Resolution of finite fuzzy relation equations based on strong pseudo-t-norms

Han, Song-Chol; Li, Hongxing; Wang, Jiayin

doi:10.1016/j.aml.2005.11.001

Cited by 30 publications

(25 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Consequently, the t-norm can be replaced by a weak t-norm, t-seminorm or strong pseudo-t-norm. See Fodor (1991), De Cooman andKerre (1994), Han and Li (2005), Wang and Xiong (2005) and Han et al (2006) for details. More general composite operators were also investigated in CuninghameGreen (1979CuninghameGreen ( , 1995, Kawaguchi and Miyakoshi (1998), Cheng and Peng (1988), Noskoá (2005), and Wu (2007).…”

Section: Discussionmentioning

confidence: 98%

“…associativity and commutativity, are not necessary in defining fuzzy relational equations and hence some general composite operators can be used without losing any particular property of interest. As a consequent, some generalizations have been made by Cheng and Peng (1988), Di , Kawaguchi and Miyakoshi (1998), Han and Li (2005), Li et al (2005), Wang and Xiong (2005) and Han et al (2006).…”

Section: Introductionmentioning

confidence: 95%

See 1 more Smart Citation

On the resolution and optimization of a system of fuzzy relational equations with sup-T composition

Fang

2008

Fuzzy Optim Decis Making

121

View full text Add to dashboard Cite

This paper provides a thorough investigation on the resolution of a finite system of fuzzy relational equations with sup-T composition, where T is a continuous triangular norm. When such a system is consistent, although we know that the solution set can be characterized by a maximum solution and finitely many minimal solutions, it is still a challenging task to find all minimal solutions in an efficient manner. Using the representation theorem of continuous triangular norms, we show that the systems of sup-T equations can be divided into two categories depending on the involved triangular norm. When the triangular norm is Archimedean, the minimal solutions correspond one-to-one to the irredundant coverings of a set covering problem. When it is non-Archimedean, they only correspond to a subset of constrained irredundant coverings of a set covering problem. We then show that the problem of minimizing a linear objective function subject to a system of sup-T equations can be reduced into a 0-1 integer programming problem in polynomial time. This work generalizes most, if not all, known results and provides a unified framework to deal with the problem of resolution and optimization of a system of sup-T equations. Further generalizations and related issues are also included for discussion.

show abstract

Section: Discussionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 95%

On the resolution and optimization of a system of fuzzy relational equations with sup-T composition

Fang

2008

Fuzzy Optim Decis Making

121

View full text Add to dashboard Cite

show abstract

“…Also, the notations ∧ and ∨ denote the minimum and maximum operations, respectively. We present the definition of pseudo-t-norm as the extension of t-norms similar to the defined pseudo-t-norm in Han et al (2006) as follows.…”

Section: Preliminary Definitions and Pointsmentioning

confidence: 99%

Linear optimization with mixed fuzzy relation inequality constraints using the pseudo-t-norms and its application

Molai

2014

Soft Comput

View full text Add to dashboard Cite

This paper studies the minimization problem of a linear objective function subject to mixed fuzzy relation inequalities (MFRIs) over finite support with regard to max-T 1 and max-T 2 composition operators, where T 1 and T 2 are two pseudo-t-norms. We first determine the structure of its feasible domain and then show that the solution set of a MFRI system is determined by a maximum solution and a finite number of minimal solutions. Moreover, sufficient and necessary conditions are proposed to check whether the feasible domain of the problem is empty or not. The MFRI path is defined to determine the minimal solutions of its feasible domain. The resolution process of the optimization problem is also designed based on the structure of its feasible domain. Procedures are proposed to reduce the size of the problem. With regard to the above points and the procedures, an algorithm is designed to solve the problem. Its application is expressed in the area of investing and covering. Finally, the algorithm is compared with other approaches.

show abstract

“…Some results of these cases were generalized for sup-T compositions with additional assumptions on a triangular norm T (Fernández and Gil 2004;Han et al 2006;Shieh 2007;Stamou and Tzafestas 2001;Wang and Xiong 2005).…”

Section: Introductionmentioning

confidence: 98%