Solution Sets of Interval-Valued Min-S-Norm Fuzzy Relational Equations

Authors:
Shunmin Wang;Shu-Cherng Fang;Henry L. Nuttle
Affiliations:
Operations Research Program, North Carolina State University, Raleigh, USA 27695-7913;Department of Industrial Engineering, North Carolina State University, Raleigh, USA 27695-7906;Department of Industrial Engineering, North Carolina State University, Raleigh, USA 27695-7906
Venue:
Fuzzy Optimization and Decision Making
Year:
2005

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Abstract

This paper introduces the concepts of tolerable solution set, united solution set, and controllable solution set for interval-valued fuzzy relational equations. Given a continuous s-norm, it is shown that each of the three types of the solution sets of interval-valued fuzzy relational equations with a min-s-norm composition, if nonempty, is composed of one minimum solution and a finite number of maximal solutions. Necessary and sufficient conditions for the existence of solutions are given. Computational procedures based on the constructive proofs are proposed to generate the complete solution sets. An example is given to illustrate the proposed procedures.