I introduce axiomatically infinite sequential games that extend von Neumann and Kuhn’s classic axiomatic frameworks. Within this setup, I define a modified backward induction procedure that is applicable to all games. A strategy profile that survives backward pruning is called a backward induction equilibrium (BIE). The main result compares the sets of BIE and subgame perfect equilibria (SPE). ...

By considering the supreme-utilities among fuzzy sets and the weights among participants simultaneously, we introduce the supreme-weighted value on fuzzy transferable-utility games. Further, we provide some equivalent relations to characterize the family of all solutions that admit a potential on weights. We also propose the dividend approach to provide alternative viewpoint for the potential a...

In this paper, we take a GL-quantale as the truth value table to study a new rough set model—L-valued fuzzy rough sets. The three key components of this model are: an L-fuzzy set A as the universal set, an L-valued relation of A and an L-fuzzy set of A (a fuzzy subset of fuzzy sets). Then L-valued fuzzy rough sets are completely characterized via both constructive and axiomatic approaches. 

The growing complexity of hardware optimizations employed by multiprocessors leads to subtle distinctions among allowed and disallowed behaviors, posing challenges in specifying their memory models formally and accurately, and in understanding and analyzing the behavior of concurrent software. This complexity is particularly evident in the IBM® Power Architecture® , for which a faithful specifi...

Axiomatic design is investigated as a design methodology for large or complex system design. Particular considerations of system design are described and the suitability of axiomatic design for such considerations is discussed. Then, tools to enable successful application of axiomatic design to systems are developed. The tools are expressed as theorems for axiomatic system design. The first the...

In a research report we have proposed an axiomatic semantics for the language of communicating sequential processes (CSP: of Hoare (1978). In this paper, we use the axiomatic semantics to prove the correctness of a number of CSY programs.

This chapter introduces a new usability evaluation method, the axiomatic evaluation method, which is developed based on the axiomatic design theory – a formalized design methodology that can be used to solve a variety of design problems. This new evaluation method examines three domains of a product: customer domain, functional domain, and control domain. This method investigates not only usabi...

In this paper, an axiomatic theory is established for studying design. Using this theory, a formal model of design is derived to represent the syntactic structure of hierarchical evolving design objects and the dynamic design process. The axiomatic theory can be used by design theorists and computer scientists as a formal logical tool to model design whereas the derived formal model can be used...

In Possibilistic Decision Theory (PDT), decisions are ranked by a pessimistic and an optimistic qualitative criteria. The preference relations induced by these criteria have been axiomatized by corresponding sets of rationality postulates, both à la Neumann-Morgenstern and à la Savage. In this paper we first address a particular issue regarding the axiomatic systems of PDT à la von Neumann and ...

Yoshikawa’s General Design Theory is an axiomatic theory of design in which design is formulated and discussed in terms of topological spaces defined by entities, entity concepts, and abstract concepts. The theory is developed on declarations called definitions and axioms of which represents the basic philosophy of the theory. In this paper, we shall show that a paradoxical situation about the ...