Fuzzy logic has difficulty producing valid answers in decision-making. Absent are theorems to prove that it works to produce results already known that are being estimated with judgments by transforming such judgments...Fuzzy logic has difficulty producing valid answers in decision-making. Absent are theorems to prove that it works to produce results already known that are being estimated with judgments by transforming such judgments numerically. The numerical representation of judgments in the AHP is already fuzzy. Making fuzzy judgments more fuzzy does not lead to a better more valid outcome and it often leads to a worse one. The compatibility index of the AHP is used to illustrate how the answers obtained by fuzzifying AHP judgments do not produce better results than direct derivation of the principal eigenvector. Other authors who did experiments with given data in decision making quoted in the conclusions section of the paper, have observed that fuzzy sets gives the poorest answers among all methods used to derive best decisions.展开更多
We address a framework for the analysis of extended fuzzy logic(FLe) and elaborate mainly the key characteris-tics of FLe by proving several qualification theorems and proposing a new mathematical tool named the A-gra...We address a framework for the analysis of extended fuzzy logic(FLe) and elaborate mainly the key characteris-tics of FLe by proving several qualification theorems and proposing a new mathematical tool named the A-granule. Specifically, we reveal that within FLe a solution in the presence of incomplete information approaches the one gained by complete infor-mation. It is also proved that the answers and their validities have a structural isomorphism within the same context. This rela-tionship is then used to prove the representation theorem that addresses the rationality of FLe-based reasoning. As a conse-quence of the developed theoretical description of FLe, we assert that in order to solve a problem, having complete information is not a critical need; however, with more information, the answers achieved become more specific. Furthermore, reasoning based on FLe has the advantage of being computationally less expensive in the analysis of a given problem and is faster.展开更多
文摘Fuzzy logic has difficulty producing valid answers in decision-making. Absent are theorems to prove that it works to produce results already known that are being estimated with judgments by transforming such judgments numerically. The numerical representation of judgments in the AHP is already fuzzy. Making fuzzy judgments more fuzzy does not lead to a better more valid outcome and it often leads to a worse one. The compatibility index of the AHP is used to illustrate how the answers obtained by fuzzifying AHP judgments do not produce better results than direct derivation of the principal eigenvector. Other authors who did experiments with given data in decision making quoted in the conclusions section of the paper, have observed that fuzzy sets gives the poorest answers among all methods used to derive best decisions.
文摘We address a framework for the analysis of extended fuzzy logic(FLe) and elaborate mainly the key characteris-tics of FLe by proving several qualification theorems and proposing a new mathematical tool named the A-granule. Specifically, we reveal that within FLe a solution in the presence of incomplete information approaches the one gained by complete infor-mation. It is also proved that the answers and their validities have a structural isomorphism within the same context. This rela-tionship is then used to prove the representation theorem that addresses the rationality of FLe-based reasoning. As a conse-quence of the developed theoretical description of FLe, we assert that in order to solve a problem, having complete information is not a critical need; however, with more information, the answers achieved become more specific. Furthermore, reasoning based on FLe has the advantage of being computationally less expensive in the analysis of a given problem and is faster.
