Abslract-A fmzy constraint satisfaction problem (FCSP) isThe other is local state-spa= search algorithms based on itan extension of the clar*ical CSP, a po~erful tool for modeling erative improvement in incons~stent, full assignments. These problems On co-ints among techniques have been developed h o s t independently, but d y , the algorithms for solving CSPs are c M e d into two categories: the mtemtic search (eomnlete methods based on recently, much attention has k n paid to hybrid methods in-~~~~~ -~ ~ ~"~~~ ~~ ~ ~~~~ ~ ~~~ A ~~~ ~~ ~~~ ~~~~~~ ~ WITh trees) and the 1-1 search methods tegrating the virtues of cach class of algorithms. An example on iterative imurovement). Both haie meritr and demerits. is the decision-renair algorithm develoned in 111. an extended ->.Recently, muchittention i;as been paid to hybrid methods for version of a pr-W-g paper pre&ntd at A~AI.2000. integatin~ both merits to solve CSPs efficientl3: but almost no FroIn the viewpoint of soft computing, however, the naattempt has been made so far for solving FCSPs.
I. tlk paper, we prsent a hybrid, approximate method ditional CSP is too rigid to formulate real world problems. for xsps. ~h~ method, eaued the ~~~d -~~~~i , -.In order to improve this situation, much work has been done Shrink (SRS) algorithm. combines a svstematic WIT^ with the on the extensions of CSPs. The fuzzv CSP (FCSP) is one of
Spr-d-~epair 6~) Qorithl~ a lo&WIT11 method recently such extensions, where constraints are represented by fuzzy developed by the authors SRS repeats spreading and * U relations, which admit incomplete solutiotlS aroviding a set of search trees in order to repair local constraints until the satbfaction decree of the worst constraints are useful information Tor solving real-world problems[2], [3], the roots of the t&) is improved. We empiricalli show that SRS out~erfonns SR and other well-known methods such as ~orn,anl'~'hrckill~ and Fuzq (;T.NET. a hen wr nant to qairkly ct.1 a xwdqualih' uppruuin~ale wlutiun uf suflicit.ntl\. lan~t. siltA constraini is a restriction on a space of possibilities; it is a piece of knowledge that narrows the scope of this space. Because constraints aise naturally in m t areas of h u m endeavor, they are the most general mcans for formulating regularities that govern our computational, physical, biological, and social worlds. Many problems arising in such domains can be naturally modeled as constraint satisfaction problem (CSPs). A CSP consists of a finite set of variables, each associated with a h i t c domain of values, and a set of const~aints among the variables. A solution is an assignment of a value to every variable such that all constraints are satisfied Since CSPs are NP-hard problems in general. no efficient and complete algorithms for solving CSPs exist and the increase in the worst-case computation time is exponential in the size of the problems. In most of the cases, however, we can obtain a solution in practical time by using incomplctc algorithms.CSP algorithms are usually categorized into two classes...