The quest for rings on bipolar scales

We consider the interval $]{-1},1[$ and intend to endow it with an algebraic structure like a ring. The motivation lies in decision making, where scales that are symmetric w.r.t.~$0$ are needed in order to represent a kind of symmetry in the behaviour of the decision maker. A former proposal due to Grabisch was based on maximum and minimum. In this paper, we propose to build our structure on t-conorms and t-norms, and we relate this construction to uninorms. We show that the only way to build a group is to use strict t-norms, and that there is no way to build a ring. Lastly, we show that the main result of this paper is connected to the theory of ordered Abelian groups.

NESIGURNOSTI I RIZICI PRI GEOLOŠKIM ISTRAŽIVANJIMA I NAČINI RJEŠAVANJA

The authors rewiev the main types of uncertainties occuring in connection with geological investigations. The general concept of handling these uncertainties are outlined. The particular features of scalar, spatial and spatial-temporal evaluations are presented. Limitations of the traditional mathematical approach – deterministic and probabilistic – applied to geological investigations are discused. In the second part of the paper nem mathematical methods are presented that are more suitable to handle uncertaintes that the traditional ones.The fuzzy set theory seems to be one of the most efficient for geological purposes, among these methods. The problems of uncertainty in risk analysis are shortly discussed. Finally, results of test calculations performed by fuzzy arithmetic are presented.Autori prikazuju glavne oblike nesigurnosti geoloških istraživanja. U glavnim su crtama izloženi postupci za rješavanje tih nesigurnosti. Posebno su prikazani rezultati skalarne, prostorne i prostorno-vremenske obrade. Ocijenjena su ograničenja tradicionalnih pristupa interpretaciji rezultata geoloških istraživanja – determinističkog i probabilističnog. U drugom dijelu članka prikazane su nove matematičke metode, prikladnije od tradicionalnih za obradu interpretacijskuh nesigurnosti. Čini se da je među tim metodama teorija fazi-postupka najefikasnija. Kritično su, ukratko, prikazani i problemi nesigurnosti u analizi rudarskog rizika. Konačno, prikazani su i rezultati nekih test-kalkulacija izvedenih fazi-aritmetikom

The Discourse/Pragmatic Functions of Japanese Okkē

Okay is one of the most commonly used words in the English language. It is also one of the most commonly borrowed English-origin loanwords across all of the world\u27s languages. Although there is a wealth of research on the communicative functions of English okay, there is comparatively little research on the many borrowings of the word in various other languages. In order to address this gap in the literature, this study explores the differences in discourse/pragmatic function between the English word okay, and the Japanese borrowing of the word, okkē. Extensive research in discourse analysis, pragmatics, and conversation analysis shows that English speakers use okay to accomplish a variety of discourse/pragmatic functions. The functions of okay established in the relevant literature are: (1) A marker of transition. (2) A structural marker in monologic speech. (3) A marker of irony or sarcasm. (4) A tag question. (5) A method of seeking or giving permission. (6) An assessment. (7) A response token. In order to determine which of the functions listed above can be accomplished by Japanese speakers when they use okkē, this study analyses audio and video data of Japanese native speakers playing an augmented reality game. Evidence from the analysed data shows that Japanese okkē is used by Japanese speakers to accomplish the following functions: (1) A marker of transition. (2) A marker of irony or sarcasm. (3) An assessment. (4) A response token. Additionally, it was found that the way in which Japanese speakers utilize okkē as a marker of transition is different in some cases from how English speakers utilize okay as a marker of transition. In group settings among Japanese speakers, the group members sometimes each repeat okkē tokens one person after another in order to indicate group consensus of readiness to transition. Other noteworthy differences found between okay and okkē are that (1) okkē tends to appear as the only word within a turn more often than okay. (2) okkē is used as a response token only to a completed utterance, while okay can be used as a response token to either a complete or incomplete utterance. (3) Unlike okay, okkē is sometimes used outside of any ongoing talk to mark physical action transitions such as walking to stopping

UNCERTANITIES AND RISK IN GEOLOGICAL ACTIVITIES AND NEW WAYS OF THEIR HANDLING

The authors rewiev the main types of uncertainties occuring in connection with geological investigations. The general concept of handling these uncertainties are outlined. The particular features of scalar, spatial and spatial-temporal evaluations are presented. Limitations of the traditional mathematical approach – deterministic and probabilistic – applied to geological investigations are discused. In the second part of the paper nem mathematical methods are presented that are more suitable to handle uncertaintes that the traditional ones.The fuzzy set theory seems to be one of the most efficient for geological purposes, among these methods. The problems of uncertainty in risk analysis are shortly discussed. Finally, results of test calculations performed by fuzzy arithmetic are presented

Conditional measures: an alternative to Cox functional equation

DP&al059International audienceIn 1946, R.T. Cox [3] tried to justify the notion of probability as a measure of belief from first principles. Relying on the Boolean algebra structure of events, he proposed three basic postulates on a degree of belief g (A|B)∈[0,1], where A,B are events A,B in an Boolean algebra S

Characterization of the ordered weighted averaging operators

This paper deals with the characterization of two classes of monotonic and neutral (MN) aggregation operators. The first class corresponds to (MN) aggregators which are stable for the same positive linear transformations and presents the ordered linkage property. The second class deals with (MN)-idempotent aggregators which are stable for positive linear transformations with the same unit, independent zeroes and ordered values. These two classes correspond to the weighted ordered averaging operator (OWA) introduced by Yager in 1988. It is also shown that the OWA aggregator can be expressed as a Choquet integral