Fuzzy logical semantics of Bayesian decision making

Peter V. Golubtsov

doi:10.1117/12.211805

13 June 1995 Fuzzy logical semantics of Bayesian decision making

Peter V. Golubtsov

Proceedings Volume 2493, Applications of Fuzzy Logic Technology II; (1995) https://doi.org/10.1117/12.211805
Event: SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, 1995, Orlando, FL, United States

Abstract

An approach to uncertainty and decision making problems alternative to probabilistic one is studied. It is based on fuzzy sets technique and has deep relations with the underlying first order fuzzy logic. In this logic not only logical connectives but also quantifiers have fuzzy interpretation. It is shown that all fundamental concepts of probability and statistics such as joint distribution, conditional distribution, etc., have meaningful analogs in new context. Thus the classical concepts obtain fuzzy-logical semantics. As a result one may treat them as formulas of first order logic. It is shown, that this appraoch makes it possible to utilize rich conceptual experience of statistics. In particular it leads to fuzzy Bayesian approach in decision making, which plays the same role in fuzzy problems of optimal decision making as its probabilistic prototype in the theory of statistical games, and provides methods for construction of optimal strategies. Connection with underlying fuzzy logic provides the logical semantics for fuzzy decision making. In this approach a priori information is represented by a fuzzy predicate and an experiment--by fuzzy universal quantifier, etc. As a result the notion 'good decision strategy' is expressed by a first order formula in this logic.

Citation Download Citation

Peter V. Golubtsov "Fuzzy logical semantics of Bayesian decision making", Proc. SPIE 2493, Applications of Fuzzy Logic Technology II, (13 June 1995); https://doi.org/10.1117/12.211805

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available