Latticized linear programming subject to max-product fuzzy relation inequalities with application in wireless communication

Yang, Xiaopeng; Zhou, Xiaoqing; Cao, Bing-Yuan

doi:10.1016/j.ins.2016.04.014

Cited by 70 publications

(49 citation statements)

References 37 publications

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“…Fuzzy relation equations [26] have been applied to a wide variety of frameworks such as artificial intelligence, information processing, pattern analysis and classification, control systems, and decision making, among others [1,9,11,18,21,27,30]. Many of these applications require the presence of variables that have a bipolar nature.…”

Section: Introductionmentioning

confidence: 99%

Abductive reasoning in normal residuated logic programming via bipolar max-product fuzzy relation equations

Lobo¹,

Piñero²,

Medina³

2019

Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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Fuzzy relation equations have recently been extended to a more general framework in which the unknown variables appear together with their logical negation connectives, giving rise to the called bipolar fuzzy relation equations. This paper shows an abductive procedure for a special kind of normal residuated logic program by means of bipolar maxproduct fuzzy relation equations. From this procedure, interesting properties relating the models of a given normal residuated logic program to the solutions of its corresponding bipolar max-product fuzzy relation equation is deduced.

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Section: Introductionmentioning

confidence: 99%

Abductive reasoning in normal residuated logic programming via bipolar max-product fuzzy relation equations

Lobo¹,

Piñero²,

Medina³

2019

Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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“…There exist three kinds of solution methods for such nonlinear optimization problem: (i) genetic algorithm for optimization problem with general nonlinearobjective function and fuzzy relation constraint. By this kind of method, only approximate solution could be found [32,33]; (ii) method to separate the main problem into a finite number of subproblems according to the minimal solutions of the 2 Complexity constraint [34,35]; (iii) specific method for the fuzzy relation problem with special objective functions [36,37].…”

Section: Introductionmentioning

confidence: 99%

Resolution of Max‐Product Fuzzy Relation Equation with Interval‐Valued Parameter

et al. 2019

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Considering the application background on P2P network system, we investigate the max-product fuzzy relation equation with interval-valued parameter in this paper. Order relation on the set of all interval-valued numbers plays key role in the construction and resolution of the interval-valued-parameter fuzzy relation equation (IPFRE). The basic operations supremum (a∨b) and infimum (a∧b) in the IPFRE should be defined depending on the order relation. A novel total order is introduced for establishing the IPFRE. We also discuss some properties of the IPFRE system, including the consistency and structure of the complete solution set. Concepts of close index set and open index set are defined, helping us to construct the resolution method of the IPFRE system. We further provide a detailed algorithm for obtaining the complete solution set. Besides, the solution set is compared to that of the classical max-T fuzzy relation equations system.

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“…Over the last decades, the solvability of FRE defined with different max-t compositions have been investigated by many researchers [36,38,39,42,44,45,47,50,53]. Moreover, some researchers introduced and improved theoretical aspects and applications of fuzzy relational inequalities (FRI) [13,16,17,23,28,52]. Li and Yang [28] studied a FRI with addition-min composition and presented an algorithm to search for minimal solutions.…”

Section: Introductionmentioning

confidence: 99%

“…The problem of optimization subject to FRE and FRI is one of the most interesting and on-going research topic among the problems related to FRE and FRI theory [1,8,[11][12][13][14][15][16][17][18][19][20][21][22][23][24]25,29,32,40,43,48,52]. Fang and Li [9] converted a linear optimization problem subjected to FRE constraints with max-min operation into an integer programming problem and solved it by branch and bound method using jump-tracking technique.…”

Section: Introductionmentioning

confidence: 99%

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An Algorithm for Solving Linear Optimization Problems Subjected to the Intersection of Two Fuzzy Relational Inequalities Defined by Frank Family of T-Norms

Ghodousian

2018

IJFCST

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Frank t-norms are parametric family of continuous Archimedean t-norms whose members are also strict functions. Very often, this family of t-norms is also called the family of fundamental t-norms because of the role it plays in several applications. In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated. The feasible region is formed as the intersection of two inequality fuzzy systems defined by frank family of t-norms is considered as fuzzy composition. First, the resolution of the feasible solutions set is studied where the two fuzzy inequality systems are defined with max-Frank composition. Second, some related basic and theoretical properties are derived. Then, a necessary and sufficient condition and three other necessary conditions are presented to conceptualize the feasibility of the problem. Subsequently, it is shown that a lower bound is always attainable for the optimal objective value. Also, it is proved that the optimal solution of the problem is always resulted from the unique maximum solution and a minimal solution of the feasible region. Finally, an algorithm is presented to solve the problem and an example is described to illustrate the algorithm. Additionally, a method is proposed to generate random feasible max-Frank fuzzy relational inequalities. By this method, we can easily generate a feasible test problem and employ our algorithm to it. Fuzzy relation, fuzzy relational inequality, linear optimization, fuzzy compositions and t-norms. KEYWORDS

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Latticized linear programming subject to max-product fuzzy relation inequalities with application in wireless communication

Cited by 70 publications

References 37 publications

Abductive reasoning in normal residuated logic programming via bipolar max-product fuzzy relation equations

Abductive reasoning in normal residuated logic programming via bipolar max-product fuzzy relation equations

Resolution of Max‐Product Fuzzy Relation Equation with Interval‐Valued Parameter

An Algorithm for Solving Linear Optimization Problems Subjected to the Intersection of Two Fuzzy Relational Inequalities Defined by Frank Family of T-Norms

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