Shin-ichi Ohnishi

A fuzzy representation for non-additive weights of AHP

AHP (Analytic Hierarchy Process) has been widely used in a domain of decision making, and there are a lot of extensions using fuzzy measure and integrals. In the previous research, we propose a kind of sensitivity analyses for AHP or fuzzy measure AHP, because it often occurs that data of AHP loses its reliability. In other words a comparison matrix there in does not always have enough consistency. Also in these cases, the authors propose one representation for weights using results from the sensitivity analysis. In this paper we refine fuzzy weights representation for fuzzy measure AHP. It can show how results of (fuzzy) AHP have fuzziness when the comparison matrix does not have relatively good consistency.

On Fuzzy Priority Weights of AHP for Double Inner Dependence Structure

Abstract The Analytic Hierarchy Process (AHP) is very popular method in decision making process, and its inner dependence extension is used for cases in which criteria or alternatives are not independent enough. Calculations and compositions of weights are very important steps in it, however using the AHP (inner dependence AHP) may cause results losing reliability because the comparison matrix is not necessarily sufficiently consistent. In such cases, fuzzy representation for weighting criteria or alternatives using results from sensitivity analysis is useful. In the previous papers, we defined local weights of criteria and alternatives for inner dependence AHP via fuzzy sets. In this paper we deal with overall weights of alternatives for double inner dependence structure AHP (among criteria and alternatives respectively). We propose fuzzy weights and two kinds of compositions. The compositions of weights depends if there are inconsistency in one level or not. Their results show the fuzziness of double inner dependence structure AHP in different way.

On a Fuzzy Weights Representation for Inner Dependence AHP

The AHP (Analytic Hierarchy Process) has been widely used in decision making. Inner dependence method AHP is one technique for the case in which criteria do not have enough independency. However using original AHP or inner dependence method, the data and results often lose their reliability because the comparison matrix does not always have sufficient consistency. In these cases, fuzzy representation for weighting criteria and alternatives using results from a sensitivity analysis is useful. In this paper, we first present weights of criteria of normal AHP by means of fuzzy sets, then modified fuzzy weights is calculated. Overall weights of alternatives can also be calculated by employing some assumptions. The results show how inner dependence AHP has fuzziness when the comparison matrix is not sufficiently consistent and each criterion has not enough independency.

Spatiotemporal Human Brain Activities by Visual Stimulus of Directional Characters and Symbols

To investigate the brain activity during human recognition of characters and symbols with directional meanings, the authors recorded electroencephalograms (EEGs) from subjects in viewing four types of Kanji (Chinese characters being used currently in the Japanese language) and four arrows presented on the CRT which means direction for Upward, Downward, Leftward and Rightward. As a result, the reaction time for each direction was almost equal, when characters or arrows were presented, regardless of the directions. However, for all the directions, the latency of peak for character was longer than that for arrow. The latency of peak for the word meaning upward or downward was a little shorter than those for other characters. EEGs were averaged for each stimulus type, and event-related potentials (ERPs) were determined. Tendencies in ERPs were compared, and marked changes in amplitude were seen near a latency of 420 ms for (upward) and (downward) and 500 ms for (leftward) and (rightward). Marked changes in amplitude were seen near a latency of 500 ms for all arrow symbols. When comparing ERPs between kanji characters and arrow symbols, differences in latency were noted, as were similarities in marked amplitude changes. When comparing ERPs between kanji characters and arrow symbols with opposing meanings, peak latencies for marked amplitude changes were predominantly similar, but polarities were opposite. Peak latency of ERPs was subjected to equivalent current dipole source localization (ECDL). ECD was estimated at a latency of around 110 ms in the MT field and then around 300 ms in the precentral gyrus. No marked differences in this tendency were noted among the eight stimuli. After ECD was estimated in the precentral gyrus, with the kanji characters, ECD was estimated in the right middle temporal gyrus regardless of direction. ECD was then estimated in areas related to language, such as the Wernickes area in the left middle temporal gyrus, the left angular gyrus and the left lingual gyrus. ECD was later estimated in the left middle frontal gyrus, left inferior frontal gyrus and prefrontal area. ECD was estimated in the precentral gyrus just before the amplitude of ERPs changed markedly. With arrow symbols, ECD was estimated in the right middle temporal gyrus, and then ECD was estimated in areas related to working memory for spatial perception, such as the right inferior or right middle frontal gyrus. Then, as with kanji characters, ECD was estimated in the prefrontal area and precentral gyrus.

Evaluation for a stability of fuzzy decision making using a sensitivity analysis

The Analytic Hierarchy Process (AHP) was proposed by Saaty (1977) and has been widely used in decision making, since it incorporates the natural feelings of human beings. On the other hand, fuzzy AHP, which is an extension of normal AHP, is one method of fuzzy decision making. We can obtain two types of decisions by using fuzzy measurement. When we actually use AHP, it often occurs that the best alternative cannot be found, since there is not a great deal of difference in the overall weights of the alternatives. Thus, it is very important to investigate how the components of a pairwise comparison matrix exert influence on the weights. Up to now two methods have been proposed as sensitivity analysis of the weights of the normal AHP. However, they have defects. Further, sensitivity analysis has not been proposed for fuzzy AHP. Accordingly, we propose new sensitivity analyses of the weights of normal AHP and fuzzy AHP. They can be easily used without changing the structure of the data.

Brain computer interface by use of electroencephalograms from right frontal area

In order to develop a brain computer interface (BCI), some of the present authors have investigated the brain activity during human recognition of characters and symbols representing directional meaning. They have recorded electroencephalograms (EEGs) from subjects viewing four types of arrows: “↑”, “↓”, “←” and “→” that were presented on a CRT. The arrows denote direction for upward, downward, leftward and rightward, respectively. Subjects were asked to read them silently. EEGs were averaged for each stimulus type and direction, and event related potentials (ERPs) were obtained. The equivalent current dipole source localization (ECDL) method has been applied to these ERPs. In both cases, ECDs were localized to areas related to the working memory for spatial perception, i. e. the right upper or the right middle frontal areas. And the opposite directional arrows had opposite dipoles in these areas. Taking into account these facts, the authors investigated a single trial EEGs of the subject precisely after the latency at 400ms, and determined effective sampling latencies for the discriminant analysis to four types of arrows. We sampled EEG data at latencies from 400ms to 900ms at 25ms intervals by the four channels such as Fp2, F4, C4 and F8. Data were resampled −1ms and −2ms backward. Results of the discriminant analysis with jack knife method for four types objective variates, the mean discriminant rate for seven sample subjects was almost 85 %.

A kind of fuzzy weights representation for inner dependence AHP

The Analytic Hierarchy Process (AHP) was proposed by Saaty T.L. and has been widely used in decision making. Inner dependence method AHP is one technique for the case in which criteria do not have enough independency. However using original AHP or inner dependence method, the data and results often lose their reliability because the comparison matrix does not always have sufficient consistency. In these cases, fuzzy representation for weighting criteria using results from a sensitivity analysis is useful. In this paper, we first present weights of criteria of normal AHP by means of fuzzy sets, then modified fuzzy weights can be calculated. We can also have overall weights of alternatives by employing some assumptions. The results show how inner dependence AHP has fuzziness when the comparison matrix is not sufficiently consistent and each criterion has not enough independency.

Localization of brain activity during perception of circle movement by use of equivalent current dipole analysis

A moving white circle on a CRT was presented to subjects. Moving patterns were downward, upward, rightward and leftward. A random movement of the circle was presented to subjects in comparison of other movements. These five movements were presented at random to the subjects. Meantime, electroencephalograms were recorded. The data was summed in each movement and the equivalent current dipole localization (ECDL) was done to estimate the source. From the results, the dipoles was estimated on the MT at latency from 80 ms to 120 ms, and after on the intraparietal sulcus, on the precentral gyrus and on the frontal eye field.

Spatiotemporal Human Brain Activities on Recalling Names of Body Parts II

The authors measured electroencephalograms (EEGs) from subjects who were looking at line drawings of body parts and recalling their names silently. The equivalent current dipole source localization (ECDL) method is applied to the event related potentials (ERPs): summed EEGs. ECDs are located in the ventral pathway. The areas are related to the integrated process of visual recognition of pictures and the retrieval of words. Some of these areas are also related to image recognition and word generation. ECDs are localized to the primary visual area V1, to the ventral pathway (ITG: Inferior Temporal Gyrus), to the parahippocampus (ParaHip), the right angular gyrus (AnG), to the right supramarginal gyrus (SMG) and to the Wernike’s area. Then ECDs are localized to the Broca’s area, to the post central gyrus (PstCG) and to the fusiform gyrus (FuG), and again to the Broca’s area. These areas are related to the integrated process of visual recognition of pictures and the retrieval of words. Some of these areas are also related to image recognition and word generation. And process of search and preservation in the memory is done from the result of some ECDs to the paraHip.

A weights representation for absolute measurement AHP using fuzzy sets theory

AHP (Analytic Hierarchy Process) has been widely used in a field of decision making. One extension, an absolute measurement method AHP is effective for bad consistency in case containing too many alternatives and can avoid the rank reversal problem. However using the absolute measurement method, the results often lose reliability because the comparison matrix (of criteria or assessment level) does not always have sufficient consistency. In these cases, fuzzy representation for weighting assessment level, criteria and also alternatives using results from a sensitivity analysis is useful. In this paper, we present fuzzy weights representation for absolute measurement AHP by employing some assumptions. The results show how absolute measurement AHP has fuzziness when the comparison matrix is not enough consistent.