino

Sessa²

2011

Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011)

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An original image is compressed with fuzzy transforms and is divided in images of sizes 2×2 on which we apply a known fragile watermarking process. A preprocessing phase is considered to determine the better compression rate for the coding process. We test this scheme in tamper detection analysis on a sample of images. The results are good in terms of accuracy for tamper detection with compressed images and in terms of dimension of the image dataset used for storage of the original images.

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Fuzzy relation equations for coding/decoding processes of images and videos

Cited by 120 publications

References 13 publications

Monomial geometric programming with an arbitrary fuzzy relational inequality

Monomial geometric programming with an arbitrary fuzzy relational inequality

Fuzzy relational equations and the covering problem

Fuzzy Transforms and Fragile Watermarking Tamper Detection on Coded Images

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