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Furthermore, a language named RELAX is developed for specifying requirements
in adaptive systems [26,27] in which certain requirements could be temporarily
relaxed in favor of others. In general, different temporal logics have been used for
formal specification of requirement. Linear Temporal Logic (LTL) has been used
in [4,11] to formally specify requirements in a goal oriented approach. In partic-
ular, LTL is extended in [31] and named A-LTL to support adaptive program
semantics by introducing an adaptation operator. [3] uses Allen's interval alge-
bra for the formal specification of service requirement. Those approaches have
limitations such that they are unable to consider environmental uncertainty and
behave in a binary satisfaction manner.
Fuzzy approach [29] is an alternative to concur such limitations of aforemen-
tioned approaches. However, the fuzzy approach may not be the only alternative
to deal with uncertainty. Different mathematical and frameworks are presented
in the literature to address the uncertainty issue and partial satisfaction of the
requirements. For example, making decisions about non-functional properties us-
ing Bayesian networks is proposed in [13] while [17] used a probabilistic method
for this purpose. Applying fuzzy logic to incorporate uncertainty and making
decisions has been proposed in other domains such as management, economy
and many aspects of computer science, however, to the best of our knowledge
there is very little of such application in adaptation of web services. As of such,
[10] proposed a fuzzy approach for assigning fitness degrees to service policies in
a context-aware mobile computing middleware. A trade-off analysis using fuzzy
approach for addressing conflicts using imprecise requirements in proposed in
[28]. With respect to partial satisfaction of requirements, [12] provided a web
service selection approach using imprecise QoS constraints.
There are several different approaches towards adaptation of web services.
This diversity yields from a missing consensus on the required decision making
to automatically perform web service adaptation. Therefore, in this paper we
propose a fuzzy adaptation approach as a possible way in providing a foundation
of such a consensus which is based on the satisfaction degree of QoS parameters.
3 Fuzzy Parameters for QoS Property Description
This section is devoted to present a formal definition of quality parameters in a
service description and is concerned with QoS property descriptions of Web Ser-
vices. The formal specification we propose has been inspired and is an extension
of our previous work [3]. We extended the work by defining fuzzy parameters
for such service description. Fuzzy parameters could be considered as fuzzy sets
and measured based on their value of membership. Satisfaction degree of fuzzy
parameters is measured according to their actual distance of the agreed quality
ranges in the contract. Having introduced the fuzzy parameters it is possible to
understand to what extent the quality parameters are violated/satisfied. This
way, partial satisfaction of parameters is allowed through measuring imprecise
requirements.
 
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