An interpretation of membership functions and the properties of general probabilistic operators as fuzzy set operators. I: Case of type 1 fuzzy sets

DOI10.1016/0165-0114(92)90279-DzbMath0815.94033OpenAlexW2005865216MaRDI QIDQ1311799

Shigeaki Mabuchi

Publication date: 27 January 1994

Published in: Fuzzy Sets and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0165-0114(92)90279-d

zbMATH Keywords

fuzzy setmembership functionrandom setprobabilistic interpretationset operators

Mathematics Subject Classification ID

Theory of fuzzy sets, etc. (03E72) Fuzzy sets and logic (in connection with information, communication, or circuits theory) (94D05)

Related Items (5)

Fuzzy sets and membership functions based on probabilities ⋮ Modeling global market entry decision by fuzzy logic with an application to country risk assessment ⋮ Supplement to ``An interpretation of membership functions and the properties of general probabilistic operators as fuzzy set operators. I ⋮ Three-valued fuzzy subgroup ⋮ An interpretation of membership functions and the properties of general probabilistic operators as fuzzy set operators. II: Extension to three-valued and interval-valued fuzzy sets

Cites Work

• Unnamed Item
• Unnamed Item
• A model for the measurement of membership and the consequences of its empirical implementation
• A general concept of fuzzy connectives, negations and implications based on t-norms and t-conorms
• The aggregation operations for decision making in probabilistic fuzzy environment
• Membership function as an evaluation
• A review of fuzzy set aggregation connectives
• Constructing membership functions using statistical data
• The concept of grade of membership
• Are grades of membership probabilities?
• Latent connectives in human decision making
• Fuzzy sets as a basis for a theory of possibility
• On the suitability of minimum and product operators for the intersection of fuzzy sets
• Infinite-valued logic based on two-valued logic and probability. Part 1.2. Different sources of fuzziness
• A CLASS OF FUZZY MEASURES BASED ON TRIANGULAR NORMS A general framework for the combination of uncertain information
• SOME PROCEDURES FOR SELECTING FUZZY SET-THEORETIC OPERATORS
• A measurement-informational discussion of fuzzy union and intersection
• Fuzzy sets

This page was built for publication: An interpretation of membership functions and the properties of general probabilistic operators as fuzzy set operators. I: Case of type 1 fuzzy sets